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Modelling and control of a hydrostatic transmission for a load-haul-dump underground-mining machine Gosal, Amritpal Singh 2004

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M O D E L L I N G A N D CONTROL OF A HYDROSTATIC TRANSMISSION FOR A L O A D - H A U L - D U M P UNDERGROUND-MINING M A C H I N E by A M R I T P A L SINGH G O S A L B .A .Sc , The University of British Columbia, 2001 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF T H E REQUIREMENTS FOR THE DEGREE OF M A S T E R OF APPLIED SCIENCE * in THE F A C U L T Y OF G R A D U A T E STUDIES Department of Mechanical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A August 2004 © Amritpal Singh Gosal, 2004 Abstract This thesis focuses on the modelling and control of the hydrostatic transmission (HST) on an extremely-low-profile, front-end-loader configuration, load-haul-dump (LHD) machine: the 88XLP, designed and built by EJC Mining Equipment Inc. of Burlington, Ontario. The machine uses four pump-motor hydrostatic closed loops to power its four wheels. Speed regulation is required on such a machine in order to achieve the differential effect needed when the machine turns, as well as to maintain consistent wheel speeds and efficiency when travelling straight. Hydraulic pressure/flow sharing/coupling techniques are commonly employed to create the differential effect: experimental evaluation of eleven such hydraulic arrangements is presented to determine the efficacy of each, based on a calculation of a drivability-index for each arrangement. A review of techniques for feedback control of HSTs is presented, and proportional-integral (PI) control is selected to implement-speed feedback control for the variable-pump-variable-motor (PVMV) HST on the 88XLP. The results of tuning and drivability tests using the PI controller are presented. A model of the HST and controller, based on offline system-identification of the HST is implemented in Simulink, including nonlinearities, such as hysteresis and controller feedback quantization, as well as the discrete-time nature of the controller. It is found that this model does not provide close correspondence to behaviour of the actual system under feedback control. This discrepancy is attributable to the nature of the HST: its components with extremely nonlinear and time-varying characteristics, which further have a strong dependence on the operating conditions. As a result of the comparison between the various hydraulic sharing/coupling techniques and speed-feedback control, it is concluded that simple feedback control does not yield the best performance for this application, and that hydraulic system redesign is a more effective means of achieving design objectives for this application. The best performing hydraulic sharing/coupling technique is identified and suggestions are made to further improve its performance through simplifying the overall configuration of the HST. 11 Table of Contents Abstract i i Table of Contents i i i List of Tables vi List of Figures vii Nomenclature x Preface xv Acknowledgements xvi 1.0 Introduction 1 1.1 The Machine 2 1.1.1 Drive-train considerations in Underground Mining Vehicles 3 1.1.2 The 8 8XLP Hydrostatic Drive 4 1.1.3 Cheater Lines and Power-Sharing Lines 7 1.1.4 Sensors 9 Speed Sensor 9 Articulation Sensor 9 1.1.5 The IQAN System 10 1.2 Issues concerning the 88XLP 13 1.3 Scope of Work 14 2.0 Literature Review 15 2.1 Applications of the Hydrostatic Transmission 15 2.2 Modelling the HST 18 2.2.1 Simple Modelling Relations 19 2.2.2 Leakage Losses 20 2.2.3 Compressibility 22 2.2.4 Friction 23 2.2.5 Models based on Systems Theory 25 2.2.6 Other Modelling Methods 28 2.3 Control 31 in 2.3.1 PI controllers 31 2.3.2 Adaptive Controllers 33 2.3.3 Fuzzy-Logic Controllers 34 2.4 Literature Review Summary 38 3.0 Experimental Methodology 40 3.1 Hydraulic-Sharing Testing 40 3.1.1 Testing S cheme 40 Configuration of test 1 41 Configuration of test 2 41 Configuration of test 3 41 Configuration of test 4 41 Configuration of test 5 41 Configuration of test 6 42 Configuration of test 7 42 Configuration of test 8 42 Configuration of test 9 42 Configuration of test 10 42 Configuration of test 11 42 3.1.2 The Test Course 43 3.1.3 Test Procedures 43 Analysis of the data 44 Articulation Angle Calculations 45 Articulation Radius Calculations 46 Drivability Index Calculations 47 3.2 System Identification 48 3.2.1 Description of Testing 50 3.2.2 MatLab for System Identification 51 3.3 Controller Design and Simulation 52 3.4 Field Implementation of the Controller 56 4.0 Results and Discussion 59 4.1 Results of Hydraulic-Sharing Testing 59 i v 4.1.1 Problems encountered during testing 64 4.2 System Identification Results : 65 4.2.1 Pump Response Results 65 4.2.2 Motor Response Results 71 4.2.3 Formulating Transfer Functions 77 4.3 Controller Simulation Results 79 4.4 Results of PI Control Implementation 81 5.0 Conclusions 84 5.1 Contributions of the research 84 5.2 Feasibility of Implementing Feedback Control 85 5.3 Design Recommendations 86 5.4 Hydraulic System Redesign - 88XLP Mark-II 87 References 122 v List of Tables Table 1: Ziegler-Nichols Rule-Table [after 28] 33 Table 2: Fuzzy Rule Set [27] 35 Table 3: Pump fuzzy rule set used by Huhtala [4] .35 Table 4: Motor fuzzy rule set used by Huhtala [4] 36 Table 5: Hydraulic sharing configurations tested 41 Table 6: Drivability indexes and their averages 61 Table 7: Sorted drivability indexes 62 Table 8: Normalized drivability indexes 63 Table 9: The best DI's often trials from all tests 64 Table 10: The worst DI's often trials from all tests 64 Table 11: Change in motor speed vs. change in pump input current 68 Table 12: Model fit summary 78 Table 13: Pi-gains used for driving tests 82 Table 14: Drivability Calc Results, Pi-Control Included 83 vi List of Figures Figure 1: The low-profile L H D developed by EJC Mining known as the 88-XLP 3 Figure 2: A simplified schematic of the hydrostatic drive for one wheel circuit 4 Figure 3: Simplified schematic of the DPR valve 5 Figure 4: Model of the pump installation 6 Figure 5: HDC control and connection ports for the M46 pump 7 Figure 6: Pump Power Sharing 8 Figure 7: HDC control of the VI2-160 motor 8 Figure 8: IQAN control, simplified inputs and outputs 11 Figure 9: Schematic of the IQAN control system 12 Figure 10: Bondraph model of the HST system [20] 28 Figure 11: PI control flow-chart (after [27]) 32 Figure 12: Course followed during testing 43 Figure 13: Articulation angle calculations 45 Figure 14: Articulation radius calculations 46 Figure 15: A detail of the turning radius calculations 47 Figure 16: Test bench at Feldcamp Equipment Ltd 49 Figure 17: The IQAN computer interface at Feldcamp Equip. Ltd 49 Figure 18: Feedback model using the simplified pump transfer function 53 Figure 19: Feedback model with the fitted pump transfer function 54 Figure 20: Pump model with feed-forward and non-linearities 55 Figure 21: Feedback control scheme 57 Figure 22: Left-turn in reverse (Test 1) 59 Figure 23: Left-turn in reverse (Test 4) 60 Figure 24: Pump response at low input speed 66 Figure 25: Pump response at medium input speed 67 Figure 26: Pump response for high input speed 68 Figure 27: Pump response for low input speed and input stepped down 69 Figure 28: Pump response for medium input speed and input stepped down 69 vii Figure 29: Pump response for high input speed and input stepped down 70 Figure 30: Pump and DPR response 71 Figure 31: Motor and DPR response for low input speed 72 Figure 32: Motor and DPR response for medium input speed 73 Figure 33: Motor speed vs. modulating pressure, a non-linear relationship [41] 74 Figure 34: Motor and DPR response for high input speed 74 Figure 35: Motor and DPR response for low input speed and signal stepped down 75 Figure 36: Motor and DPR response for medium input speed and signal stepped down. 76 Figure 37: Motor and DPR response for high input speed and signal stepped down 76 Figure 38: Compared pump response of the real and modelled data 77 Figure 39: Pump-response using feedback and PI controller (without feedforward or dead-band) 79 Figure 40: Effect of Hysteresis on the model (without feedforward or dead-band) 80 Figure 41: Complete model response 81 Figure 42: Pi-Controller tuning on the machine (on stands) 82 Figure 43: Pump step input 0-12.5% 103 Figure 44: Pump step input 12.5-25% 103 Figure 45: Pump step input 25-37.5% 104 Figure 46: Pump step input 37.5-50% 104 Figure 47: Pump step input 50-62.5% 105 Figure 48: Pump step input 62.5-75% 105 Figure 49: Pump step input 75-87.5% 106 Figure 50: Pump step input 87.5-100% 106 Figure 51: Pump step input 100-87.5% 107 Figure 52: Pump step input 87.5-75% 107 Figure 53: Pump step input 75-62.5% 108 Figure 54: Pump step input 62.5-50% 108 Figure 55: Pump step input 50-37.5% „.. 109 Figure 56: Pump step input 37.5-25% 109 Figure 57: Pump step input 25-12.5% 110 Figure 58: Pump step input 12.5-0% 110 Figure 59: Motor step input 0-12.5% 111 Figure 60: Motor step input 12.5-25% 111 Figure 61: Motor step input 25-37.5% 112 Figure 62: Motor step input 37.5-50% 112 Figure 63: Motor step input 50-62.5% 113 Figure 64: Motor step input 62.5-75% 113 Figure 65: Motor step input 75-87.5% 114 Figure 66: Motor step input 87.5-100% 114 Figure 67: Motor step input 100-87.5% 115 Figure 68: Motor step input 87.5-75% 115 Figure 69: Motor step input 75-62.5% 116 Figure 70: Motor step input 62.5-50% 116 Figure 71: Motor step input 50-37.5% 117 Figure 72: Motor step input 37.5-25% 117 Figure 73: Motor step input 25-12.5% 118 Figure 74: Motor step input 12.5-0% 118 ix Nomenclature a Empirical constant a Actual swashplate angle a pump swashplate angle ai Displacement setting of the primary unit a2 Displacement setting of the secondary unit A C Alternating Current Ae Effective control piston area Ai area of the large actuator a0 Desired swashplate angle V area of a single piston As area of the small actuator Av control valve spool area b Empirical constant B The bulk modulus b Moment-arm length at the swashplate b hydraulic fluid bulk modulus n projection of control moment arm to neutral position x area of the control P piston (ARcosa) C Empirical constant Ci.. Cp Empirical constant/losscoefficient C A D Computer-Aided Design C A N Control-Area-Network Cf Coulomb friction torque loss coefficient Cf0 Empirical constant ch Hydrodynamic friction coefficient Cs Leakage coefficient Cst Turbulent slip coefficient C v Viscous friction torque loss coefficient d Empirical constant D, Volumetric displacement of the primary unit D2 Volumetric displacement of the secondary unit DI Drivability Index DPR Direct-Pressure-Reducing valve e Empirical constant s Empirical constant EDC Electronic Displacement Control Ek Speed-error EVPS Earth-moving Vehicle Powertrain Simulator / Empirical constant FB Feedback FF Feedforward FSC Fuzzy state controller g Empirical constant g pressure carry-over angle on the port-plate 7 pump flow constant G The DC-gain of the system GP pump displacement gain (same as K p above) Gs control gain HDC Hydraulic Displacement Control HPS Hydraulic position servo HST Hydrostatic Transmission Hz Hertz / mass moment of inertia of the motor and load 1VT Infinitely Variable Transmission Jsp swashplate moment of inertia k, Empirical loss constant k2 Empirical loss constant Kc controller flow gain Kd effective control line fluid bulk stiffness Kcp control piston fluid effective bulk stiffness Kcs control valve spool stiffness K i Integral Gain KI system leakage gain K P Proportional Gain KP pump flow gain kph kilometers per hour Kpp effective pump plenum fluid bulk stiffness Coefficients of an empirical equation relating torque to swashplate angle and •«vpr velocity Ksp swashplate return spring rotational stiffness Ku The ultimate-gain that causes oscillatory response kW Kilo Watt L moment arm of actuator acting on the swashplate L Large lbs pounds L H D Load-Haul-Dump machine LPF Low pass filter LRT Linear Resistive Transducer M Medium X I Mi M2 M D C M D M M L MH. Mn+ Mp. Mp+ mph ms MS My n N n. n+ nt n2 NDI P P-P+ Palm PD Pe P F M V Ph PI PID Po P V M F P V M V qi Qc Qi QL Qn-Torque at the input shaft of the primary unit Torque at the output shaft of the secondary unit Manual Displacement Control Master Display, Mini Medium-large Torque function obtained from polynomial fitting of the data corresponding to the minimum angular speed used in the test, n. Torque function obtained from polynomial fitting of the data corresponding to the maximum angular speed used in the test, n+ Torque function obtained from polynomial fitting of the data corresponding to the minimum pressure used in the test, p-Torque function obtained from polynomial fitting of the data corresponding to the maximum pressure used in the test, p+ miles per hour milliseconds Medium-small control valve spool mass Empirical constant total number of pistons Minimum speed used in test Maximum speed used in test Speed of the primary unit Speed of the secondary unit Normalized drivability index Pressure gradient Minimum pressure used in test Maximum pressure used in test Atmospheric pressure Discharge pressure Proportional-Derivative Effective control piston pressure Fixed Pump, Variable Motor dynamic hose pressure Proportional-Integral Proportional-Integral-Derivative constant hose pressure Variable Pump, Fixed Motor Variable Pump, Variable Motor Flow from the primary unit Flow to the secondary unit Amount of compressed flow Ideal flow Flow lost to leakage Flow function obtained from polynomial fitting of the data corresponding to the minimum angular speed used in the test, n. xii Qn+ QP-p r Rd Rep Rev Ru Rin Ri Rm out R, RP R P M RPS Rsp Rv S S,... S3 Sin SOC Sout T Te Tf TF v TL Tu tUfflactual turnpred Tv M Mi V D C Flow function obtained from polynomial fitting of the data corresponding to the maximum angular speed used in the test, n+ Flow function obtained from polynomial fitting of the data corresponding to the minimum pressure used in the test, p. Flow function obtained from polynomial fitting of the data corresponding to the maximum pressure used in the test, p+ Fluid density piston rotational radius pump control line resistance control piston leakage resistance control valve orifice resistance motor inter-chamber leakage resistance Radius of the inside wheels in a turn resistive load at motor motor plenum leakage resistance Radius of the outside wheels in a turn pump plenum leakage resistance Revolutions per minute Revolutions per second swashplate rotational damping coefficient control valve spool damping coefficient Small Simplified pump model constants Speed of the inside wheels in a turn Self-organizing fuzzy-logic controller Speed of the outside wheels in a turn The time constant of the first-order function Small torque losses Coulomb friction torque loss Transfer function Ideal torque Total torque loss Time-period of the oscillations Actual turning ratio (Rin/R0ut) Predicted turning ratio (Rin/Rout) Viscous friction torque loss Fluid viscosity tangent of the pump swashplate angle (tan a) Voltage — Direct Current xiii vh volume of discharge hose V L Very-large Vm motor volumetric displacement vm input flow of the motor Vo reference volume of the large actuator Vr Ratio of total clearance volume to swept volume at maximum displacement VS Very-small Vso nominal servo volume CO Angular speed OJc The cut-off frequency for the low pass filter G)m angular speed of the motor shaft G>max Maximum angular speed of the unit 0)n The natural frequency C00 Empirical constant 0J0 desired motor speed COp pump angular velocity X L P Extremely Low-Profile zoh Zero-order-hold xiv Preface The author, Amritpal Singh Gosal, completed a Bachelor of Mining Engineering degree at the University of British Columbia, in 2001. He started his work on the Master of Applied Science degree in the department of Mechanical Engineering, in 2002, under the supervision of Dr. Robert Hall and Dr. Laeeque Daneshmend. The research was a part of a collaborative agreement between EJC Mining Equipment, the University of British Columbia and Queen's University, funded in part by an NSERC CRD grant. Under the agreement, the students (including the author) gained access to EJC's equipment for study, while EJC benefited from the research resources available at the universities and the pool of knowledge and research expertise provided by the thesis supervisors. xv Acknowledgements This work would not have been possible without the blessings of God - first and foremost thanks to Him. I would like to thank my thesis supervisors Dr. Robert Hall and Dr. Laeeque Daneshmend for all their help and guidance. I would also like to thank Dr. Farrokh Sassani and Dr. Ian Yellowley for sitting on the thesis examination committee. A special note of appreciation goes to Mr. Patrick Murphy and Mr. David Sargent, as well as others from EJC Mining Equipment, Burlington, Ontario, for providing direction with research goals and the opportunity as well as the means to pursue an experimental undertaking of such magnitude, and to Mr. Larry Feldcamp and Mr. Rick Taylor from Feldcamp Equipment Inc. for their technical expertise. Many thanks go to my family for providing support through love and encouragement. xvi 1.0 Introduction Mining has been an integral part of society for millennia. As with other technological pursuits, the practice of mining has evolved with time. Currently, having taken the form of a competitive industry, it too faces significant socio-economic challenges. Cost reduction is important for mining to stay profitable, like other industries. As mines get deeper and ore-bodies get more complex and challenging to mine, the demand for specialized equipment is increasing at an accelerated rate. Labour is being replaced by mechanization as standards for safety and production are raised all over the world. In some places, such as South Africa, the shift to mechanization is dictated by the forecast lack of labour in the near future, resulting in a push towards acceptance of new technology. The South African Platinum mines are a good example of changing mining practices worldwide, where low mine headings are required to stay profitable as only the valuable raw materials are extracted, and mechanization is readily accepted as it results in higher production rates and safer working conditions. To meet the needs of a growing market, a hydrostatic machine was designed and built by EJC Mining Equipment Inc. in Burlington, Ontario, in 2002. The purpose of the machine was to fulfill the demand of a specialized market, specifically the South African Platinum mines, where an extremely low profile, front-end loader machine was needed, to improve production efficiency and personnel safety. The design was conceptualized as a machine that would use a hydrostatic transmission to transfer power from a diesel engine to its four wheels. A purely hydrostatic transmission, without a gearbox, required that a controller capable of meeting sophisticated control requirements be selected. A C A N (control-area-network) based controller (called IQAN®, built by Parker) was chosen for this task. Due to the absence of mechanical differentials for power distribution, a method needed to be devised to facilitate transmission of power where required. Based on previous experience with similar transmissions, the designers chose hydraulic pressure sharing to accommodate the differential distribution of power between the left and right side wheels. The degree of effectiveness of the hydraulic sharing was not known. It was required for the hydraulic sharing to be tested and documented, and alternative methods 1 to be researched. One of the objectives of this research was to test various arrangements of hydraulic sharing/coupling and rate them, based on their performance results, and also, to develop an alternative if required. This thesis commences with a review of the literature as applicable to the task at hand. Other applications where the hydrostatic transmission (HST) method was selected are discussed. Various modelling techniques used by the researchers in the literature, to predict the behaviour of the HST, are also reviewed. An overview of the various control schemes applied to the HST in the literature is also given. The aforementioned machine is then presented in the form of a case study, where the currently practised methods of HST control are evaluated. The methodology for conducting the various tests, analyzing the results and designing a model and a controller is presented. Results from the testing are then presented and discussed. Finally, conclusions and recommendations regarding design and control of the HST are presented. 1.1 The Machine In order to increase productivity and worker-safety in narrow reef platinum mining of South African mines, a low-profile load-haul-dump (LHD) machine was designed by EJC Mining Equipment [1]. Mechanization was desirable to relieve the intensive manual labour associated with mining in the low mine headings, only 1.1-1.2m in height. The machine was to replace the existing battery-powered machines adapted from coal applications. These machine experienced problems such as insufficient battery life to last a whole shift, which is undesirable as it interrupts production. A significant design constraint was posed by the low working environment of the machine. The low-profile design precluded the use of conventional hydro-mechanical transmissions utilizing torque-converters. It was decided to use a hydrostatic transmission powered by a diesel power-plant, with four independent pump-motor closed-circuits. Control of the transmission and other machine functions was to be facilitated by the Parker IQAN system. The production of the first 88XLP, serial number 3445, was completed in November of 2002. This machine became the in-house prototype machine - it would never be shipped to the field but would stay at the plant in Burlington for prototyping of 2 any design changes. The 88-3445 was also used for this research for testing and experimentation. Figure 1 shows a schematic-drawing of the 88XLP. 1549 mm I 3098 mm J * 7743 mm * Figure 1: The low-profile LHD developed by E J C Mining known as the 88-XLP The 88XLP, unlike traditional mechanically driven loaders, is a hydrostatic machine, which uses no differentials in either the front or the rear axles. The machine's small size does not allow utilization of mechanical differentials because of spatial constraints. Like most underground mining equipment, it is centre articulated; this means that the front wheels are laterally fixed and turning is facilitated by articulating the machine about its centre hinge, by making use of hydraulic steer cylinders. A 94-kW diesel powered engine is situated in the rear half of the machine that provides the power for all machine functions. Control of the machine is achieved by means of drive-by-wire. A C A N (control-area-network) interface enables exchange of system information and operator commands between the controller and the operator. Electronic commands from the controller are physically realized through hydraulic actuators. 1.1.1 Drive-train considerations in Underground Mining Vehicles Underground mining vehicles have distinct design requirements to meet the harsh demands of the underground mining environment. Various considerations have to be made when selecting components in an underground mining vehicle design. For instance, size is a constraint that has to be met by all underground vehicles. The maximum size of an underground machine is dictated by the size of the underground opening. Similarly, the specified task of a machine demands further requirements. For instance, a loader requires better traction abilities than a haul-truck and the latter more climbing power versus the former. Also, because of traction requirements, underground mining loaders are invariably four-wheel drive, so that power can be made available 3 where needed, for best traction performance. As underground mining vehicles, operate on rough surfaces formed by broken rock, efforts must be made to reduce or eliminate wheel spin so useful power can be sent to the wheels with the most traction. On the 88-XLP, each of the four wheels has a hydraulic motor that is independently driven by a hydraulic pump. The pumps are driven via a triple-pump drive by a Deutz diesel engine. Between each pump and the motor, a closed-loop hydraulic circuit is implemented. The closed loop circuit consists of a charge pump, a hydraulic pump and motor, and a common hydraulic reservoir. The inlet of the charge pump is directly fed from the reservoir. The inlet and the outlet of the drive pump are connected to the outlet and the inlet of the motor, respectively; hence the term closed loop hydraulic circuit. Four pumps were chosen to independently drive four motors because of the flexibility available with being able to independently control the amount of power sent to each wheel. Traction control of independent wheels equates to power available to only the wheels doing work, and therefore, a higher efficiency. The pumps and motors have hydraulic-displacement-control (HDC) implemented. Other commercially available control options include electronic-displacement-control (EDC) and manual-displacement-control (MDC). The HDC was selected because of cost benefits over the EDC. Figure 2 shows a simplified schematic of one wheel circuit of the hydrostatic drive. Figure 2 : A simplified schematic of the hydrostatic drive for one wheel circuit Among the selected components for the 88XLP hydrostatic transmission are the Sauer-Dan Foss M46 series axial piston pumps and Parker V12-160 series axial piston 1.1.2 The 88XLP Hydrostatic Drive 4 motors. The hydraulic control pilot pressure to the pumps and motors, which actuates motion of the swashplate, is metered via DPR (Direct Pressure Reducing) valves (Figure 3), which in turn are controlled by proportional electric solenoids. The current signal sent to the DPR valve-solenoids is calculated and provided by the onboard IQAN controller, built by Parker. The key components of this electro-hydraulic drive system are: the IQAN M D M , IQAN satellite modules, DPR valve stack, and the HDC pump and motor controls. From Charge Pump (21 bar) IQAN Analog Out To Pump/Motor HDC Figure 3: S impl i f ied schematic o f the D P R valve The hydraulic pumps and motors have various ports that are used for working connections, as well as test ports. Two #16 ports (ports A and B) on the M46 pump are dedicated to main-pressure. Depending on the direction the swashplate is displaced, which one of the two ports will be high pressure is determined. For example, i f the operator has engaged forward on the transmission control, the pump will swash in a given direction, which will be opposite to the swashing direction when reverse on the transmission is selected. The direction the swash plate is displaced dictates whether port A or B will have a higher pressure or energized fluid. The lines connected to ports A and B on the pump are directly connected to the motor main-pressure A and B ports in a closed-loop hydraulic circuit. In equipment equipped with hydraulic displacement control (HDC), a higher hydraulic pressure on either side of the control spool pushes it in the opposite direction, which, through mechanical and hydraulic linkages, causes the swashplate to displace in the prescribed direction, by the prescribed amount. As mentioned earlier, the M46 pumps and the V12 motors used on the 88XLP are equipped with hydraulic displacement 5 control. The motor swashplate is unidirectional, i.e. it is not allowed to travel over-centre. The direction of motion of the machine is governed by the direction in which the bidirectional pumps are swashed. The Sauer-Dan Foss pumps as installed are called M46-PT. The "T" in the nomenclature stands for "tandem". Two pumps are connected together with a gerotor-gear charge pump in between. As configured on the 88XLP, two banks of tandem pumps are installed on a triple-gear pump drive, and each bank is dedicated to provide power to motors on only one side. Furthermore, each of the pumps in the tandem orientation drives one motor each. A 3D CAD model of this arrangement is shown in Figure 4. The third location on the triple-pump-drive is reserved for two more pumps: the implement and cooling pumps (not shown in Figure 4 for clarity). For further pump and motor physical specifications, please refer to APPENDIX A. TANDEM PUMP INSTALLATION Figure 4: Model of the pump installation 6 Since the machine does not have conventional differentials to account for the speed variance between the left and the right side wheels, hydraulic coupling between the various pump and motor ports was employed (a.k.a. cheater lines and power-sharing lines). 1.1.3 Cheater Lines and Power-Sharing Lines The cheater lines allow pressure balancing between A and B lines of two pumps via ports M l and M2 (see Figure 5). By allowing flow to be shared through the cheater lines, the pump that experiences more resistance from its connected motor sheds flow toward the pump with lesser resistance. This is the simplest way of creating the differential effect during turning. Figure 5: HDC control and connection ports for the M46 pump Power-sharing lines are used to render the internal feedback in the HDC control less effective. Two test-gauge ports (#6 or Vs") on each side of the servo piston of the pump (M4 and M5) are connected to similar ports on the opposite side pump. A high pressure is created on one of the sides of the control-servo-piston when the pump experiences resistance caused by the infighting due to the lack of a differential effect. This causes the internal feedback to demand a greater swashplate stroke setting. This concept is illustrated in Figure 6. The darker shading in the figure depicts areas with higher pressure than the areas depicted by the lighter shade. When the machine is turning without a differential in place, the inside wheels fight the turning by attempting to go at 7 the same speed as the outside wheels (A and B). With the internal feedback working nominally, the resistance caused by turning at the inside wheels demands a higher flow, making the problem of fighting even worse (M4 and M5). Servo Piston M4 B M5 Figure 6: Pump Power Sharing On production 88XLP machines, power-sharing is also employed on the wheel motors. Ports XI and X6 from the front and rear left motors are connected to similar ports on the front and rear right motors through 0.9-mm (0.035-in) diameter control orifices (see Figure 7). Figure 7: HDC control of the V12-160 motor Power-sharing lines help to make the internal feedback in the pump and motor internal control less effective. By preventing the inside wheels from speeding up and by shedding the higher pressure at the servo-piston to the opposite pump, power-sharing 8 should cause the outside wheels to turn faster, resulting in the desired, but somewhat unregulated, differential effect. The 88XLP, as it is currently produced, uses pump and motor power-sharing lines. Cheater-lines have never been used on a production 88XLP machine. Power-sharing lines between the motors have 0.9-mm (0.035") diameter orifices controlling the amount of flow sharing. The appropriate orifice size was determined through experimentation by others. 1.1.4 Sensors Several sensors are used on the 88XLP that enable feedback to the IQAN controller. Currently, feedback is only used for diagnostic purposes, not for enabling or maintaining control. Some sensors of interest include: four speed sensors, one position sensor and eight pressure transducers. A l l IQAN compatible sensors are excited by the controller voltage of 5-VDC and output a signal ranging from 0.5 to 4.5-VDC, except the speed sensor, which is excited by the machine power (24-VDC) and outputs a digital signal. Speed Sensor Four Parker speed sensors are used on the 88XLP-prototype. The sensors are installed in the speed-sensor port made available on the VI2-160 series motors. The sensors are magnetic Hall-effect proximity sensors that detect teeth on the motor shaft. There are thirty-six teeth per revolution on the motor shaft. The signal, in the form of a square-wave, is sent to the IQAN frequency-counter-connection for speed detection. The frequency counter on the IQAN system is interrupt driven and runs at a frequency of 10-kHz. Number of pulses counted per scan time is converted to a frequency within the IQAN controller and further scaled to give the motor R P M . Articulation Sensor One position sensor is located within the steering cylinder and is used to detect steering extension which allows calculation of the articulation angle. The sensor is a linear-resistive-transducer (LRT). This sensor is essentially a voltage divider that sends a portion of the input voltage to the output connector, based on the position of its moving 9 brush. As the steering-cylinder extends, the resistance is increased and so is the voltage at the output connector. 1.1.5 The IQAN System The IQAN system is a C A N (control-area-network) based system that is primarily designed for control of industrial and mobile hydraulic equipment. Satellite modules are connected to the M D M (Master Display, Mini) through C A N . Please see APPENDIX B for detailed specifications of the IQAN components. Analog and digital information is exchanged between the controller and the sensors and actuators via channels on the modules. The 88XLP has four satellite modules: two IQAN XS, and one of each IQAN-XP2 and IQAN-XT2 modules. Each module is designed with a specific purpose governed by the type of channels it offers for input and output. For instance, the XT2 is SAE-J1939 ready: it is capable of interfacing with the diesel engine controller. J1939 is the most widely accepted heavy-duty diesel engine controller CAN-protocol. The IQAN-M D M is the main controller, but it is incapable of input or output itself: it acquires data and sends actuator commands by communicating with satellite modules over the C A N bus. Therefore, at least one satellite module must be used in conjunction with the M D M . The M D M has a display where critical system information, such as alerts and warnings, are made available for the operator or the maintenance personnel. The M D M also allows connection with a computer running the IQAN-develop software through a serial port. The IQAN-develop software is used to write programs for the M D M which are loaded over the serial connection. Limited data-acquisition capabilities are also available with an online computer while tests are being conducted. In the graph window of IQAN-develop, up to ten channels of data acquisition can be displayed in real time. The acquired data can be transferred in ASCII format to supporting programs for further manipulation. If more than ten channels need to be monitored, another stand-alone module must be used, such as the IQAN-TOC8 module. Since the TOC8 has no serial connection, a test box was constructed to facilitate its installation. The test box provided a serial connection for computer and banana jacks for channel-signal connections. On the 88XLP, all machine functions are controlled through programming of the I Q A N - M D M . Driving with the hydrostatic transmission is made possible by the IQAN 10 system, as it controls the pump and motor swash plate angles, while monitoring the engine speed, to prevent the engine from stalling (anti-stall). The feedback for the anti-stall loop is engine rpm, over the J1939-bus. The controller gets the throttle and brake (inch-pedal) inputs and controls the DPR solenoid currents to change pump and motor swash-plate settings (see Figure 8). The two pumps for each side share the same pilot hydraulic signal from the DPR's. A total of four pilot signals are sent to the pumps: two for each side - for forward and reverse driving directions. A l l four motors share a single pilot signal. So under ideal conditions, the two pumps for each side have the same swashplate setting and so do all four motors. Figure 9 depicts the workings of the IQAN system: in the open loop system described in Figure 8, the box labelled IQAN is further detailed in Figure 9, without the articulation corrections for differential compensation. Engine RPM Current output to drive DPR-solenoids E n g i n e C o n t r o l l e r I Q A N Throttle I n c h - P e d a l D P R s t a c k Lef t D r i v e ^ P u m p s R i g h t D r i v e j P u m p s r Pi lo t S i g n a l t o M o t o r s Drive Forward Pilot Drive Reverse Pilot L_ Drive Forward Pilot L Drive Reverse Pilot J Figure 8: IQAN control, simplified inputs and outputs 11 Current out values to DPR's are limited between 0 and 100% of the min and max range IQAN To Pump DPR's T H R O T T L E 0-100% 16.5 850 •Q : To Motor DPR Predetermined Factor 1. 1 iVCAN7.i.939Vi Engine Controller — * — Fuel Regulator Engine Tach| Sensor Figure 9: Schematic of the I Q A N control system The 8 8 X L P decelerates through hydrostatic-braking. Mechanical brakes are installed for safety reasons, for emergency stops and for parking. The brakes are applied and will remain applied i f there is not enough hydraulic pressure to release them (fail-safe). The pressure required to release the brakes is supplied by the charge pumps, and is only available when the engine is running. Pushing the emergency stop button releases the pressure and the brakes are applied for situations when abrupt stopping is required. Hydrostatic braking works by reversing the roles of the hydrostatic pumps and motors. Inertia of the machine is transferred by the motors to the pumps, which in turn, drive the diesel engine as a compressor. The hydrostatic braking comes into effect by depressing the inch-pedal or automatically, as the machine is allowed to coast with the accelerator 12 pedal released. A l l of these functions are effected by the IQAN system, by swashing the motors and pumps as required. The IQAN controller monitors and controls multiple functions on the 88XLP. A function on the M D M , known as "utilization", monitors resource usage and translates the value to a percentile of the maximum available resources. The optimum cycle time (refresh time) was found to be 50-ms (20-Hz), based on resource utilization, through trial and error. If this is reduced any further, the controller utilization exceeds acceptable levels and information is lost as the controller tries to prioritize tasks. 1.2 Issues concerning the 88XLP • Since the 88XLP does not have conventional differentials distributing power from side to side, power-sharing lines are used between the hydrostatic pumps and motors, as mentioned before. However, the functionality of any flow-sharing was not fully understood. There are numerous combinations of flow-sharing that can be conceptualized. Through experience, certain combinations were known to work better than others. Other than the operator's subjective evaluation, no method was available to quantify the efficacy of flow-sharing. • Several hours of setup time is required to finalize the IQAN minimum and maximum currents for DPR control for every machine. This procedure requires that all power-sharing lines to be removed when settingTup the IQAN currents. Installation and removal of power-sharing lines during setup opens up ports through which contaminants can enter the hydraulic system. The author witnessed several cases where a wheel motor (sometimes two) had to be replaced, because its performance became erratic during setup. The cause for such cases, when the motors were inspected, was mostly dirt blocking an internal orifice. A l l of these problems with the initial setup result in unplanned person-hours and cost money. EJC is, therefore, seeking ways to reduce the setup time and improve setup methods so that dirt is not introduced into the hydraulic system. • The machine drives shakily, especially while turning. This is attributed to the lack of an adequate differential effect, which causes disagreement between the speed of the inside wheels compared to the outside wheels. This tendency of the inside wheels to 13 travel faster than required causes the machine to react against the steering cylinders by trying to drive straight and causing the machine to shake. The shakiness is significant enough to cause operator discomfort. • Cost cutting has caused the removal of some sensors: only one speed sensor is installed on all production units and the articulation sensor is also not available any longer. Any new improvements on the 88XLP must be geared toward reducing the overall cost. 1.3 Scope of Work • Based on the problems encountered with the current hydraulic setup and to combat the inadequacies experienced with the existing control, this research focuses initially on testing the hydraulic flow and pressure sharing arrangements, to develop a better understanding of their efficacy. • System-identification of the drive as a whole, to capture the interaction of the DPR valves with the pump and motor dynamic components is conducted. • To develop a drive controller employing speed feedback, a simple model of the system as a whole is created, based on system identification using experimental data. A Simulink/MatLab® simulation model of the drive is created to evaluate stable ranges for Pl-controller-gains. • The Pi-controller is designed and implemented on the 8 8XLP-prototype, and drivability results are compared with the results from the various hydraulic sharing/coupling configurations. • An assessment is performed based on the above analysis with respect to the most feasible control/design strategy to be employed on the hydrostatic transmission of the 88-X L P machine. 14 2.0 Literature Review No publications pertaining to design guidelines or design constraints for flow or pressure sharing in hydrostatic transmissions could be found, specifically using power-sharing lines and cheater lines (please see section 1.1.3), even after a thorough search of the published literature. The search was then directed towards hydrostatic transmissions with feedback control. It was found that designers have utilized feedback control with hydrostatic transmissions, in applications similar to the one that is the focus of this research. Speed as feedback for control of HSTs was found to be universally adopted. Various applications with slip control using speed comparison for multi-wheel drive machines were located [35, 36]. Various control strategies were also encountered: PI, fuzzy, hybrid fuzzy-PI and so on [4, 23, 25, 27, 29, 30]. 2.1 Applications of the Hydrostatic Transmission A hydrostatic transmission (HST) works by converting mechanical energy from a prime-mover (a diesel engine or an electric motor) into hydraulic energy in a primary hydrostatic unit, and by reconverting the hydraulic energy into mechanical energy in a secondary hydrostatic unit. The primary and secondary hydrostatic units are commonly referred to as pump and motor, respectively. In contrast to a hydrodynamic transmission, energy in a HST is transferred by the high static pressures and relatively lower fluid velocities or lower dynamic pressures [2]. The hydraulic energy is carried by a nearly incompressible hydraulic fluid from the input shaft of the pump to the output shaft of the motor, via an arrangement of pistons in rotation-groups in both pumps and motors. If air is entrained in the fluid, compressibility can become an issue. Generally in HST design, provisions are made for the air to escape the fluid and to prevent further mixing of air into the fluid. Air entrainment is primarily a result of highly turbulent fluid velocities in the reservoir. To prevent this from happening, provisions should be made in the design to allow the fluid to settle, allowing the entrained air to escape before it is reintroduced into the hydraulic circuit. To prevent air-entrainment, turbulent fluid should be kept from coming in contact with the atmosphere. 15 HST's are used in a wide range of applications: agriculture, mining, earth-moving, turf-maintenance, cranes, as well as stationary equipment applications. Design considerations of a HST and component selection concerns for a turf-maintenance application are presented by Betz [3]. Being able to changing vehicle speed without shifting gears or varying engine-speed are attractive features of the HST for the turf-maintenance industry. Maximum desired tractive-effort is used to determine the expected value for the pressure generated in the system, which is used in component selection and in fail-safe mechanisms selection, such as relief valves. The HST is preferred in applications where a high power to size ratio (power density) is desired. Some of the advantages of the HST as listed in the literature include [4, 5]: • Continuously variable output speed • High stiffness • Flexibility • Ease of assembly • Good controllability • Simplicity in operation • High starting torque • Self lubricating and cooling • Upgradeable modular design The efficiency of the HST is low compared to mechanical transmissions, as energy transformation takes place in two stages: from mechanical to hydraulic-pressure in the primary unit and back to mechanical in the secondary unit. Mechanical gear boxes are often used in conjunction with the HST to improve the overall efficiency. An example of such an application is the Infinitely Variable Transmission (IVT) of John Deere 7000 T E N Series tractors [6]. The IVT has an electro-hydraulic closed loop controller with speed feedback. The HST discussed in [6] consists of a variable and a fixed hydrostatic unit. The HST is installed as a single module, unlike other applications where the primary and secondary units are connected with hydraulic hoses and are found at the engine and the wheel pr the mechanical differential, respectively. The HST module 16 is connected to a clever arrangement of gears and clutches to effect desired speed/torque requirements. In another example, an HST design by International Transmissions Ltd. (ITL), offers a maintenance free, noise free and compact transmission for small mobile equipment, such as forklifts and telehandlers. The transmission uses Hall-effect sensors for speed monitoring and feedback control [7]. The sensors are installed in a non-contacting position close to gear-teeth in the transmission. An HST built by Poclain, termed SmartDrive™, allows customization of system parameters through programming. A software package, known as Phases, allows the user to connect a PC to the HST controller, and display and change functional parameters. The listed features that can be programmed are: maximum speed, acceleration and deceleration control, braking control, an inching feature, motor displacement management and an engine anti-stall feature [8]. A hydrostatic-mechanical hybrid, termed "the S-matic power split drive," was developed by Steyr Antriebstechnik in Austria. This transmission benefits from the advantages of both hydrostatic and mechanical transmissions as continuous variability of speed is made possible by the hydrostatic transmission, and high efficiency and durability are provided by the mechanical component of the S-matic power split drive [9]. Pedersen and Nielsen [10] presented an application of the HST in a city bus in Aarhus, Denmark. The low floor of the city bus (0.325 m) precluded the use of a mechanical transmission. However, the lower efficiency of the HST was a concern. To combat the inefficiencies associated with HST's and to lower fuel consumption by the prime mover (diesel engine), a computer controller aimed at optimizing fuel-efficiency was employed. The diesel engine and the P V M V HST transmission were directly controlled by the computer through electronic actuators. The controller was aimed at controlling the hydraulic unit displacements to generate the torque demanded by the application, as a function of the vehicle speed. In iterative-loops, the unit displacement indices and the engine rotational speed were changed to result in values that demand the lowest fuel consumption, while meeting the driving demands. Application of the computer controller resulted in fuel savings of up to 2.4%. 17 2.2 Modelling the HST With the advent of microprocessor controllers and their acceptance in industrial control applications, system designers are now able to implement controllers which improve the machine performance in such areas as efficiency and safety. This trend towards computer control has also motivated further efforts to understanding the internal workings of hydraulic systems, in order to base controller designs on valid system models. Models also need to be established to compare performance and performance constraints of various configurations of the HST, allowing component and configuration selection to be made prior to the implementation stage, hence shortening the product design and development cycle, and consequently, saving time and money and improving competitiveness. As hydraulic pumps and motors are the key components of an HST, a majority of the relevant modelling research is focussed on quantifying functional parameters and prediction of the dynamic and steady-state behaviour of these components. Computer simulations that are helpful in making informed decisions require accurate models to give meaningful and useful results. Some of the published models range from simple physical relations to detailed mathematical derivations of the parameters affecting performance. Where test data is available and experimental modelling is preferred, empirical relationships are drawn to model functional parameters, such as losses and fluidic effects, like compressibility. As mentioned before, hydraulic fluid is nearly incompressible; however, at high pressure levels, compressibility can result in lower than ideal flow from a pump. The machining tolerances in internal components of pumps and motors can allow hydraulic fluid to leak, causing less than expected flow from a pump and less than expected speed from a motor for a given flow. These loss effects are modelled at great lengths in the literature and examples are given in sections 2.2.2, 2.2.3 and 2.2.4. Leakage is also necessary as it is responsible for cooling and lubricating moving components. It also prevents development of hot-spots within the pumps and motors and prolongs component life by providing cooling, lubrication and flushing of particles resulting from wear. Leakage flow generally drains from a separate port on the housing of the hydraulic unit and is filtered and cooled in a heat-exchanger. When reintroduced 18 into the system, the purified and cooled oil helps in improving cleanliness and reducing temperature of the entire hydraulic system. 2.2.1 Simple Modelling Relations The primary and the secondary hydraulic units can each have either fixed or variable displacements. In a simple arrangement with a variable primary and fixed secondary, the flow produced by the primary is dependent only on its displacement setting, provided the input shaft speed is kept constant. Therefore, the output shaft speed is dependent only on the displacement setting of the primary unit. This relationship can be represented algebraically by equation (1) [2, 11], where n\ and n2, qi and q2 are speeds and flows (per revolution) of primary and secondary units, respectively, and aj is the displacement setting (ranging from -1 to 1 for a reversible pump, or 0 to 1 otherwise) of the primary unit. n2=nx —ax (1) This equation ignores leakage losses and compressibility of the fluid. However, the maximum possible speed of the output shaft or the ideal speed for a given displacement setting of the primary is correctly represented. In a more practical arrangement, the primary and the secondary are both variable, in which case the relationship is given by equation (2). Clearly, from equation (2), the secondary unit cannot have a displacement setting (a2) equal to or close to zero, as this would result in very high speeds of the secondary unit. In mathematical terms, n2 approaches infinity as a2 approaches zero. The minimum displacement setting of the secondary unit in practice is mechanically limited based on the rated maximum speed by the manufacturer or speed demands of a specific application. qx «, n2 = nx (2) q2 a2 The Principle of Conservation of Energy also leads to equation (3), where in a lossless transmission, torques of the input (Mi) and output shafts (M2) can be related [2]. 19 M2=M^^- ( 3 ) q2 a2 Reiterating, losses due to leakage result in a less than ideal amount of flow at the outlet port of a pump and less than ideal speed in a motor. The ideal flow and speed can be calculated according to equations (4) and (5) [12]. The volumetric displacement of the pump is denoted by Dj and the motor volumetric displacement by D2. qx = nxD, (4) ni = — = — (5) 2 D2 D2 As mentioned before, leakage in pumps and motors causes behaviour that is different from the idealized models presented. To accurately predict the behaviour of hydraulic units, leakage has been modelled in various ways and examples from published literature are summarized next. 2.2.2 Leakage Losses Examples of many loss models are found in the literature. Dorey [13] suggests that losses in hydrostatic units are attributed to slip or leakage due to pressure gradients, and fluid compressibility. Since clearance in hydrostatic units is small, resulting Reynolds numbers are also small, and therefore, leakage flows are laminar. The leakage and friction coefficients are also taken as variables by Dorey over the entire range of operation of the units. The leakage coefficient (Cs) is described as a dimensionless value relating the flow lost to leakage (QL), ideal flow (Qi), pressure gradient (P), fluid viscosity (ju), and angular speed (co), as shown in equation (6). Qi MG> Dorey [13] suggests that significant changes in the internal geometry of hydrostatic units are caused by pressure, speed and fluid viscosity. So, Cs cannot be taken as constant over the entire range of operation to correctly characterize hydrostatic units. Instead, Cs* correctly describes leakage dependence on speed and pressure, as shown in equation (7), where a and b are coefficients of a linear relationship of Cs with speed. The coefficients a and b are determined experimentally. In equation (7), Cs is defined as the product of 20 the ra te o f c h a n g e o f f l o w w i t h r e s p e c t to the p r e s s u r e d r o p a c r o s s the h y d r a u l i c u n i t a n d ju/V, w h e r e the a n g u l a r - s p e e d i s k e p t c o n s t a n t ; a n d V i s the v o l u m e o f the f l u i d u n d e r p r e s s u r e ( o r i n the u n i t . ) Patm d eno t e s the a t m o s p h e r i c p r e s s u r e , a n d comax i s the m a x i m u m a n g u l a r s p e e d o f the u n i t ; e q u a t i o n (7) r e s u l t s i n a d i m e n s i o n l e s s C*. c; = c. c. = f p N a + b\ f co N V^max J (7) idQ) [dp) CO w I n the 1 9 4 0 ' s , W . E . W i l s o n p u b l i s h e d a f l o w m o d e l f o r h y d r o s t a t i c m a c h i n e s a s s u m i n g l a m i n a r l e a k a g e . O t h e r s h a v e e x t e n d e d W i l s o n ' s m o d e l b y i n c l u d i n g e m p i r i c a l l e a k a g e a n d f r i c t i o n a l t e r m s . W i l s o n ' s l e a k a g e m o d e l i s s h o w n i n e q u a t i o n (8) [4 , 1 3 ] , w h e r e D i s v o l u m e t r i c d i s p l a c e m e n t p e r r a d i a n . QL=C, PD (8) S c h l o s s e r i n c l u d e d a t e r m i n W i l s o n ' s m o d e l c o n s i d e r i n g l e a k a g e to b e t u r b u l e n t , e q u a t i o n (9 ) , w h e r e Cst i s a t u r b u l e n t s l i p c o e f f i c i e n t , a n d p i s the f l u i d d e n s i t y [4 , 1 3 ] . PD IP 2 / QL=C— + C — D* M V P (9) T h o m a , u s i n g the s i m p l e W i l s o n m o d e l a n d a c c o u n t i n g f o r t u r b u l e n t l e a k a g e f l o w s , f o u n d that l o s s c o e f f i c i e n t s e x h i b i t e d a s i g n i f i c a n t v a r i a t i o n , o f u p to 2 0 % , d e p e n d i n g o n the o p e r a t i n g c o n d i t i o n s . E x a m i n i n g m o d e l s f o r g e a r - t y p e p u m p s , T e s s m a n n m a d e l e a k a g e l i n e a r l y d e p e n d e n t o n s p e e d , u s i n g e m p i r i c a l l o s s c o n s t a n t s , k i a n d k.2, as s h o w n i n e q u a t i o n ( 1 0 ) [4, 13 ] . QL = -kxa>D + k. PD (10) Z a r o t t i a n d N e r v e g n a c r e a t e d a n e m p i r i c a l m o d e l w h e r e l e a k a g e w a s d e p e n d e n t o n the s q u a r e o f p r e s s u r e , o n s p e e d to the p o w e r o f 1.5, a n d s l i g h t l y o n d i s p l a c e m e n t . T h e y a l s o i n c l u d e d e m p i r i c a l t e r m s to a c c o u n t f o r c o m p r e s s i b i l i t y . I n t h e i r m o d e l , s h o w n i n e q u a t i o n ( 1 1 ) , Q to Cs are e m p i r i c a l l o s s c o e f f i c i e n t s a n d a i s the u n i t ' s d i s p l a c e m e n t 2 1 setting as described before. Also, Qi in equation (11) shows the total flow lost to both leakage and compressibility [4, 13]. Q* = C,P + C2P2 + C3P2co]S + C4Pco{C5 + Da) (11) Huhtala [4] experimentally examined all of the models discussed thus far. His results showed poor correlation between the predicted and experimental results over the entire operating range of the tested hydraulic unit. Satisfactory correlation was found near the verification points; i.e., in the range close to where empirical constants or model coefficients were determined. Huhtala proposed two line models for pumps and motors. The modelling technique involved determining the system variables at two points in the operating range. First, by keeping the pressure constant at a low value and varying the speed from minimum to maximum, and repeating with the pressure held constant at a higher value, gave dependence of leakage losses on speed. Second, for pressure dependence, speed was held constant at two values and pressure was varied from minimum to maximum. Using polynomial fitting, two curves were produced from the data that defined the extremities of the range where flow and torque losses are dependent on speed. Flow from a hydraulic unit is modelled by equation (12), where Qp+, Qp., Qn+ and Qn. are flow functions obtained from polynomial fitting as described above and p+,p. and n+, n. are notations used for the maximum and minimum test pressures and speeds. Qn,P=[QPM)-QPSn)\ (Qn+(p)-QnSp)Y ( n-n ^ Kn+ -n_j + QAP) + Qp_(n) (12) 2.2.3 Compressibility Similar to leakage, compressibility also affects flows at the pump and motor outlets. Losses due to compressibility of hydraulic fluid are noticed as a reduction in the amount of flow at the pump outlet as fluid is compressed, and as an increase in the amount of fluid flow at the outlet of the motor, where the oil is allowed to expand. Compressibility of hydraulic fluid in a hydrostatic unit can be derived from the definition for bulk modulus. A change in pressure AP of a volume Vof fluid causing it to compress and decrease in volume by AV, gives the definition of bulk modulus as shown in equation (13). 22 B = -—V (13) AV The negative sign accounts for the negative change in volume as the fluid is compressed (V~2<Vj). The volumetric flow due to compressibility of fluid may be written as shown in equation (14) [13, 14, 15]. Qc'^-D „ 4 > Li Dorey [13] suggests that the actual compressed flow volume is higher than as described by equation (14) above because of "clearance-volumes within the unit": the actual volume of compressed oil is increased due to the clearance volumes. For variable units, varying the displacement has an effect on the volume of compressed oil. Equation (14) is modified to include these compressibility effects, resulting in equation (15). Vr is the ratio of total clearance volume to swept volume at maximum displacement [13] and a is the unit displacement setting. v+l±SL (15) 2.2.4 Friction Losses due to friction are manifested as torque losses. Two types of friction losses are discussed: friction caused by viscous forces between moving parts due to the presence of a film of fluid known as viscous friction, and dry friction taken to be dependent on pressure, called coulomb friction. Both types of friction cause the resulting torque to be less than ideal. The ideal torque in a motor may be given by equation (16). Tt = PD (16) Torque loss attributed to viscous friction rv, equation (17), is speed dependent and to coulomb friction loss Tf, equation (18), is pressure dependent. Cv and Cf are viscous friction and coulomb friction coefficients, respectively, // is absolute fluid viscosity, co is angular velocity of the shaft, P is the difference in pressure of the inlet and outlet ports, and D is volumetric displacement per radian of the hydraulic unit. Tv = CvpcoD (17) 23 rf = CfPD (18) Wilson's torque loss TL can be summarized by equation (19) [13]. Te in this equation is a small torque loss that is dependent on neither speed nor pressure. Tl = CvjucoD + CfPD + Te (19) Schlosser introduced a relationship replacing Te in Wilson's model based on hydrodynamic torque loss as shown in equation (20), where Ch is a hydrodynamic friction coefficient [13]. zL = CvfiaD + CfPD + Chpco2D^ (20) Thoma suggested that hydrodynamic friction cannot be independent of unit displacement, a. His addition to Schlosser's model is shown in equation (21) [13]. Tl = CvjucoD + CfPD + Chpa co D/3 (21) Hibi and Ichikawa used the Wilson model by modifying the coulomb friction coefficient to describe torque losses in hydraulic units. They formulated an empirical relationship of coulomb torque loss being dependent on the unit's port pressures, Pi and P2. Equation (22) describes their model, with C/0, co0, sand n being empirical constants [13]. Tl = Cvp.coD + 1+ *>/ co„ PD + T (22) Zarotti and Nervegna, similar to their flow loss to leakage model in equation (11), created a non-linear empirical model of torque loss with Cj to Cg being the empirical constants of their model as shown in (23) [13]. rL =co(c}+C2coa3)+C3P-(l + ^ L+ C^ a + C6" } V 1 I 4P CO + C 7 + • C, co + Ca (23) Dorey proposes that all of the empirical models lose generality and flexibility of application from one unit to another. Also, extensive testing is a prerequisite to most of the empirical models as empirical constants must be derived from test data. Similar to his leakage flow model, Dorey suggests modification of the coefficients in the Wilson torque 24 model, as detailed in equation (24) below, where C* and C / are the modified friction coefficients [13]. Tl = C'ficoD + C/PD (24) Cv' =Cv(a + ba) In the above equation for C*, a and b are terms that define C v to be a linear function of the displacement, a. Similarly, coefficients c, d, e, f, and g define Cf to be a quadratic function of angular velocity co, in the following Dorey model. C , = C , a + b-co + c < CO * (d + ea) Torque in hydraulic units is also modelled by Huhtala as shown in equation (25), using a formula similar to the flow formula from equation (12). Here Mp+, Mp., Mn+ and M„_ are torque functions obtained from polynomial fitting as described before and p+, p. and n+, n. are notations used for the maximum and minimum test pressures and speeds [4]-Mn,p=[Mp+(n)-Mp_(n)\ (Mn+(p)-Mn_(p))-( n-n ^ + M„_(P) + M(n) (25) 2.2.5 Models based on Systems Theory Schoenau et al [16] created a mathematical model of a variable displacement pump by analyzing the torques acting on the swashplate due to the control mechanism, rotating pistons, and associated frictional forces. The resulting model is complex and non-linear. Some of the model non-linearities were linearized for simplification, and terms causing insignificant effects were neglected. In this model, torque exerted by the pistons on the swashplate due to the line pressure was also considered. Swashplate angle was shown to have a strong dependency on the return spring constant. The results of the modelled swashplate angle showed good correlation with the physical measurements. Also, the simplified-linearized model showed "virtually no difference" from the complete mathematical model. Implementation of such a model for control purposes is not viable because of the complexity associated with the modelling. This model is only applicable 25 to the Vickers No. PVB5 pump, for which it was specifically formulated. Online calculation of the coefficients in the model and real-time acquisition of the various measurable parameters in the model would require significant computer power and instrumentation - hence further rendering the model unacceptable for control purposes due to its complexity. In equation (26), the simplified model by Schoenau et al [16] is shown. The Kpr terms are coefficients of an empirical equation relating the torque generated by pressure to the swashplate angle (a) and swashplate angular velocity. Si, S2 and S3 are simplified pump model constants. Ae is the effective control piston area; Pe is the effective control piston chamber pressure; b is the moment arm length of the control piston on the swashplate; APp is the differential pressure of the pump; and Ie is the moment of inertia. - PeAeb + Kpr2APp + 5, = (S2 - KpriAPp )cc-S,d + Tea (26) A similar model, based on simple principles of physics, to develop equations describing torques acting on the swashplate of a pump, was created by Manring and Johnson [17] for a pressure compensated pump. Swashplate dynamics were justifiably considered negligible with respect to the control actuator. Their model is built on the assumption that "destabilizing forces of the discharge-pressure" are combated by the "restoring forces of the control actuator." The dynamic system model is expressed in equation (27), where a, aQ and Pa are the actual swashplate angle, desired swashplate angle and discharge pressure, respectively; coefficients a, b, c, d, e and f are composed of physical internal dimensions of the constituents of the pump and flow-characteristic constants. • a a b a e • — + c d A. (27) a = {AsL-NApry/(27r)yo Kc (A,L- NApry/{l^ > ° = / Kl -Kp- A,L ULfVh c = —Kp, d = ——K,, e = -a and f =-c 26 As = area of the small actuator Ai = area of the large actuator Ap = area of a single piston KP = pump flow gain Ki = system leakage gain Kc = controller flow gain L = moment arm of actuator acting on the swashplate N = total number of pistons r = piston rotational radius r pressure carry-over angle on the port-plate v0 reference volume of the large actuator vh volume of discharge hose , In a different publication by Manring and Luecke [18], based on the work of modelling a variable pump in [17] and by including models for the motor and the hose, a complete model of the HST was developed. The load-torque acting on the motor is considered constant in this model, as shown in equation (28). b 0" — u 0 / Ph + 0 (28) 0 — i a w iJt(IiJK'-u=Tp' + T-Tmiw--g^ = angular speed of the motor shaft Ph = dynamic hose pressure a = pump swashplate angle Vm = motor volumetric displacement I = mass moment of inertia of the motor and load P = hydraulic fluid bulk modulus Gp = pump displacement gain (same as Kp above) Vso = nominal servo volume Gs = control gain Po - constant hose pressure COo = desired motor speed 27 Tafazoli, de Silva and Lawrence [19] created a non-linear friction model of an apparatus for decapitation of salmon. The decapitating blade was moved to the correct position with the aid of a digital camera. The position of the blade was controlled by varying the current to the electro-hydraulic valve. The force acting at the hydraulic actuator was modelled by considering coulomb friction between the lubricated metal guide ways. The coulomb friction was estimated online using the modified Friedland-Menzelopoulou's coulomb friction observer algorithm. Only a simple model of the hydraulic-valve controlling the position of the blade was considered because pressures after the control-valve were measured and used to calculate the acting force. It was recognized that hydraulic-actuator dynamics resulted in a fixed delay in the response of the blade in following a command. To remedy the delay, feed-forward compensation was suggested but not implemented. 2.2.6 Other Modelling Methods Dasgupta has presented a model of an open circuit HST with a variable pump and a low-speed-high-torque, orbital-rotor motor [20]. Using Bondgraphs, he created a model of the HST consisting of a pump, an integrated pressure control valve and a motor to study the dynamic performance of the system. The bondgraph model of the HST, as presented by Dasgupta, is shown in Figure 10. r D«D_T p.oiT t j r i t n n ~~ "1 i PUMP I R-.Rp c:KP P-r . I »T> -^Ppc-T-R;Rm MOTOR T ! -4ST' - S E : f (vm,RU,Ri) j J & c-x, 1 1 '"SiTrT ! s e : S E « > c : SE:SEV CONTROL | VALVE 1 ^ T F %Sv1 p C K C S R : R V | I Figure 10: Bondraph model of the HST system [20] 28 The equations pertaining to system dynamics can be deduced from the bondgraph model. Each bond represents a directional flow of relating effort or flow variables between two considered components. The product of the bond effort and flow variables equals power. The term "bondgraphs" is a concise form of power-bondgraphs. SF in the bondgraph model of Figure 10 represents a flow source, i.e., the pump. Similarly, the motor is shown as an effort source (SE) where the effort, torque, is originating due to a load. S and P junctions are used to show series and parallel connections (analytic, not necessarily physical) in bondgraphs. An S junction signifies that the flow variable through the junction is constant and the effort is distributed; whereas a P junction is used where the effort variable is constant and the flow variable is distributed. For a further examination of the Bondgraph simulation techniques, please see references [21] and [22]. In Dasgupta's model, the variables are defined as: r = pump flow constant (Dp = pump angular velocity Mi = tangent of the pump swashplate angle (tana) Kpp = effective pump plenum fluid bulk stiffness RP = pump plenum leakage resistance R/n = motor plenum leakage resistance Vm = input flow of the motor Ru = motor inter-chamber leakage resistance Ri = resistive load at motor Rci = pump control line resistance Kci = effective control line fluid bulk stiffness Rev = control valve orifice resistance Rep = control piston leakage resistance KCp = control piston fluid effective bulk stiffness P = projection of control moment arm to neutral position x area of the control piston (ARcosa) RSP = swashplate rotational damping coefficient = swashplate return spring rotational stiffness Jsp = swashplate moment of inertia Av = control valve spool area Rv = control valve spool damping coefficient Kcs = control valve spool stiffness My control valve spool mass 29 Dasgupta examined his model experimentally. He found a delay in the experimental response of the swashplate and the control piston spool when compared to the theoretical response, and attributed it to positional stiction; this quantity was not modelled in the analysis. Some of the values required for the model were experimentally determined: spring constants, control piston leakage and pump leakage. It was shown that the pump leakage varies almost linearly with pressure. The test speeds were slow compared to real applications. The tests were conducted at 125, 158 and 195 revolutions per minute. From the data presented by Dasgupta, a slight dependence of leakage on speed can be observed. Njabeleke et al [23] used a hydraulic system modelling software package, known as BATH/p, developed at the University of Bath, to obtain linearized system equations to represent the components of the hydraulic system. They have suggested that non-linear mathematical models of hydraulic components are complex and their application to system design even more difficult, where system components and parameters can be easily changed. This is truly the case with HST's, where components may be replaced for maintenance purposes and component behaviour changes with use and wear. The response of a system to an applied input can be measured and a transfer function can be deduced i f the system is treated as a black-box. A degree of complexity of the system has to be assumed and the input and output data can be fitted to acquire a transfer function of the assumed shape. The classical approach of black-box identification has two distinct steps: data acquisition and transfer-function deduction. Some of the disadvantages of using the classical approach listed by Landau [24], include: • Test signals during data-acquisition are not characteristic of the real process. In other words, the input signal in the classical approach is generally a step signal and the real process seldom experiences such signals. • The end result has a reduced accuracy. • Disturbances are not modelled. For a system that is assumed to have a first-order response, the resulting transfer function takes the form of equation (29), where t is the delay in response, r is the time constant and G is the DC gain or the steady state value of the response [24]. 30 T(s) = f- (29) l + ST A n example of offline system identification of a hydraulic test-rig is available in [25], where an "earthmoving vehicle powertrain simulator (EVPS)" is modelled by collecting the process data and making use of M A T L A B to develop the transfer-function. Landau [24] suggested the use of high-performance, recursive algorithms that are capable of real-time identification. The recursive algorithms result in discrete-time models of the plant and are suitable for application to a digital controller. A simple system-identification technique was used by Tafazoli et al [26] to model a position controlled hydraulic cylinder, using the least-squares method to maximize model accuracy by minimizing the error between the model and the collected data. A first-order system was assumed to represent a hydraulic cylinder. Having presented various methods used for modelling the process, the next section will show examples of control strategies employed by researchers in controlling hydrostatic transmissions. 2.3 Control Various control strategies such as PI (proportional-integral), adaptive PI, fuzzy, and hybrids of fuzzy and other control-techniques have been applied to the control of hydrostatic transmissions. Since the HST is a highly nonlinear plant, the application of purely linear controllers like PI is limited; however, PI or PD control has been applied to other hydraulic components such as actuators and valves. 2.3.1 PI controllers Publications dealing purely with the application of PI controllers to hydrostatic transmissions could not be located in the literature; however, ones comparing the performance of linear (PI) and other control techniques were found. Ambuel et al [27] conducted tests to control the output speed of a variable-pump, fixed motor (PVMF) HST, implementing a PI and a hybrid PI controller. The motor load was simulated by a flywheel and a load pump that pumped into a relief valve. The control scheme was transformed to the discrete-time domain to implement with a digital controller having, a 31 cycle time of 50ms. A flowchart of the PI controller is shown in Figure 11. Ambuel et al's approach to a hybrid PI controller will be discussed in the next section. Compute Speed Error at Time T = Tk Ek = Speed Error = Setpoint - Speed Compute Proportional Term using Proportional Gain Kp P = KpxEk Compute Integral Term Using Integral Gain Kj k-\ Ik = K i x E k + h-x» where7t_, =Kix^JE} Determine Total Output 0 = P + I = KpxEk+KixfjEj 7=1 Figure 11: PI control flow-chart (after [27]) For the PI controller, values of 0.2 for the proportional gain and 0.1 for the integral gain resulted in an under-damped response, whereas values of 0.1 and 0.05 for the former and latter, respectively, resulted in an over-damped response. Tests were repeated on the system when it had aged and experienced wear. It was shown that the PI controller's performance degraded as the system's behaviour changed with age. The same gain values that resulted in an over-damped response previously, outputted a high overshoot and a slow rise-time. Huhtala [4] discussed application of a PI controller to a hydrostatic transmission, specifically, to a hydrostatic unit (pump or motor). His end result took the form of an adaptive PI controller, which is discussed in the next section. The gain of the PI controller was shown to strongly depend on the unit's displacement setting. He suggested that a controller with a fixed gain could not be implemented to provide sufficient control over the entire operating range of the unit. Huhtala showed that a 32 controller tuned at a low speed setting of the hydraulic-unit results in an under-damped behaviour at high speeds. For the inverse case when the tuner is tuned at a high unit speed, a longer rise-time or a slower response is resulted. Tuning of P, PI and PI D controllers is discussed by Jantzen [28] by citing the Ziegler-Nichols method. The proportional gain is increased until stable oscillations are achieved to determine the ultimate gain (Ku), at which point, the time-period of the oscillations is measured (Tu). Finally, using the Ziegler-Nichols rule-table (Table 1), the PID gains are estimated. Table 1: Ziegler-Nichols Rule-Table [after 281 CONTROLLER KP T (K^Kp/Tj) Td(KD=KP*Td) P Q.5KU PI 0A5KU TJX 2 PID <d.6Ku TJ2 TJl.S 2.3.2 Adaptive Controllers The adaptive controller designed by Plurnrner and Vaughan [29] utilizes the technique of pole placement to adapt rapidly to changes in load and supply pressure in a hydraulic positioning servosystem. The control-strategy is formulated in the discrete-time "z-plane" for implementation on a digital controller. The algorithm performs online estimation of controller and system parameters through the use of recursive-least-squares to result in the desired response. An electro-hydraulic servosystem used as a positioning device for a large inertial load was modelled through off-line system-identification techniques. The adaptive controller was compared to a fixed controller and was found to result in a lower steady-state error and a quicker response (rise-time). Lee and Wu presented a self-tuning control scheme employing pole placement as applied to a hydrostatic transmission [30]. They compared performances of P V M F , PFMV, and P V M V types through a series of simulations, while changing the load inertia, line pressure, pump speed, and with application of an external disturbance torque. They used a variable forgetting factor in their recursive least squares parametric estimation. Using a pole-placement method, closed-loop poles are assigned to desired locations to give the desired response. The adaptive controller performed adequately for the P V M F case. For the P F M V case, the unit displacement needs to be decreased to result in an increase in the response - the adaptive controller managed to provide adequate control 33 for this case as well. For the P V M V case, the pump displacement is increased to maximum initially. To increase the speed further, motor displacement is decreased subsequently. Their experimentation showed that the P V M F case performed the best under varying system parameters, followed by the P V M V and P F M V cases, which exhibited lower tolerance to changing system parameters. For the P F M V case, the motor displacement was varied to increase system response. However, when the load was increased, the system responded by decreasing the motor displacement to increase the system speed, which resulted in reducing the available torque and in a slower acceleration and a longer rise-time. 2.3.3 Fuzzy-Logic Controllers Fuzzy logic was invented by L . A . Zadeh in 1965. Of several advantages offered by fuzzy-logic over the conventional control techniques, the most important are: a mathematical model of the process is not required but a qualitative understanding of the operation of the system is needed, and fuzzy controllers are inherently better-suited for systems with non-linearities. Where understanding of the process is not available, test data under various operating conditions is required to create a fuzzy-rule set. In [27], Ambuel et al discussed a hybrid fuzzy-PI controller for a HST. In their approach, i f the error between the actual and desired outputs was above a predetermined value, fuzzy logic was used to control the process, and when the error was reduced to within the user-defined value, the controller resorted to PI to reduce the error to zero. As claimed by Ambuel et al, purely fuzzy control could also have been used to eliminate the error, instead of a hybrid controller. The fuzzy rule set presented in [27] is based on the motor speed error and the motor torque. Seven linguistic rules ranging from very small (VS), to very large (VL) were created. The other rules in the rule set matrix of Table 2 are small (S), medium small (MS), medium (M), medium large (ML), and large (L). Given any value of motor torque and motor speed error, a corresponding change in output can be found from the rule set matrix. However unlike conventional rule-based controllers, fuzzy ranges overlap. In other words, memberships of any given values are not limited to their corresponding squares from the matrix. Triangle functions that overlap with the adjacent 34 ranges define fuzzy memberships. The degree of membership within a range is found by linear interpolation of the sought point on the membership triangle function. Each value has memberships in two ranges, resulting in a total of four activated ranges. The final output is found by the process of defuzzification, by employing the method of calculating centre-of-mass, where the degree of membership of a rule is analogous to the mass of the object and the output of the rule is analogous to the object's distance from the origin. Table 2: Fuzzy Rule Set [27] Motor Speed Error X V S S MS M ML L V L vs VS MS M ML L VL VL s vs MS M ML L VL VL MS vs MS M M ML L VL M vs MS MS M M ML L ML vs MS MS MS M M M L - S MS MS MS MS MS V L In another example, Huhtala presented an adaptive-PI controller. The adaptive behaviour of the controller was achieved through gain-scheduling. As mentioned earlier, the gain (also the damping ratio and the natural frequency) depends strongly on the unit-displacement, which suggests that a PI controller with fixed gain would only be suitable for a fixed capacity unit. As the HST benefits from the smooth variability of speed, which is achieved only because of the variable displacement nature of the hydrostatic unit(s), Huhtala suggested that a variable gain PI controller should be employed. Gain scheduling of a PI controller was made possible by fuzzy logic as presented next. In Table 3 and Table 4, pump and motor fuzzy rule sets used by Huhtala for gain scheduling are shown. The gains for the units can be read in the rule-set matrices depending on the actual and desired output speeds. Huhtala showed that performance was greatly improved with the use of the adaptive PI controller versus the pure PI controller. Table 3: Pump fuzzy rule set used by Huhtala [4] 35 actual/desired RPM 100 600 1200 100 0.00020 0.00016 0.00016 600 0.00016 0.00013 0.00010 1200 0.00016 0.00010 0.00007 Table 4: Motor fuzzy rule set used by Huhtala [4] actual/desired RPM 100 600 1200 100 0.000055 0.000045 0.000035 600 0.000045 0.000028 0.000018 1200 0.000035 0.000018 0.000010 Wang and Mendel in [31] applied a fuzzy controller to a truck "backer-upper" control and showed that the fuzzy controller performed as well as a neural controller. In their approach, input and output data must be collected and linguistic rules also must be developed from human experience with the process. Also, they demonstrated that numerical data is usually incomplete without the linguistic data and vice-versa. Their tests showed that the performance degenerated when the numerical data was used without the linguistic data in generation of the fuzzy rule set. They summarized the development of their fuzzy controller method in the following five steps: 1) Divide the input and output data into fuzzy regions. 2) Generate fuzzy rules from the data. 3) Assign a degree to each of the rules to resolve conflicts. 4) Create a rule base that is a combination of the generated and linguistic rules. 5) Determine a mapping from the input space to the output space through the process of defuzzification. A fuzzy state controller (FSC) was proposed by Zhao and Virvalo [32] for controlling a hydraulic position servo (HPS) with an unknown load. Typically, when the load is known, the controller performance parameters (gains) can be tuned to effect a desired performance. However, i f the load is changed, the same gains can "cause overshoot or even loss of system stability." As a fast response was required in controlling the HPS, an adaptive controller was not deemed suitable. The FSC was demonstrated to be a robust controller for a varying load. Dale and Gil l [33] compared the performances of a self-organizing fuzzy logic controller (SOC) and a traditional proportional-derivative (PD) controller in controlling 36 the attitude of a flexible satellite. The foremost benefit of the SOC over the PD controller is that for a matched performance of the two, only a limited knowledge of the process is required for the SOC, whereas a mathematical model must be developed for application of the PD controller. Their algorithm allows addition and deletion of fuzzy rules based on the output of the process, hence the name self-organizing fuzzy logic controller. Williams [34] describes fuzzy logic's functionality and benefits over traditional control strategies. The widely realized benefit of fuzzy logic is the fact that knowledge of human experts can be used to control a process through a set of linguistic rules. He described through an example of a one touch washing-machine with a fuzzy-logic controller that a tremendous amount of tuning of the rules may be required, after a prototype is built based on the initial rule set. The membership functions have to be adjusted according to the actual performance exhibited by the prototype. In another example [35], a fuzzy-based controller was used for controlling wheel slippage in an off-road application. With the use of speed sensors and local processors, each hydraulic motor was effectively converted into a Mechatronics unit. A global processor was also used, which allowed for fault-tolerance and determining of wheel slippage by comparing a wheel's speed to other wheel-speeds. The local processor monitored the wheel speed and acceleration: the wheel was assumed to slip i f the instantaneous acceleration was higher than a predetermined value. It was found that using only the local controllers was not sufficient to result in adequate performance. The system performed better with a global controller also monitoring slippage as the local controller did not always detect slippage. Slippage was controlled by application of brakes to the wheel where slippage was detected. Nevala et al presented an anti-slip controller for a forest-tractor with a hydrostatic transmission [36]. The slippage was controlled through the application of brakes. Efficiency was also targeted in this study, by optimizing the power of the diesel engine. The signal communications were facilitated by making use of a CAN-bus system, which also allowed modularity. Each axle was equipped with a local controller, with a main or global controller overseeing the diesel engine and main pump controls and monitoring wheel slippage for the whole vehicle. The control strategy for monitoring and controlling slippage was very similar to that used in [35]. 37 An example of a fuzzy-PI hybrid controller was presented by Schmidt et al [37]. The authors suggest that design of a controller based on a simplified, linearized model of a hydraulic positioning system, is difficult because of the uncertainties faced by the application. The mass of the load being positioned and the external disturbance-forces acting against the mass are unknown and variable. In the application minimum overshoot and no steady-state error are desired. Based on the performance requirements and system characteristics, adaptive PI control is suggested, where the variability in the PI gains is achieved though fuzzy-logic. Examples of fuzzy-based controllers for HST are abundant in the literature. Some applications of fuzzy-logic to hydraulic actuator control, excluding the HST, were not summarized here; e.g. Sepehri et al [38] and Corbet et al [39]. 2.4 Literature Review Summary A significant amount of work has been done in the area of modelling hydraulic systems. The motivation for modelling has varied from a basis for control design to performance prediction of the hydraulic system components as a tool for hydraulic system design. It became evident from the literature review that complex models that attempt to predict the behaviour of the HST in detail tend to become unusable for control purposes - they have to be reduced through simplification before they can be used for practical control design because of limitations on available computing power in practical applications. In terms of the HST, the complexity of the whole system precludes complete, detailed and accurate modelling. Researchers have modelled individual components but due to their complexity, as mentioned before, such models are not suitable for use in control design. Most of the work on control of hydrostatic drives has focused on using fuzzy-logic, primarily due to non-linearities in the individual components and the fuzzy-controller's 'human-like' adaptive capabilities to cope with the non-linearities. It is also apparent that although interesting from an analytical point of view, it is not practical at this point to build a controller based on a comprehensive physical-mathematical model of the HST. Given the above, the approach in this thesis will be to explore the efficacy of PI 38 control for HST, using system-identification to build a simple model of the machine, solely for controller validation purposes. 39 3.0 Experimental Methodology 3.1 Hydraulic-Sharing Testing The drive component of the hydraulic system on the machine is subject to variability due to inherent non-linearities in the hydraulic components and the unpredictable nature of the operating conditions. Environmental influences that may affect the outcome of a test are: hydraulic-fluid temperature, hydraulic fluid cleanliness at a given point in time, response of the hydraulic components, and so on. The fluid viscosity is a function of the fluid temperature. When the machine has been running for some time, the fluid temperature increases causing the viscosity to decrease and the machine to perform better. Fluid pathways can become partially or fully blocked by dirt or metal debris from working components, causing undesired effects. These particles will get filtered out once they encounter filtration in the system. Hydraulic control components, such as DPR valves and the pump and motor HDC controls, exhibit a non-repeatable behaviour due to the complex interaction between the non-linear elements inherent in them. The error in response of these controlling components may cause an undesired response as well. A l l of the abovementioned factors affect the performance of a test. To obtain representative data, ten trials of each test were conducted. 3.1.1 Testing Scheme To gain a better understanding of the efficacy of all of the various hydraulic sharing arrangements, eleven were selected for testing as shown in Table 5. A l l cheater and power-sharing ports were connected through % inch (#4) hose, with the exception of test 11, which used 3 / g inch (#6) hose. Eight pressure sensors were used for all tests except tests 1, 2 and 3, where the number of pressure sensors used was reduced to four due to the sharing of main pressure ports ( M l and M2) through the use of cheater lines. Also, the steer sensor was used only in test 9 to calculate and create a differential effect, based on the turning (articulation) angle (see sections and 40 Table 5: Hydraulic sharing configurations tested Test# Configuration 1 Cheater lines Left to Right + PS Front to Rear and Left to Right 2 Cheater Lines Left to Right; No PS 3 Cheater Lines Front to Rear 4 No Cheater lines or PS lines 5 Pump PS Left to Right 6 Pump PS Front to Rear 7 Pump PS Left to Right and Front to Rear 8 Pump PS Left to Right and Motor PS Left to Right 9 Test 8 w/ articulation correction calculations 10 Motor PS Left to Right 11 Pump PS Left to Right and Front to Rear using # 6 hoses ( 3 / 8 " ) Configuration of test 1 Test 1 is configured by installing cheater-lines between the right and left pumps and also power-sharing lines (PS lines) between the left and right pumps and between the front and rear pumps. By doing this, the left and right side pumps and the front and rear pumps interacted, by sharing pressure from the internal pump feedback. Of all the configurations tested, test 1 was expected to perform the best. Configuration of test 2 In test 2, the PS lines were removed and the ports were plugged. The test was run with cheater lines as configured in test 1: between the left and right pumps, for both the front and rear pump combinations. Configuration of test 3 Cheaters lines were installed between the front and rear pumps on both tandem pump arrangements connecting ports M l and M2. Configuration of test 4 All flow and pressure sharing was removed for test 4. This test was expected to perform the poorest, as no aid was available to promote the differential effect. Configuration of test 5 PS lines between the left and right pumps were installed for test 5. Comparing this test to test 4 would allow evaluation of the efficacy of pump PS lines. 41 Configuration of test 6 It was decided that pump PS lines should also be evaluated for front and rear, as fighting may be occurring between the front and rear wheels causing the jittery behaviour of the machine. Therefore, test 6 was conducted with PS lines between the front and rear pumps. Configuration of test 7 A combination of front and rear, and left and right pump PS lines was tested in test 7. A cumulative effect of tests 5 and 6 would be realized in this test. Configuration of test 8 PS lines between left and right motors and left and right pumps was the configuration tested in test 8. This arrangement was tested because all production machines are shipped with PS lines as installed here. Configuration of test 9 Test 9 had the same PS configuration as test 8, but with the articulation steer sensor activated for calculating the speed variance required for an ideal differential effect. This was achieved by calculating the differential ratios and metering the current to the DPR valves accordingly through the IQAN system. The objective of this test was to determine the effectiveness of controlling the HST in this way. Configuration of test 10 The effectiveness of motor PS in helping with creating a differential effect was tested in test 10. PS lines between the left and right motors were installed. Configuration of test 11 It was thought that perhaps by increasing the size of the PS lines, their effectiveness could be improved. A l l previous tests utilized #4 hose (%") for PS lines. In test 11, the size was changed to #6 hose (3/s")- Similar to the configuration in test 7, pump PS lines between left and right, and front and rear pumps were tested in this test. 42 3.1.2 The Test Course A l l of these tests were conducted at EJC's production facility in Burlington, Ontario. A schematic of the course that was followed during the testing is shown in Figure 12. A course that was least affected by the production traffic was selected in the warehouse secondary storage area. The various turns and straight sections were deemed ideal for testing the efficacy of each of the eleven hydraulic-sharing configurations in creating a differential effect. ] [ ] [ 2 3 8m 8m yV A 8m START/FINISH 8m 33m 22m ] [ ] [ Figure 12: Course followed during testing 3.1.3 Test Procedures Since the number of channels to be recorded was greater than ten, a T O C 8 module from Parker was installed for data acquisition, with its own laptop computer for interfacing. This required two laptop computers to be installed on the machine, along with the T O C 8 test-box and the required wiring for interfacing. The I Q A N system recorded the four wheel-motor speeds, the engine power, and the currents sent to the steering solenoid, left-drive-pump DPR's, right-drive-pump DPR's and the motor DPR. 43 The TOC 8 monitored the eight main drive pressures and the articulation sensor feedback. To synchronize the two computers, a digital switch from one of the joysticks from the operator's cab was wired into one channel on each of the two systems. Ten tests for each of the aforementioned eleven configurations were conducted and upon completion, data from the IQAN-develop software was copied into MS Excel. The test began with the machine traveling in reverse. Selected channels on the IQAN-systems were recorded and displayed in a graph window. The recording was initialized and the trigger switch from one of the joysticks from the operator's cab was used to synchronize the two computers acquiring separate data. After the test was complete, recording was stopped on both computers. The files in the two computers were saved in I Q A N format as graph files. At completion of ten tests for a given configuration, hydraulic hoses were re-arranged to result in the next configuration, and the course was repeated until all of the eleven configurations were tested. After tests were completed for all eleven configurations, data from the I Q A N graph files was exported into MS Excel. The data from the two computers was compiled by locating the trigger on both of the files and merging the data accordingly. As a result, 220 files of raw data were converted into 110 Excel files for further analysis. Graphs were generated from the pressure data and steering and speed data. It was then understood that the information was too abundant to meaningfully display in graphs at one time. It was decided to further condense the data through calculations, to acquire a format that would facilitate comparison of the performance of each configuration. A "drivability index" was calculated from the motor R P M and the articulation data, which resulted in condensing hundreds of lines of data into a single, dimensionless value. The drivability index is a measure of compliance of the differential effect resulting from a given configuration to that of the ideal differential requirement to negotiate a turn (discussed further in section Analysis of the data In order to calculate the drivability index, predicted and actual differential ratios needed to be calculated. The actual differential ratio can simply be extracted from the acquired data, but the predicted ratio required further calculations. Based on the 44 articulation feedback, the articulation angle and the radius of turn can be determined as shown in the following section. Articulation Angle Calculations The articulation angle calculations are based on simple geometry. Applying the Law of Cosines resulted in the articulation angle as shown in equations (30) and (31). Figure 13 below shows a geometric representation of the steering arrangement on the 88XLP, based on which the articulation angle was calculated. F R O N T Steer Cylinder Pin b Centre Hiiiae Steer Cylinder REAR \ Steer Cylinder Pin Figure 13: Articulation angle calculations FB2 =b2 +c2 -2bc-cos(ZA) ZA = cos _ 1 | (30) rb2+c2-FB2^ 2bc The b and c dimensions in the above equations are constants found to be 1.265-m (49.83-in) and 0.391-m (15.38-in). When the machine is not articulated, the angle A is 74°. This value must be subtracted from A when the machine is articulated to calculate the actual articulation angle. ZArt = ZA- 74° (31) 45 Articulation Radius Calculations Having determined the articulation angle, the turning or articulation radius can be deduced from geometry by applying the Law of Cosines. Figure 14 shows the geometry of the machine in articulation. Calculations are performed for the circle formed by the centres of the axles. The front and rear axles follow the same path because the wheelbase is evenly-split about the hinge point. Figure 14: Articulation radius calculations Figure 15 shows details required for the turning radius calculations. By applying the law of cosines on the triangle formed by sides d, d and s, a relationship, as in equation (32), can be found. s2 = 2d2 -2d1 cos(l80-ZArt) = 2d2[l + cos(ZArt)] (32) Similarly, another relationship is apparent when the Law of Cosines is applied again on the larger triangle formed by sides R, s and R, equation (33). s2 = 2R2 - 2R2 cos(ZArt) = 2R2 [l - cos(ZArt)] (33) By combining equations (32) and (33), and by solving for R, a relationship is derived where R depends on d, a constant equal to 1.55m (61"), and on the cosine of the articulation angle. 46 1 / Figure 15: A detail of the turning radius calculations Equation (34) shows the calculations required to obtain the articulation radius. By making use of MS Excel, the turning radius was easily calculated for each data point for j every test. Since equation (35) results in the path followed by the centre of the axles in the front or the rear of the machine, a constant equal 0.770m (or 30.38", half the machine track width) must be added and subtracted to obtain the outer and the inner turning radii, respectively, as shown in equations (35) and (36). 3 . 1 . 3 . 1 . 3 D r i v a b i l i t y I n d e x C a l c u l a t i o n s In M S Excel, columns were created for calculating the articulation angle and the articulation radius. Using the articulation feedback from the acquired data, these values were calculated for all data points. The predicted differential ratio (Turnpred) was calculated in another column using the formula shown in equation (37). It is simply (34) (35) Rin 0.770 (36) 47 obtained by dividing the inside turning radius (Rjn) by the outside turning radius (Rout)-Fortuitously on the 88XLP, the front and the rear turning radii are identical, because of its symmetrical construction: the distance from the articulation hinge point to the centre of the front axle is the same as the distance to the centre of the rear axle (no actual axles exist on the machine). This geometrical attribute simplifies the calculations significantly. turnpred = -f- ( 3 7 ) Kout The actual differential ratio is calculated by dividing the lesser of the motor speeds, from the right or the left wheels, by the greater speed as shown in equation (38). tumactual = -^S- ( 3 8 ) Two columns were created for the actual differential ratio: one for the front and one for the rear. Conditional statements were introduced to avoid division by zero speed, when the machine was stationary or just beginning to move. Two more columns in MS Excel calculated the absolute difference between the predicted and the actual ratios. And as a final calculation, the numbers in the columns containing the absolute difference between the actual and the predicted ratios were averaged. In this calculation, data-points corresponding to zero motor R P M were excluded because they have no contribution to the meaning of drivability as it is discussed here. Steps leading to the calculation of the drivability index (DI) can be summarized by equation (39), where N is the number of used data points. DI = — V \turn, ' pred 'tUrnactual] (39) 3.2 System Identification For purposes of controller design, a model of the HST was required, to enable simulation of the controller prior to implementation on the machine. The classical approach of system-identification, which requires collection of response data through data acquisition with a known applied input, and fitting of a response of predetermined complexity to the data, was chosen for the system-identification task. For this work, 48 testing was conducted using a test bench at Feldcamp Equipment Limited, in North Bay, Ontario. The M46 pump and the V12 motor were connected in a closed circuit, representing one of the four circuits existing on the 88XLP. The test bench allowed variability of the input shaft speed of the M46 pump, and with the IQAN system available, the pump and motor swashplate settings could also be varied in a controlled manner (Figure 16 and Figure 17). As seen in Figure 16, the motor has no external load connected to its shaft. The test bench had no provisions for application of an external load to the motor shaft. \ Figure 16: Test bench at Feldcamp Equipment Ltd. Figure 17: The IQAN computer interface at Feldcamp Equip. Ltd. 49 3.2.1 Description of Testing As the pump and the motor were connected in a closed circuit, an effect of any change to the motor or pump displacement setting would be seen as a change in the motor shaft speed. Closing the circuit with a motor connected to the pump is identical to the operational configuration of the HST as it is installed on the 88XLP, and thus provides advantages over measuring the flow responses of the pump and motor individually, using flow meters. DPR valves were also used to simulate the functionality of the HST as it exists on the 88XLP. The DPR valves provided controlled pressure signals to the pump/motor HDC, converting the IQAN current signal to a proportional (theoretically) pressure value. A range of tests were conducted in order to collect the most representative data. Every test was conducted twice to examine repeatability and as contingency, in case data was corrupted or had anomalies. The pump response was tested by leaving the motor displacement at its default setting of maximum and changing the pump displacement with a current signal that was stepped up in increments of 12.5%, eight times from 0 to 100%. Eight steps were chosen because it was easier to program eight steps in IQAN than any number higher than eight. The signal was stepped up every five seconds and it was noticed that in some cases, five seconds was not enough time for the signal to acquire steady-state. The step time was increased to fifteen seconds, thenceforth. The step-up test was conducted at three different input shaft speeds: low (close to 800 rpm), medium (close to 1400 rpm) and high (close to 2000 rpm). A l l tests were repeated with the signal stepped down in the same manner from 100% to 0%, at decrements of 12.5%. Additional tests were conducted by using three steps instead of eight. The pump and the motor were stepped up and down using steps of: 0 to 25%, 25% to 75% and 75 to 100%. Tests were conducted at three different input shaft speeds. The first set of tests was conducted to collect the pump response data, where the motor was not stroked and the pump displacement was varied in the manner described in section 3.2.1. Eight steps of equal value would give insight into the linearity of the system. A definition of linearity is given by equation (40), as superposition and homogeneity are properties of linearity [40]. If a system's response to an input xi(t) is yi(t) and is y2(t) to X2(t), then the principle of superposition requires the response to be equal to yj(t) + y2(t) to an input of 50 xi(t) + X2(t). The property of homogeneity requires that i f the input is scaled by a factor a, the output must also be scaled by the same factor a. f(h+t2) = f(tx)+f{t2) (40) f(ar) = qf(r) Visual Basic® and MatLab® were used to manipulate the data further and to obtain transfer-functions of the pump and the motor for all tested steps of 12.5%. In Visual Basic, a program was written to separate data corresponding to each of the steps in the form of ASCII text files. Subsequently, the data for each of the steps was inputted into the MatLab System-Identification toolbox to obtain a discrete-time transfer function. 3.2.2 MatLab for System Identification A function was written in MatLab (named pre) to reformat the ASCII data, so that it could be easily utilized in the MatLab system-identification toolbox (see APPENDIX C.) First, the function used a user-input to identify the data file for the test to be modelled. After identifying the input/output columns in the data file, the function looked for the step in the input data array. Third, the function filtered the data based on the low-pass filter transfer-function shown in equation (41). The continuous space, low-pass-filter shown in equation (41) was converted to discrete-time space to extract the parameters required by the MatLab built-in command filter. The value of coc (the cut-off frequency) used in the filter was 25 rad/s. It was deemed sufficient to exclude dynamics resulting from high-frequency components as they are not the object of this study. This was based on observation of the data, which showed a high frequency component at around 30 rad/s. LPF = -^— (41) s + coc Finally, the function pre outputted the filtered data as an iddata object, which was easily imported into the system-identification toolbox for purposes of model fitting. In the toolbox, after the data was imported, it was pre-processed to remove the means. It was found that the toolbox yielded better fits i f the means were removed prior to model fitting. Data-fitting was limited to result in a second-order model, such as the 51 one shown in equation (42), using the arx parametric model fitting, where the function arx results in discrete-time models. a(s + J3) G = ——- — — r (42) s + 2£cons + con The fitted models were exported to the MatLab workspace and further operated upon with the built in function d2c to convert to the continuous space. A function was written to facilitate quick use of repetitive operations while model fitting. The function called post2, which was used to transform discrete functions to the continuous space, is shown in APPENDIX C. The function post2 required the discrete model fitted by the toolbox as input. In addition to transforming the model to continuous space, the function calculated the two poles and the dc-gain of the system. A l l of the calculated values were bunched together as a struct type variable and outputted as the result of the function post2. A script file was written (see APPENDIX C) to format the graphs plotted by the system-identification toolbox. The script file created the legend and resized and restyled all of the text labels to a predefined format. The graphs of the acquired data and the fitted models are shown in APPENDIX D. A goodness-of-fit value produced by the toolbox is also included in the graphs. Further, the function used in the toolbox, namely arx, and its parameters are also shown. The first value in the arx function parameters is the number of desired poles {na), followed by the number of desired zeros plus one (nb) and the delay in terms of sampling periods (nk). While converting to continuous space, a zero was added to the models by MatLab and delay equivalent to one sampling period was eliminated. 3.3 Controller Design and Simulation MatLab's simulation module, Simulink, was used for controller design and simulation. Pump data corresponding to an increase in input from 75% to 87.5% was chosen. This range was selected because the pump had a good response to the input signal in this range, and this range is representative of the greatest duty cycle of the pump. The selected transfer function is shown in equation (43) (derived as discussed in section 4.2.3, with its fit shown in Figure 49, APPENDIX D.) 52 T.F. = e -0.2s 12.17 5 + 1423 s2 + 46.46 s + 297.2 (43) Simulink allows input of transfer-functions in a block-model form and outputs the overall response of the various model components. In Simulink, initially a simple feedback model using the transfer-function from the aforementioned data was created. Subsequently, a feed-forward model was created to improve the response time of the system. It was then realized that correct representation of the controller on the machine would require a translation of the model controller to discrete-time domain as the digital controller on the machine has a finite sampling frequency. This would also mean that depending on the sampling rate used by the controller (which is set by the user and is predetermined based on available system resources), a different set of controller gains could be required to maintain system stability. A simple feedback model using the pump transfer-function shown in equation (43) was created with the zero and the delay removed (see Figure 18.) Using the Routh-Hurwitz stability criteria (APPENDIX E), it was determined that a Kj (integral-gain) of greater than 46.46 would cause system instability when KP (the proportional-gain) is equal to zero. In the model shown in Figure 18, Kp = 2 and Kj= 17. The response of the model in the form of vectors composed of time and behaviour data was exported to the workspace in MatLab, where it was plotted (plots are shown in the results section: section 4.3.) Step 2S+17 Controller 297.2 +46.46S+297.2 PVMF resp_ To Workspace inp_ To Workspacel Figure 18: Feedback model using the simplified pump transfer function Addition of the zero to the model caused the system to become responsive. Adding the delay in the form of the block shown as Transport Delay caused sluggishness. The model shown in Figure 19 resulted in the desired response with controller gain values of KP = 0.057 and Ki = 0.28. The delay was also added to make the model reflect 53 the fitted model. A value of 0.2s was used in the Transport Delay block. The source of delay in the HST was multilayered: a delay was caused by the extremely non-linear behaviour of the DPR valves and also, a delay was inherent to the response of the HST units. It is difficult to separate the individual delays from the overall delay of the identified model of 0.2s. However, an assumption can be made that the majority of the delay is a result of the DPR valves. Step Input 57S+280 s Gain Controllerl Transport Delay 12.17S+1423 s 2 +46.46S+297.2 0.2088 P V M F Normalizing Gain Output inp_ Input Figure 19: Feedback model with the fitted pump transfer function To make the model more representative of the real system, non-linearities were also added. Backlash with a parametric value of 0.25 was introduced into the model to loosely reflect the behaviour of the hydraulic components, especially the DPR valves. The controller in the above model was time-discretized with the zero-order-hold function, to correctly show the behaviour of a digital-controller. The purpose of the block labelled as "Quantizer" is to quantize the response as read into the controller for feedback, to show the behaviour of the controller as it reads the feedback signal. The function used for quantization is Quantizer with a fixed quantization value of 1/491. This value was arrived at based on the maximum speed of 820 R P M , in the fixed motor case, and the thirty-six pulses per revolution transmitted by the motor-speed sensor. By converting the maximum speed of 820 R P M to pulses per second, a value of 491 was arrived at based on the number of divisions from 0 to 492. Figure 20 shows the model after all of the abovementioned functions, including a feedforward path, were added. Keeping the same gains as above, caused a large overshoot in the response. The gains were tuned until reasonable overshoot and rise-time were achieved. The optimized gains for the system with feedback were found to be KP = 0.1 and Ki = 0.2. The model shown in Figure 20 attempts to capture some of the non-linearities exhibited by the system. 54 I npu t z o h 2 s + 1 7 Con t ro l l e r B a c k l a s h T r a n s p o r t D e l a y 1 2 . 1 7 s + 1 4 2 3 s 2 + 4 6 . 4 6 s + 2 9 7 . 2 P V M F M A T L A B F u n c t i o n s i g n a l l | < s igna !2 2 % Er ro r D e a d B a n d Q u a n t i z e r l 0 . 2 0 8 8 N o r m a l i z i n g G a i n r e s p _ O u t p u t inp_ I n p u t l Figure 20: Pump model with feed-forward and non-linearities 55 An error band of 2% of the final value was introduced into the model. It was witnessed while tuning the controller on the machine that the speed response went into oscillations and the signal never reached steady-state. The oscillations were low-frequency and irregular. It was thought that the integral wind-up, along with the non-linearities in the system caused the oscillations. To remedy this problem, an error band was introduced that acted as a switch for the PI loop: it turned off the output from the controller when the error was within the prescribed value by making the feedback the same as the command, and turned it on again when the error fell outside of the error-band. This allowed usage of higher gains, which helped improve the system response time. 3.4 Field Implementation of the Controller A program was written in the IQAN-Develop software for implementation of the feedback control scheme, utilizing a PI controller with feedforward on the 88-XLP prototype machine. The machine was lifted and secured on stands to clear the wheels off the ground. Implementation of feedforward required knowledge of scaling between the DPR input current and the desired speed: a linear relationship was used as an approximation. Also, as the machine was raised off the ground, the HST only had to drive the inertia induced by the wheel assemblies and the wheel-end planetary gears. For the implementation of the PI controller, the engine speed was fixed at maximum (2500 RPM). Therefore, the engine anti-stall function was disabled in the IQAN program as the engine had enough power available at full rpm to overcome the aforementioned inertia. The response motor-speed was plotted in the IQAN graphical display, along with the input current to the pump-control, DPR valve-solenoid. Therefore, the motor response could be compared to the changing input and the controller gains tuned accordingly. A schematic of the new control scheme is shown in Figure 21. The block labelled as "Differential" contains calculations shown in sections and for trimming the speed of the wheels on the turn side. The blocks named as "Hydrostatic X X loop" contain the HST and the PI controller. 56 Glnch Trim Speed % Inch-Pedal GThrottle Set Speed % +r c Articulation Feedback GArt Articulation Angle Left Hydrostatic RL Loop Actual RL co Hydrostatic FL Loop Actual FL co Right , Hydrostatic RR Loop Actual RR co Hydrostatic FR Loop Actual FR co , Figure 21: Feedback control scheme It was originally decided to create a PI control loop around each one of the four wheels. This would have required independent displacement control pilot signals to all four pumps and motors - a total of twelve DPR valves. For the purposes of studying PI controller efficacy, i f only forward direction of motion was considered, the number of DPR's could have been reduced to eight. Addition of any more DPR's would have required additional control signals for DPR solenoids, which are provided by the I Q A N system. With the existing setup on the 88-XLP, all of the current outputs were being utilized. This would require additional control modules to be installed in IQAN's C A N -structure. Addition or removal of modules is easily accomplished with C A N systems: the only changes required are reprograrnming the master module and wiring changes to facilitate connection of the new modules. It was soon realized that i f a feedback control loop was created around each motor and pump, the memory on the master module allocated to perform math-functions would be over-loaded. This posed a concern in terms of practicability of the suggested method. It was then decided that for the purposes of this study, no plumbing or wiring changes would be made and the machine would be tested with feedback around the rear-pumps only. The motor displacement was also disabled; now the machine would only attain 2.9 krn/hr, not the maximum speed of 8 km/hr. The rear wheels were used for feedback but the same control current was used to control the front wheels, as the pumps on the same side share the same pilot signal. 57 With the machine raised, the feedback program was uploaded to the master module and tuning of the feedback controller commenced. The controller gains were made variable. Through the graphical interface of the MDM (master module), the gains were changed and the input was stepped up and down to determine system controllability. The input to the system and the system response were simultaneously plotted in the IQAN graph window. It was witnessed that controller gains that worked at a higher input range, did not control the HST well at a lower input range. Also, the controller efficacy varied when the step magnitude varied considerably: controller gains resulting in a desirable response for an input command of+10%, resulted in an oscillatory response for a larger magnitude input. The controller was tuned until a set of gains that resulted in an adequate speed of response and enough damping to prevent oscillations was obtained. The final phase of testing involved driving the machine on the original course with feedback from motor speed sensors enabled, and all hydraulic sharing disabled. This test was conducted so that the feedback controller efficacy could be determined through the calculation of a drivability-index and compared to the results obtained from hydraulic sharing testing (section 3.1.) 58 4.0 Results and Discussion The results from various testing are presented and discussed in this section. Results conducted to test the efficacy of hydraulic sharing are presented in section 4.1. The system identification results are discussed in section 4.2, and the controller simulation in section 4.3. Results of the Pi-controller implementation are presented in section 4.4. 4.1 Results of Hydraulic-Sharing Testing Various graphs were produced from the collected data, as mentioned before. However, comparing two graphs from random trials of any two tests did not provide an adequate evaluation. Figure 22 shows a left turn in reverse for trial 3 of test 1. Figure 23 depicts the same turn for trial 7 of test 4. The negative steering (secondary y-axis) indicates that the machine was turning left. It is apparent that the actual ratio follows the predicted ratio much more closely in test 1 than test 4. 3.30 Differential Ratio Plot 7.30 9.30 11.30 13.30 Time (s) 15.30 17.30 19.30 21.30 Figure 22: Left-turn in reverse (Test 1) 59 Other than a visual comparison, the graphs provide little value for an objective evaluation of the tests. The two graphs shown here are distinguishable because the data displayed is from two extremes: test 1 performed the best and test 4 the worst. When comparing two closely performing configurations, graphs are not suitable. A n evaluation of the drivability indexes provides a much better comparison. Differential Ratio Plot 100.00 150.00 200.00 Time (s) Figure 23: Left-turn in reverse (Test 4) Table 6 shows the drivability indexes and their averages for all 110-trials. 60 Table 6: Drivability indexes and their averages DRIVABILITY INDEX Test# Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Trial 8 Trial 9 Trial 10 Average Test 1 0.0528 0.0542 0.0506 0.0487 0.0446 0.0532 0.0453 0.0446 0.0471 0.0470 0.04880 Test 2 0.0484 0.0447 0.0482 0.0468 0.0516 0.0501 0.0561 0.0632 0.0555 0.0525 0.05171 Test 3 0.0498 0.0481 0.0535 0.0487 0.0470 0.0487 0.0479 0.0479 0.0553 0.0524 0.04994 Test 4 0.0936 0.1271 0.1247 0.1020 0.0957 0.1066 0.1061 0.1041 0.1007 0.0959 0.10566 Test 5 0.0887 0.0887 0.0938 0.0876 0.0891 0.1003 0.1026 0.0909 0.1056 0.0952 0.09426 Test 6 0.1009 0.0914 0.1002 0.0972 0.1109 0.0914 0.0852 0.0942 0.1035 0.0992 0.09742 Test 7 0.0717 0.0850 0.0774 0.0720 0.0793 0.0828 0.0785 0.0890 0.0597 0.0716 0.07670 Test 8 0.0825 0.0977 0.0918 0.0879 0.0694 0.0797 0.0711 0.0704 0.0733 0.0695 0.07933 Test 9 0.0823 0.0693 0.0706 0.0718 0.0606 0.0685 0.0751 0.0713 0.0737 0.0701 0.07135 Test 10 0.0783 0.0850 0.0936 0.0769 0.0704 0.0912 0.0720 0.0750 0.0791 0.0713 0.07928 Test 11 0.0938 0.0905 0.0971 0.1064 0.0916 0.0979 0.0883 0.0973 0.0878 0.0884 0.09391 61 A lower drivability index (DI) of a test means that it has a better drivability. The resistance to steering commands is lower in a configuration with a lower DI, as a differential ratio closer to the ideal ratio is realized. So for a setup when the machine behaves ideally, the DI should be equal to zero. Table 7 shows the DI's sorted from the best to the poorest performing hydraulic arrangement based on the overall average of each test. Table 7: Sorted drivability indexes Test# DIavg T e s t l 0.04880 Test 3 0.04994 Test 2 0.05161 Test 9 0.07135 Test 7 0.07670 Test 10 0.07928 Test 8 0.07933 Test 11 0.09391 Test 5 0.09426 Test 6 0.09742 Test 4 0.10566 A l l but one test above behaved as expected; test 3 (cheater-lines front to rear) was expected to perform worse than test 2 (cheater lines left to right). A differential effect is desired between the left and the right wheels in the front and the rear axles, when the machine is travelling through a turn. By installing cheater lines as installed in test 2, the desired differential effect is created. However in test 3, cheater lines were installed between the front and the rear pumps. It seems unlikely for this test to perform as well as it did. Without the following critical information, the results of test 3 are perplexing. A modification occurred on the machine after the fourth trial of test 3 was completed that resulted in a weight reduction on the machine: the canopy constructed from 1-inch thick steel, weighing roughly 400-lbs was removed. The discrepancy in numbers can thus be explained. The actual overall evidence of efficacy of hydraulic sharing is also provided by the above results. Comparing test 4 to test 1, the worst arrangement with no sharing and the best arrangement with cheater lines and power-sharing lines between the left and 62 the right side pumps, the magnitude of improvement becomes apparent. Table 8 was obtained by normalizing the results of all tests with respect to the DI of test 4. It can be seen from Table 8 that the disagreement between the actual and desired differential effects in test 1 is 46.2% of test 4, where NDI means normalized DI. Table 8: Normalized drivability indexes Test# NDI Test 1 46.2% Test 3 47.3% Test 2 48.8% Test 9 67.5% Test 7 72.6% Test 10 75.0% Test 8 75.1% Test 11 88.9% Test5 89.2% Test 6 92.2% Test 4 100.0% Evaluating different trials of any given test, sheds further light on the effectiveness of hydraulic sharing and its dependency on environmental conditions. Test 1, which has the lowest average over the ten trials, did worse than some of the other tests when only one trial is compared. In trial 1, test 2 was the best performing test. Therefore, it is worthwhile to tabulate other variations of these results. Table 9 shows the sorted results from the best trial of all tests. Table 10 shows results of the poorest performance of all tests from the ten trials. The results indicate that averaged, rather than individual, test performance should be evaluated so as to achieve a valid comparison. 63 Table 9: The best DI's of ten trials from all tests Test# DIa Vg NDI Test 1 0.04459 47.6% Test 2 0.04472 47.8% Test 3 0.04695 50.2% Test 7 0.05968 63.8% Test 9 0.06062 64.8% Test 8 0.06941 74.2% Test 10 0.07037 75.2% Test 6 0.08522 91.1% T e s t 5 0.08756 93.6% Test 11 0.08783 93.9% Test 4 0.09359 100.0% Table 10: The worst DI's often trials from all tests Test# DIavg NDI Test 1 0.05416 42.6% Test 3 0.05531 43.5% Test 2 0.06323 49.7% Test 9 0.08235 64.8% Test 7 0.08903 70.0% Test 10 0.09359 73.6% Test 8 0.09774 76.9% Test 5 0.10558 83.0% Test 11 0.10640 83.7% Test 6 0.11092 87.2% Test 4 0.12713 100.0% 4.1.1 Problems encountered during testing Some unforeseen problems were encountered during testing. The laptop computers failed to withstand the rough environment of testing. The hard-drive on one of the two laptops experienced a problem that caused the computer to crash at random. This caused data from a few tests to be lost and required that the tests be repeated. The second computer had a problem with the onboard battery-charger and required the battery to be charged frequently. The hard-drive problem was solved by replacing the hard-drive. The power problem was solved by purchasing a power-inverter from Canadian Tire that 64 converts the 12V battery power available from the machine battery to 110V-60H.Z A C power. In addition to the data-acquisition system troubles, a problem of overheating with the diesel engine caused the testing operation to be suspended periodically till the temperature cooled to safe levels. A safety routine in the controller programming causes the hydraulic system to cut power when the temperature gets above a set-point (108°C for the engine coolant and 60°C for the hydraulic fluid). Power is limited by not swashing the motors at all and results in a reduced top speed of the machine of 2.9 krn/hr (1.8 mph) from 8 km/hr (5 mph) normal top-speed. Since the differential inadequacies are predominant at high speeds, testing had little value when the machine only reached 2.9 lan/hr. The problem of overheating was found to be caused by the radiator surface being blocked with a mixture of oil and dirt. The radiator was removed from the machine, thoroughly cleaned and reinstalled, and the overheating problem disappeared. 4.2 System Identification Results As described earlier in section 3.2, tests were conducted at Feldcamp Equipment Ltd., in North Bay, Ontario, in order to collect data for system identification of the HST. As already discussed, a M46 pump and a VI2 motor were connected in a closed circuit r and step inputs of varying magnitude were applied at the pump and motor DPR valves to test the response of each. 4.2.1 Pump Response Results The tests were conducted at three different pump shaft speeds: low (about 800 rpm), medium (about 1400 rpm) and high (about 2000 rpm). In Figure 24, a plot of the results obtained for the pump-response at low pump rpm is shown. 65 - CURRENT [%] - MOTOR [RPM] Pump Step Up (Increments of 12.5%) Speed = 226 rpm 100 INPUT SHAFT SPEED = 840-RPM Speed = 200 rpm 80 40 20 0 m Speed = 170 rpm Speed = 143 rpm 200 150 Speed = 120 rpm •f 100 o Speed = 93 rpm Speed = 70 rpm + 50 Speed = 45 rpm 60 Time (s) Figure 24: Pump response at low input speed In the definition for linearity in equation (40), a change in the input results in a proportional change in the output. In Figure 24, the change in the input is 12.5% and the corresponding change in the output speed at each step is 45, 25, 23, 27, 23, 27, 30 and 26. The first step is highly irregular as compared to the rest, where a change in speed of 45 rpm is experienced. Similarly for medium pump speed, the results are shown in Figure 25. 66 - CURRENT [%] - MOTOR [RPM] Pump Step Up (Increments of 12.5 %) 120 100 Speed • 380 rpm INPUT SHAFT SPEED = 1380-RPM 80 Speed = 335 rpm 60 Speed = 290 rpm 40 Speed = 245 rpm r ^ \ Speed = 205 rpm Speed = 165 rpm Speed = 131 rpm Speed = 85 rpm 20 60 Time (s) 120 Figure 25: Pump response at medium input speed The change in speed at each incremental current input is 85, 46, 34, 40, 40, 45, 45, and 45. The first step results in a highly irregular response with a change in speed of 85 rpm, similar to the response with low input speed. For high input speed, the results are shown in Figure 26. The change in speed for each step for the case with a high input speed was 140, 65, 55, 56, 57, 63, 65, and 60. Again the first step of current increments resulted in a highly irregular response. 67 20 - C U R R E N T [%] - M O T O R [RPM] Pump Step Up (Increments of 12.5%) Speed = 558 rpm Speed = 498 rpm INPUT SHAFT SPEED = 1980-RPM Speed = 431 rpm Speed = 368 rpm Speed = 311 rpm Speed = 255 rpm Speed = 205 rpm Speed = 140 rpm 20 40 60 Time (s) 100 600 500 400 s o. 300 o 200 100 120 Figure 26: Pump response for high input speed Similar plots were also produced with the input signal stepped down from 100% to 0% at decrements of 12.5% each. The results are shown in Figure 27, Figure 28 and Figure 29. The change in speed for each test is tabulated in Table 11. Table 11: Change in motor speed vs. change in pump input current Input current step Low input speed Medium input speed High input speed 100%-87.5% 2 rpm 0 rpm 5 rpm 87.5% - 75% 20 rpm 50 rpm 51 rpm 75% - 62.5% 33 rpm 55rpm 91 rpm 62.5% - 50% 37 rpm 50 rpm 67 rpm 50% - 37.5% 28 rpm 47 rpm 62 rpm 37.5% - 25% 25 rpm 38 rpm 63 rpm 25% - 12.5% 24 rpm 44 rpm 55 rpm 12.5% - 0% 71 rpm 116 rpm 173 rpm 68 CURRENT [%] MOTOR [RPM] Pump Step Down (Decrements of 12.5%) INPUT SHAFT SPEED • 780-RPM 60 40 Speed = 238 rpm Speed = 218 rpm Speed = 240 rpm Speed = 185 rpm Speed = 148 rpm Speed = 120 rpm Speed = 95 rpm 300 250 S Q. a. o S 4- 100 Speed = 71 rpm 50 20 40 60 80 Time (s) Figure 27: Pump response for low input speed and input stepped down 120 •CURRENT [%] - MOTOR [RPM] Pump Step Down (Decrements of 12.5%) Speed = 400 rpm INPUT SHAFT SPEED = 1380-RPM Speed = 400 rpm — Speed = 350 rpm Speed = 295 rpm 400 + 350 Speed = 245 rpm Speed = 198 rpm Speed = 160 rpm Speed = 116 rpm \ 300 5 Q. 250 £ 200 + 150 45 65 85 Time (s) 105 Figure 28: Pump response for medium input speed and input stepped down 69 0 20 40 60 80 100 120 140 Time (s) Figure 29: Pump response for high input speed and input stepped down It is evident from Table 11 that the change in the response is highly irregular for the first and the last steps. There is virtually no change for the first decrement of 12.5%, from 100% to 87.5% of the pump DPR current step. To investigate this non-linearity in response, the DPR response must be studied. The current output from the I Q A N is sent to the DPR solenoid, which converts it to a pressure signal for the pump/motor HDC. The DPR response for the test with signal decremented at high input speed is shown in Figure 30. The large change in motor speed resulting from the step from 12.5% to 0% can be explained by the DPR pressure plot. The pump displacement follows the DPR pressure quite adequately since the motor speed follows the DPR response. However, the small change (or no change at all) in motor speed resulting from the first step of 100% to 87.5% input current is not explained by the DPR plot, since a change in the DPR pressure due to the step does not result in a change in the pump response. This can be explained by examining the internal workings of the pump control. To increase the pump displacement, pressure is applied to one side of the pump displacement-control-piston. The movement of the control piston is opposed by the centering spring. To 70 decrease the pump displacement, pressure is taken away from the displacement increasing side of the control piston, and the centering spring is allowed to push the piston to the centre position. As the spring pushes the piston to the centre position, the fluid in the opposite chamber passes through a control orifice, the purpose of which is to slow the returning motion of the swashplate. However, the delay in response due to the first step cannot be explained by the above explanation. The lack of response at the first step is a classic example of stiction inside the pump that induces a hysteresis type non-linearity. Since this lack of response is evident in all three test speeds (Figure 28, Figure 29 and Figure 30), it can be concluded that it is a characteristic of the pump. Pump and DPR response 80 40 0 II DPR response 1 Motor Speed / Current Signal Input 40 60 80 Time (s) 100 120 600 500 400 S 0. 300 200 100 - 0 140 Figure 30: Pump and D P R response 4.2.2 Motor Response Results The motor response was measured by setting the pump displacement at maximum, to effect the maximum flow from the pump, and by stepping the input to the motor D P R . Similar to the pump response test, the motor response tests were also 71 conducted at three different input shaft speeds and by incrementing and decrementing the current signal. Figure 34 shows the motor and DPR responses for the low input shaft speed of 840 rpm. The motor response does not follow the current signal well but it follows the DPR signal nicely. The non-linearity in the DPR response is evident. This response is of little practical value as in application, the motor is not stroked at low input speeds. In practical applications, such as the case study of this research, a high torque is demanded at low engine rpm (low input speed), which is attained by a P V M F arrangement, or by fixing the motor and varying the pump displacement. CURRENT [%] DPR % MOTOR [RPM] Motor Step Up (Increments of 12.5%) 100 40 20 INPUT SHAFT SPEED = 840-RPM 20 40 60 Time (s) + 250 -450 400 350 o 5 100 + 50 120 Figure 31: Motor and DPR response for low input speed From Figure 32 and Figure 34, the non-linearity of the motor response is evident without comparing steady-state values for each step; therefore, unlike the pump response plots, these values are not shown. The second step in Figure 32 and the third step in Figure 34 results in no change in either the motor or the DPR responses. Also, unlike the pump response, which clearly showed a nearly linear range in its response, the motor 72 response seems to be nonlinear over the entire range of inputs. Clearly, the motor follows the input from the DPR much more closely than the pump. However, the motor output is more non-linear than the pump. It is well understood that the motor is non-linear: the rate of change of speed increases as the motor is stroked to minimum displacement. This information is available in published sales manuals for all hydraulic pumps and motors [ 4 142]. Figure 33 clearly shows that the motor speed varies non-linearly with control pressure. -CURRENT [%] - D P R % - MOTOR [RPM] Motor Step Up (Increments of 12.5%) 120 100 80 40 20 INPUT SHAFT SPEED = 1380-RPM + 800 J L jTFiiniiinin r * r LIU njUUUUIIUIIIULLJ 900 700 600 CL 500 £ 4- 400 300 200 100 20 40 60 80 Time (s) 100 120 Figure 32: Motor and D P R response for medium input speed 73 Shaft speed Min displ. fr J \ / \ Max displ. 1 i i ! Threshold pressure Modulating oressure -ilc: pressure Figure 33: Motor speed vs. modulating pressure, a non-linear relationship [41] The inadequacies in motor response are an effect of DPR malfunction. The DPR valves are inherently quite non-repeatable, but the one controlling the motor displacement in these tests is plagued by a particularly severe stiction type characteristic. It is quite representative of the real problems faced by service personnel, who without the aid of measurement facilities would not be able to pinpoint the source of the problem. -CURRENT [%] - D P R % MOTOR [RPM] Motor Step Up (Increments of 12.5%) 120 100 80 3 6 0 20 INPUT S H A F T S P E E D = 1980-RPM Jirnniiininirt _LLU IIII] I "TTT jf III III II llll 1400 1200 1000 800 a. 600 5 o 400 200 20 40 60 Time (s) 100 h 0 120 Figure 34: Motor and DPR response for high input speed 74 Motor response with the input signal stepped down is shown in Figure 35, Figure 36 and Figure 37. Similar to pump response, the motor exhibits hysteresis as the high input signal is stepped-down, with the exception of the case with high engine speed. In this case, the non-linear behaviour of the motor is very evident. From the three step-down signals plotted for the motor response, the high input shaft speed of the pump (high engine rpm) has the greatest value. Decreasing the motor displacement causes the machine to travel faster - an effect that is desired at high or full engine throttle or maximum available power. -CURRENT [%] -DPR% - MOTOR [RPM] Motor Step Down (Decrements of 12.5%) 1 2 0 4 0 2 0 INPUT SHAFT SPEED = 780-RPM + 3 5 0 4 3 0 0 4 5 0 4 0 0 Q_ 2 5 0 £ 2 0 0 1 5 0 1 0 0 + 5 0 Z i 2 5 4 5 6 5 8 5 Time (s) 1 0 5 1 2 5 1 4 5 Figure 35: Motor and DPR response for low input speed and signal stepped down 75 -CURRENT[%] -DPR% -MOTOR [RPM] Motor Step Down (Decrements of 12.5%) 120 100 80 5 60 40 20 INPUT SHAFT SPEED - 1380-RPM T T T 7 -JIIUUII II II I 20 40 60 80 Time (s) 120 + 500 £ 900 800 700 600 400 | 300 •f 200 100 140 Figure 36: Motor and DPR response for medium input speed and signal stepped down -CURRENT [%] -DPR% -MOTOR [RPM] Motor Step Down (Decrements of 12.5%) 120 100 80 4 3 6 0 40 20 n fail n All JI n mn INPUT SHAFT SPEED = 1980-RPM i r 20 llll I iLTLJ—U T LTIL 40 60 80 Time (s) 100 1700 1500 1300 1100 g o s 4 900 700 500 140 Figure 37: Motor and DPR response for high input speed and signal stepped down 76 4.2.3 Formulating Transfer Functions As discussed, transfer functions were formulated from acquired data using MatLab. To evaluate modelling accuracy of the used method, the normalized response to a step input to the modelled transfer functions was plotted with the real data. The pump response is shown in Figure 38 to a step input from 75% to 87.5% value. The resulting goodness-of-fit value is also shown in the figure, which was found to be 80.837. Additional comparison charts for various input levels are shown in APPENDIX D. Similarly, model fits were also evaluated for the motor system-identification cases. Real versus Modelled Response 0 5 10 15 time(s) Figure 38: Compared pump response of the real and modelled data In Table 12, a summary is presented of the fit models for all of the steps for both the pump and the motor. The dominant pole is shown in the column labelled Pole 1. The incremental gain is calculated by dividing the dc-gain of the fit model by the step input magnitude of 12.5. The gain provides insight into the non-linearity of the system: for the same input magnitude, the resulting gain resides over a wide-range, especially for the case of the motor. 77 Table 12: Model fit summary Model Pole 1 (rad/s) Pole 2 (rad/s) Incremental Gain Delay (s) Goodness of Fit % Pump - 0-12.5% -2.7 -32.5 0.8 0.5 70.1 Pump - 12.5-25% -0.8 -47.5 0.4 0.1 60.0 Pump - 25-37.5% -1.2 -49.2 0.3 0.2 60.1 Pump - 37.5-50% -2.5 -46.8 0.3 0.3 67.6 Pump - 50-62.5% -4.6 -41.6 0.4 0.2 76.0 Pump - 62.5-75% -6.3 -40.1 0.4 0.2 78.3 Pump - 75-87.5% -7.7 -38.8 0.4 0.2 80.8 Pump - 87.5-100% -8.3 -40.2 0.4 0.2 79.8 Pump - 100-87.5% -9.6+31.3i -9.6-31.3i 0.0 0.7 2.6 Pump - 87.5-75% -4.5 -27.6 0.4 0.2 79.2 ! Pump - 75-62.5% -2.9 -22.8 0.5 0.2 72.5 Pump - 62.5-50% -2.4 -22.7 0.4 0.2 68.4 Pump - 50-37.5% -3.5 -24.1 0.4 0.2 74.2 Pump - 37.5-25% -2.9 -24.8 0.4 0.2 76.5 Pump - 25-12.5% -3.2 -26.3 0.4 0.2 81.8 Pump - 12.5-0% -2.8 -9.4 1.1 0.1 76.9 Motor - 0-12.5% -22.5+17.4i -22.5-17.4i 0.1 1.1 55.0 Motor -12.5-25% -18.3 -26.7 0.3 0.4 80.9 Motor - 25-37.5% -14.5+35.9i -14.5-35.9i 0.0 0.6 8.8 Motor - 37.5-50% -14.2 -32.4 0.4 0.3 82.7 Motor - 50-62.5% -8.8 -40.0 0.5 0.3 85.7 Motor - 62.5-75% -4.2 -49.6 0.7 0.2 87.2 Motor - 75-87.5% -3.2 -42.7 0.9 0.2 86.8 Motor-87.5-100% -3.9 -45.8 1.2 0.2 87.7 Motor - 100-87.5% -2.8 -41.1 2.8 0.2 85.8 Motor - 87.5-75% -4.0 -46.7 1.0 0.2 88.8 Motor - 75-62.5% -3.9 -48.4 0.8 0.2 87.7 Motor - 62.5-50% -4.5 -51.1 0.6 0.2 87.4 Motor - 50-37.5% -5.4 -47.0 0.4 0.1 84.1 Motor - 37.5-25% -13.0 -35.5 0.3 0.3 80.6 Motor - 25-12.5% -16.8+30.6i -16.8-30.6i 0.0 0.2 27.8 Motor -12.5-0% -18.2+24. Ii -18.2-24.li 0.2 0.3 71.8 78 4.3 Controller Simulation Results The Simulink response plots are shown and discussed in this section. As discussed in section 3.3, a simple feedback model using the selected transfer-function, with the delay and the zero removed, was created and tuned. With controller gains of Kp = 2 and Kj = 17, the response shown in Figure 39 was obtained. Simulink Model Response 0 8 O 0.6 to DC CO 0.4 0.2 Input Response Rise Time (10-90%) 0.1s Maximum Overshoot 5% Settling Time 0.3s 0 1 0.2 0 3 0.4 0.5 time(s) 0 6 0.7 0.8 0.9 Figure 39: Pump-response using feedback and PI controller (without feedforward or dead-band) As mentioned previously, non-linearities were added to the system model. Adding the delay to the system caused it to go unstable for high controller gain values. Also, the controller was time-discretized using the zero-order-hold function, to mimic the behaviour of a digital controller. It was witnessed that i f high proportional gain values were used, the system went into diverging oscillations. It should be noted that this was not the case with the continuous system, where increasing the value of KP did not cause system-instability. Since the gain has to be considerably larger than the operating range gain (see section 4.4) to cause system instability, it is unlikely that the system would become unstable i f the operating conditions were varied; however, as an unrealistic scenario, i f the system became considerably stiffer or undamped, the controller gains would cause the system to go unstable. 79 Hysteresis caused the system response to have sustained oscillations at gain values that resulted in adequate response otherwise (refer to Figure 40.) With KP = 2 and Ki= 17, the system went into sustained oscillations, which decayed over time. In the case where the model for hysteresis was not used, the decay in oscillations occurred much faster. This analysis leads to the conclusion that hysteresis adds to further system instability under varying operating conditions. Effect of Hysterisis 0.8 cu C/) c o CL "> CD a. CL s 0.4 0.2 / \ I. \ \ Input No hysterisis Hysterisis 2 3 4 time(s) Figure 40: Effect of Hysteresis on the model (without feedforward or dead-band) Addition of the error band into the model resulted in shifting the final value of the response by a value within the error-band-width. It also allowed the usage of higher gain values. The error-band was added after the controller was implemented on the machine and the response was found to follow slow oscillations. Tuning of the controller parameters did not eliminate the oscillatory behaviour; hence a 2% error band was introduced, which made the error in the PI loop equal to zero when the error was within the 2% band. The system non-linearities were fairly well modelled by the Simulink model. However, the key difference between the model and the real system was that the modelled non-linearities are repeatable and, hence, predictable, whereas the real non-linearities were unpredictable. 80 Using the controller gains of 2 and 17 for KP and Kt, respectively, the response shown in Figure 41 was obtained to the complete model of Figure 20. The overshoot has disappeared and the response has gotten much slower as compared to Figure 40. This is attributable to addition of the delay of 0.2s to the model. 1.4 Simulink Model Response 1.2 1 CD 1 0.8 a ") ' ' i i i 1 — ^ INPUT -" 2 % RESPONSE CD CC §• 0.6 w 0.4 -0.2 0 I I I I -C 1 2 3 4 5 6 7 time(s) 8 9 10 Figure 41: Complete model response 4.4 Results of PI Control Implementation The PI controller was implemented on the 8 8XLP-prototype machine. Only feedback from the rear wheels was used for control, as mentioned earlier. The machine was raised so that the wheels would not make contact with the ground and the controller was tuned. The results from controller tuning and gain selection will be shown, followed by the driving-test results and drivability calculations resulting thereof. Figure 42 shows results of tuning the PI controller with machine on stands with gains (KP = 30 and Kj = 7). A difference in performance of the right versus the left side HST is evident from Figure 42, even though both sides use identical components, with the exception of hose lengths, which vary by small amounts. 81 Performance of PI Control on Machine 850 -> 800 750 S 0-BC — 700 T3 01 3 a f 650 o o 2 600 550 500 r irnnnrwWWTw • S e t S p e e d Right Motor - Left Motor 10 20 30 40 50 Time (s) 60 70 80 90 Figure 42: Pi-Controller tuning on the machine (on stands) Driving tests were conducted next, to determine the efficacy of feedback control. It was found that putting the machine on the ground changed the system dynamics and caused the HST to behave differently. The right side response became more oscillatory. The gains were tuned again and the final set of gains used for driving test is shown in Table 13. Table 13: Pi-gains used for driving tests Kp Ki Right Pump Left Pump 15 25 5 10 The left-side gains are higher, perhaps, because the machine is heavier on the left side - the engine is mounted more towards the left as space is required for the drive pumps on the right side. No other explanation is available for the discrepancy in the gains. The machine was driven on the course shown in Figure 12. 82 Drivability indexes were calculated for the feedback tests. The combined results including the drivability-index results from hydraulic sharing testing are shown in Table 14. It can be seen that the PI control did not perform the best. The feedback control performance is better than all of the power-sharing tests; however, it did not perform better than the tests with cheater lines. Also while driving, the performance did not seen to improve as the shakiness while driving through turns still existed. Table 14: Drivability Calc Results, Pi-Control Included Test* Dl a v g Test 1 0.04880 Test 3 0.04994 Test 2 0.05161 Test PI 0.06481 Test 9 0.07135 Test 7 0.07670 Test 10 0.07928 Test 8 0.07933 Test 11 0.09391 T e s t 5 0.09426 Test 6 0.09742 Test 4 0.10566 83 5.0 Conclusions 5.1 Contributions of the research This thesis research focused on the design and control of the hydraulic transmission for the EJC-88-XLP. The 88-XLP has a fully hydrostatic transmission; hence a practical scheme for controlling the variable displacement pumps and motors is required. Feedback control with speed feedback from the motor-speed sensors was evaluated. In the literature review, various methods of modelling the hydrostatic system were studied. The classical approach to system-identification was selected because it was well understood and feasible to implement given the limited available on-board computing power on the machine. Various control schemes were reviewed: fuzzy control seemed to be the most favoured of all in the literature. Due to its simplicity of application and low computational requirements, PI control was selected for controlling the output speed of the wheel motors. Feedback from the hydraulic-articulation-cylinder was used to calculate the amount of reduction in speed required (differential effect), from side-to-side, when a turn was made. Various hydraulic compensation configurations were evaluated with the help of a novel method, which involved calculating a drivability-index for each test. The drivability-indexes indicated that the PI control scheme performed better than many hydraulic arrangements, but fell short of meeting the desired performance quality: the machine still shook excessively while turning. The specific contributions of this thesis include: • The various different configurations of hydraulic flow and pressure sharing arrangements were experimentally evaluated. Configuration 1, with cheater-lines between the right and left pumps as well as power-sharing lines between the left and right pumps and between the front and rear pumps, was shown to outperform the other configurations, as measured using the developed "Drivability Index". This result is in line with the expected outcome, based on an understanding of how the pumps and motors function: the left and right side pumps and the front and rear pumps interacted, by sharing pressure from the internal pump feedback. 84 • System identification of the overall HST was performed using experimental data from bench tests. This encompassed the interaction of the DPR valves with the pump and motor dynamics. A simple second-order transfer function with a pure time delay was found to be a good approximation at low speeds. • The simple linear model arrived at using system identification was augmented with addition of nonlinearities to more closely reflect the physical system: hysteresis was added to address the various sources of such behaviour including the DPR valves and the pump swash plate, and quantization to reflect the limited resolution of the speed sensor. The entire model was then converted to discrete-time and implemented as simulation model in Simulink/MatLab®. • A Pl-controller was designed and tested using the developed simulation model. • The Pl-controller was implemented on the 88XLP-prototype, and drivability results for the system with feedback control were compared with the results from the various hydraulic sharing/coupling configurations. While the Pl-control yielded a drivability index superior to most of the sharing/coupling configurations, it did not perform as well as the best sharing/coupling configurations (e.g. Configuration 1). • A deeper understanding of the design constraints of variable-pump-variable-motor HST configuration was developed, especially with respect to limitations on controllability. 5.2 Feasibility of Implementing Feedback Control One of the design specifications for the machine was that it should be easily maintainable. The Pl-control which was evaluated required four motor speed-sensors and an articulation sensor to function. In case of sensor malfunction, the control scheme would become inoperable, until the problem was diagnosed and corrected. Because of the lack of appropriately trained maintenance personnel in the target market of the 88-X L P , the feasibility of feedback control depends on the ability of the machine to perform adequately, even when the feedback is absent due to a malfunction. However, with the studied scheme, no fail-safe mode is available. 85 The fours speed sensors and the articulation feedback sensor added to the overall cost of the machine. Due to its robust design, the articulation sensor added a significant cost of approximately US$1,000. Each of the original speed-sensors used on the 88XLP also cost approximately US$500. The author was able to procure equivalent yet inexpensive speed sensors, which were significantly lower in cost at approximately $50US, and made adding four sensors on each machine economically feasible. However, the initial cost of these components is not the only obstacle in the decision making process: the likelihood of poor maintenance by the end-user severely limits the practicality of this control scheme. 5.3 Design Recommendations • Feedback control is not the best option for the target market of the 88XLP at the present time. Performance enhancement through hydraulic sharing is recommended because of its ease of implementation and maintainability. From the drivability-index table (Table 14) comparing the various hydraulic sharing techniques, the best performing arrangement, Test 1, with cheater-lines and power-sharing lines is recommended. However, the concerns with a lowered efficiency because of flow going to the wheels with lowest resistance, still stand. • Other options include changing the hydrostatic arrangement. Instead of four pumps and four motors, two pumps and fours motors may be used. With this arrangement, the overall cost is also reduced as fewer components are needed. • Alternatives to hydraulic pilot-control are suggested. Pumps and motors are available with electric displacement control and are favoured as they eliminate the need for DPR valves. The DPR valves were found to be the largest contributors to nonlinearity and lack of repeatability, leading to unpredictability of the system and poor performance of feedback control. • System-identification tests should be performed with the machine on stands. A better approximation to the actual HST could perhaps be realized using experimental data, which included the inertial load of the wheel-tire assembly acting on the system. 86 • More computing power should be made available on board the vehicle, so that sophisticated control strategies, such as adaptive control with classical, fuzzy, neural-networks, etc., can be implemented on the machine. 5.4 Hydraulic System Redesign - 88XLP Mark-ll A Mark-II version of the 88XLP was designed and built by EJC Mining Equipment Inc. in 2004. The drive system of the 88XLP-MII consisted of two pumps driving four wheel motors: each pump drives one axle (front or rear two motors) through a flow divider, which can be locked by the operator to supply 50-50 flow to each motor when traction is lost. The pumps and the motors were downsized to result in a higher system pressure than original - higher pressure equates to a higher overall system efficiency as more power is available at the wheels. The Mark-II machine performed much better than the original 88XLP in every'respect: the draw-bar pull test proved that the Mark-II machine has more available traction force than the original machine, and the mark-II machine drove smoothly through turns, without any shakiness experienced in the operator's cab. Because of a reduced number of components, the installation of the Mark-II machine is cleaner - more access is available to components, which results in an improved maintainability. Thus hydraulic system redesign has been shown to be a more effective and appropriate means of achieving the HST's system's overall design objectives, in terms of performance, price, and maintainability in the target market. This illustrates the point that while feedback control is a powerful technique for improving hydraulic system performance, it is not a substitute for a well formulated hydraulic system design based on an in-depth understanding of system components and their intrinsic performance constraints. 87 APPENDIX A Sauer-Danfoss M46 Pump and Parker VI2-160 Motor specifications, as installed on 88XLP. DPR Valve and control coil specs are also shown in this appendix. [43, 44] Series 40 Pump Model M46 PT Displacement (cm'Vrev) 46.0x2 Weight (kg) 59 Moment of Inertia of the internal rotating parts (kgm2) 0.0100 Type of Mounting SAE "B" Integral Charge Pump (cmJ/rev) 22.9 Charge Relief Valve Setting (bar) 19.5 System Pressure Regulation (bar) 140-345 Input Shaft Splined Control Option HDC Filtration Configuration Remote Charge Pressure Filtration Speed Limits (min"1) Minimum Speed . 500 Rated speed at maximum displacement 4000 Maximum speed at maximum displacement 4100 Case Pressure (bar) Continuous pressure 1.7 Maximum pressure 5.2 System Pressure Range (bar) Rated pressure 210 Maximum pressure 345 Theoretical Flow (litre/min) At rated speed 166 Inlet Vacuum (bar) Rated pressure 0.8 Minimum pressure (cold start) 0.7 Temperature Range (°C) Intermittent (cold start) -40 Continuous 82 Intermittent 104 Viscosity (mm2/s) 89 Minimum 7 Recommended operating range 12-60 Maximum 1600 Cleanliness Level Recommended (3x-ratio for charge pressure filtration Bi5-2o=75 90 V12-160 Motor Displacement (cm3/rev) max, at 35° 160 min, at 6.5°. 32 Operating pressure (bar) max intermittent 480 max continuous 420 Operating speed (min"1) at 35°, max intermittent 3200 max continuous 2500 at 6.5°-10°, max intermittent 5000 max continuous 4000 min continuous 50 Flow (l/min) max intermittent 510 max continuous 400 Theoretical Torque at 100 bar (Nm) 255 Output power (kW) max intermittent 280 max continuous 170 Corner power (kW) intermittent 640 continuous 450 Mass moment of inertia (kgm2) 0.0146 Weight (kg) 58 Catalog HY15-3500/US Technical Information DA. N.C Proportional Reduce/Relief Valve Series DPR103C General Description Direct Acting. Ncrnally Closed. Proportional Pressure Reducing/Relieving Valve. For additional information see Technical Tips on pages PV1-PV6 Features • On-off type soteoaas • Low hysteresis • F'.W signal preferrea • V a r L S I override star a B r a • I i r e : : t a a t i r g a s s i g n Specifications Rated Flow Maximum Inlet Pressure 210 Bar (3000 PSI) Maximum Reduced Pressure DPR103C03 • 20.6 Bar (300 PSI) S . 7 A DPR103C06 - 41 Bar (600 PSI) @.7A Maximum Leakage 52 oc/mir. 'with 0 control current Hysteresis @ 200 Hz PWM 4% Cracking (Dead band) 20% of Input Signal Frequency 100 - 400 I Iz 1200 1 \i Prefer real Maximum Control Current 12VDC 24V DC 1.61 A .B4A Cartndge Matenal All parts steel All operating parts hardened steel. Operating Temp. Range (Ambient) -40 C to +93.3 C iNitnlei i A':. F tc. >200 F) -31.7 C t o + 1 2 1 1 C (Fkiorocarbon) i. 25 F to '250 Fi Filtration ISO Code 16/13. SAE Class 4 or better Fluids Vireral based or synthetic with lubricating properties al viscosities of 45 to 2000 SSU (6 to 420 cSt) Approx, Weight .59 kg (1.3 lbs.) Cavity C10-3 Form Tool Rougher NrTlO-3R Finisher NFT10-3F Performance Curves ISO 125 too a !* e PSI wr i v ii a. Pressure Drop vs. Flow ' 1 ,>»aj.c OI 150 SSU © 1 CO-F ;32 cSli Flow | Q | Pressure Gain MjfdrjJicQI 150 5SUO 100"F(32cSli *r10Jc »-»S5 tt 1.03 OMtta ICOSW Input Current - 12VDC, High Watt Coil, 200 Hi arkcr P V 3 ' Parker Hannifin Corporation • ':-J--::;-:J •|y:J- :.. : s [1 v •*:>* - ' 5 anas, USA 92 Catalog HY16-3500'US Technical Information D S C o i l Series 5/8* I.D. Features • C:::rnpH:1 >re pwr,K K r : : a p s L l a t t ! : : : : e s i g r • Min imal amperage c r a w • Numerous terminals ana vo l tages • High wat t ses ig r optional • Heavy gauge r-obr :::x:ea lean wi re with built-ir strair relief • 150 C Class H wi re s ta rs arc • 2 0 0 C C lass N wire on h igh wat t mode ls Specifications Wattage 11 Watts — Stanoara - Black Coil 3-0 Watts High Watt Rerj Coil Duty Rating Continuous @ 100% voltage Wins Class Class H for all voltages 17 Watt Class N for all voltages 30 Watt A.C. Rectifier Integral lull wave bricge Lead Wire H i :jai.:je \-A" long SOD volt rating Lead Wire Strain Relief 34 kg (75 lbs.) Q 21 C (70 F) & 18 kg (40 lbs.) @ 93 C (2 00'F) Encapsulating Material lass filler: r y b r , resistant to m o i s t L r e . caustic solutiors. fungus, arc lemp.eralures Irom - 4 0 C (-40 T ) to 200 C (392 Fi AC Coil Assembly No inductive cr capacitive leads can be installed between surge suppressor and rectified valves J AC Cot Assembly Suppressor {Thyredor > NOTE: Parker A C Coils incorporate integrally molded full wave rectifiers which are rated for reverse voltage p-eaks cf *0OC vclts maximum. For voltage transients greater than 'CCS volts P.I.V., Harris Thyrector V' 5CLA' CA or V 5CLA2CA for " 5 VAC and V250LA15A or V250LA4CA for 200 VAC is recommended. dsS8pnS5 » 103 arkcr CL9 Parker Hannifin Corporation M«gr*t«d HydiaJics Dwiaon Uncomaftire. iitmas JSA APPENDIX B IQAN specifications: IQAN M D M , IQAN X S , IQAN X P 2 and IQAN X T 2 (J1939 capable module). [45, 46, 47, 48] 94 Technical Data Electronic Remote Controls IQAN-MDM General Weight Rated power supply Mirv'max power Op eratin g t em pe ratu r e Protection Current consumption Data interface 0,2 kg 12-24Vdc 9 /32Vdc - 3 0 ° C t o + 7 0 ° C (-30°Cto 0°C reduced display update) outdooruse max 0.1 A ( 2 8 V d c ) . m a x 0,18 A (14 Vdc) Parker I CP (IQAN CAN Protocol) ® © ® (S> LED back-lit LCD 202x32 pixels 1 pes high side switch max 1.2 Adc RS232 "handshake" 57,6 Kbit's PARKER IDP Display Type Resolut ion Digital output Number Type Output Serial communication Interface Bit rate Protocol Environmental Protection EMI I S 0 1 1 4 5 2 - 2 (immunity vs EM field) I S 0 14982 (radiated emission) I S 0 1 1 4 5 2 - 4 (immunity vs injected RF) ISO 7637-2.-3 ( immuni tyvs supply transients) ESD EN 61000-4-2 (externaD Mechanical environment IEC 68-2-64 Fh (random)) IEC 68-2-29 Eb(bump) Climate environment IEC 68-2-18 Rb2 (water) IEC 68-2-30 Db (va r l , damp, cyclic) IEC 68-2-3 Ca (damp, heat steady state) IEC 68-2-2 Bb (heat) IEC 68-2-1 Ab (cold) IEC 68-2-14 Nb (changs of temperature) Chemical environment IEC68-2 -52 Kb (salt mist, cyclic) 72 PC communicat ion port unit = mm Power LED Power and CAN-bus connection 95 Technical Data Electronic Remote Controls IQAN-XS General Weight Rated power supply Min/max power Operat ing temperature Protection Current consumpt ion (idle) Data interface Digital inputs Number Signal range Act ive range 0.7 Kg 1 2 - 2 4 V d c 11/32 V d c -25 to +70 X in-cab use 0,1 A (28 Vdc), 0,1 A (14 Vdc) Parker ICP ( IQAN C A N Protocol'! 16 pes 0-32 Vdc "0"=0.O-1,2 Vdc , "1 a=4,0-32,0 Vdc / / / / / Digital outputs Number Type Signal Analog/Digital inputs Number Signal range Act ive range Resolut ion Environmental protection Electr ical disturbance by conducting and coupl ing Radiated susceptability Radiated susceptability Radiated emiss ion Conducted emiss ion Conducted susceptability E S D , electrostatic d ischarge Vibration, random Shock Bump High temperature A pes high side switch 0.1 A d c 10 pes 0,0-5,0 V d c 0.5-4.5 V d c 5 mV ISO/DP 7637-2-3 E N V 50140 (EN 61000-4-3) E N V 50204 E N 55022. c lass B E N 55022 EN61O00-4 -6 E N 61000-4-2 I E C 68-2-64 Fh IEC 68-2-27 E a IEC 68-2-29 Eb IEC 68-2-2 Bb rnMitimriRnnrinnn Temperature, cyc l ic Low temperature Damp heat, cycl ic Damp heat, steady state Salt mist, cycl ic Sealing IEC 68-2-14 Nb IEC 68-2-1 A b IEC 68-2-30 Db var, 1 IEC 68-2-3 C a IEC 68-2-52 Kb IEC 529 96 Technical Data Electronic Remote Controls IQAN-XP2 General Weight Operating temperature Protection Voltage supply Current consumption ( idle) Data interface Outputs Propor t i ona l cur ren t o u t p u t s Number Signal range Dither frequency Dither amplitude Resolution 0.7 Kg -40 - +70 "C out door use 9 - 34 Vdc 105 mA (28 Vdc) 90 mA (14 Vdc) Parker ICP (IQAN CAN Protocol) 4 double 20-1800 mA 25 -150 Hz 0 - 500 mA 0.7 mA Digital/ PWM (no current feedback) outputs '< Nurn ber Type Max load P v\M frequency Inputs Vo l tage /Frequency Number Signal range Resolution Frequency range 4/ 2 double high side switch 3A 25 - 2000 Hz 4/2 0 - 5 Vdc 5mV 1-30000 Hz B7 rnnvMSjxZI ItTheOisiisI sod PWM outputs sha re me asms physical pin. Pin cor.fcursiion, =s either OfeSstorPi/VM outputs is carried oui with iQANdcv'dop. Environmental Protection EMI EN 61000-4-3 EN 50204-4-3 ESD EN 61000-4-2 (external) Mechanical environment IEC 68-2-64 Fh (random, 10- 250 Hz) IEC 68-2-27 Es (shock, 11ms) IEC 68-2-29 Eb (bump, 6ms} Cl imat env i ronmen t IEC 68-2-18 Rb3 (water) IEC 68-2-30 Db (varl, damp, cyclic) IEC 68-2-3 Ca (damp, heat steady state) IEC 68-2-2 6b (heat) IEC 68-2-1 Ab(cold) IEC 68-2-14 Nb (change of temperature) Chemical environment IEC 68-2-52 Kb (salt mist, cyclic) 2) The volume eixi frequencyinputs stoieaertio physical input plie. Pincorifeuraikjn, 3 5 either'Voasoeor rre<^jencyinpuis is carriedoui wdh IQANd<v«3op. 97 Technical Data Electronic Remote Controls I Q A N XT2 General Weight Operating temperature Protection Voltage supply Current consumption (idle) Data interface Addit ional C A N hub Outputs Proportional current outputs Number Signal range Dither frequency Dither amplitude Resolution 0,7 Kq - 4 0 - + 7 0 ° C outdoor use 9 - 3 4 V d c 180 m A ( 2 8 Vdc) 170 m A ( 1 4 V d c ) Parker ICP (IQAN C A N Protocol) J1939 orother byte-aligned C A N protocol 2 double 20 - 1 8 0 0 m A 2 5 - 1 5 0 Hz 0 - 500 mA 0,7 mA Dig i ta l / P W M (no cur rent f eedback ) ou tpu ts Number 6 / 3 d o u b l e Type high s ide switch M a x load 3 A P W M frequency 25 - 2000 Hz E -gas /Se rvo mo to r output ( P W M H-b r idge) Number 1 Signal Range Max load Inputs V o l t a g e / F r e q u e n c y Z l Number Signal range Resolution Frequency range 0-100% rated power 2.5A 10/3 0 - 5 V d c 5 m V 1-10000 H z 0 7 mm.W£<<5) 1) The Digital and PWM output* share trie same physical pin. Pin configurator) fci either 'Digital or PWM output is carried cut with lOANdevelop. Environmental Protection EMI I S 0 1 1 4 5 2 - 2 immunity vs E M field) ISO 14982 (radiated emission) ISO 11452-4 (immunity vs injected R F ) ISO 7637-2 (immunity vs supply transients) E S D EN51000-4 -2 (external) M e c h a n i c a l env i r onmen t IEC 68-2-64 F h (random, 10 -250 Hz) IEC 68-2-2? E s fshock, 11ms) IEC 68-2-29 Eb (bump, 6ms) Cl i mato c n v i ro nme nt IEC 68-2-18 R b 3 (water) IEC 68-2-30 Db (va r l , damp, cyclic) IEC 68-2-3 C a (damp, heat steady state) IEC 68-2-2 Bb meat) IEC 68-2-1 Ab(co ld) IEC 68-2-14 Nb (change of temperature) C h e m i c a l env i ronmen t IEC 68-2-52 Kb (salt mist, cyclic) 2) The votlsce «rtd frequency inputs share the s a n s physical input pins. Pin configuration for either Voltage or Frequency input is cauled out with ifjANdevetop. 98 APPENDIX C MatLab programs were used to facilitate quick formulating of the transfer functions by automating some repeated tasks, such as pre-filtering the data for each step and formatting the produced graphs. The *.m files written for MatLab are presented in this appendix. Function pre: manipulates the data so it can be easily imported and used in the system identification toolbox. The script file shown reformats the graphs. Function ans_: converts the continuous space transfer functions to discrete-time domain and calculates the poles and the dc-gain of the transfer-function. 99 function out_=pre(); filename = uigetfile ('*.txt', 'Select a data file'); mydata = dlmread (filename); dl = mydata(:,l); d2 = mydata(:,2); len = length(dl); ifrem(dl(len), 12.5) ==0 if rem(dl(l), 12.5) == 0 ul =dl(l:len); yl =d2(l:len); end else ul =d2(l:len); yl =dl(l:len); end a=0; len = length(ul); for a = 1 :len iful(a+l)~=ul(a) break end end r y l = rms(yl(a-50:a)); w = 25; lpf=tf(w,[l,w]); lpfd = c2d(lpf, 0.02); B = [lpfd.num{l}]'; A = [lpfd.den{l}]'; ylf=filter(B, A, yl, r_yl); y = ylf(a-50:len); u = ul(a-50:len); data = iddata(y, u, 0.02); set(data, 'Tstart', 0.00); out_= data; ident % text data file path from user-interface prompt % identify input/output columns % search for the step in the input % mean initial value % cut-off frequency for digital filter in rad/s % low-pass-filter: 25/(s+25) % convert to discrete-time domain % filter parameters: filter numerator % filter parameters: filter denominator % apply filter % start time of data; t=0s % run Ident GUI 100 a = gca; set(a, 'FontSize', 12.5); set(a, 'XLim', [0 15]); xlabel('time(s)', 'FontSize', 16); ylabel('Normalized Output', 'FontSize', 16); title('Real versus Modelled Response', 'FontSize', 20); legend('Real', 'Model'); function ans_ = pro2(sys) sysl = d2c(sys); sys2 = tf(sysl); sys3 = sys2(l,l); poles = roots(sys3.den{l}); ans_.sys = sys3; ans.polel =poles(l); ans_.pole2 = poles(2); ans.gain = dcgain(sys3)/12.5; 101 APPENDIX D Pump and Motor response curves are compared with the real data collected during the System-Identification testing conducted at Feldcamp Equipment in North Bay, Ontario. The transfer-functions obtained using MatLab to model the system response are also presented. P U M P - Increasing Input Real versus Modelled Response 501 1 1 0 5 10 15 time(s) Figure 43: Pump step input 0-12.5% 20 Real versus Modelled Response 10 0 Real Model | - 1 0 / A / ' ' arx(2 1 4), 60.006 o fr ,-o.o6s 1.4595 + 173.2 1 -20 s2 +48.315 + 36.44" CO E | -30 // -40 -50 -60 ( i i 5 10 time(s) 15 Figure 44: Pump step input 12.5-25% 103 20 r Real versus Modelled Response Real Model arx(2 1 9), 60.142 1.9155 + 229.1 s2 +50.445 + 58.81 -50 time(s) 10 15 Figure 45: Pump step input 25-37.5% 20 r Real versus Modelled Response 10r g-ior •o a N I-20L O z -30 h -40 h -50 L Real Model 0.26i arx(2 1 14), 67.624 3.7845 + 449.9 5 2 +49.315 + 116.6 10 15 time(s) Figure 46: Pump step input 37.5-50% 104 Real versus Modelled Response 20 | : , , 3 -10 O. S -20 E -30 -40 -50 -60 Real Model arx(2 1 11), 75.990 7.16s+ 839.3 s 2 + 46.22s + 191.2 10 15 time(s) Figure 47: P u m p step input 50-62.5% 20 10h -10 S- -20 D o -40 -50 -60 -70 h -80 Real versus Modelled Response Real Model arx(2 1 11), 78.282 10.4s + 1218 s2 + 46.36s + 251.3 10 15 time(s) Figu re 48: P u m p step input 62.5-75% 105 20 r Real versus Modelled Response 10h -10r S- -20 [• T 3 . P. -30 r CO E -40 r -50 h -60 Real Model arx(2 1 11), 80.837 12.175 + 1423 s2 +46.465 + 297.2 -70 h -80 10 time(s) 15 Figure 49: Pump step input 75-87.5% 10h "3 O | -20F co E i o z •30 h -40 F -50 -60 L Real versus Modelled Response Real Model -0.185 arx(2 1 10), 79.791 12.955 + 1525 5 2 +48.585 + 335.7 10 15 time(s) Figure 50: Pump step input 87.5-100% 106 ^ M P - Decreasing Input 10 •o <B 15 E -10 Real versus Modelled Response Real Model arx(2 1 34), 2.610 -0.66s 0 . 7 1 4 5 + 7 3 . 5 9 s 2 + 1 9 . 1 4 5 + 1 0 7 0 10 15 time(s) Figure 51: Pump step input 100-87.5% 60 50 3 30 Q. 9. 20 10 -10 -20 Real versus Modelled Response Real Model -0.2s arx(2 111), 79.195 4 . 9 9 5 5 + 5 5 6 . 7 5 2 + 3 2 . 0 6 5 + 123 10 15 time(s) Figure 52: Pump step input 87.5-75% 107 80 70 60 50 Real versus Modelled Response & 40 T 3 CP 30 CO E o z 20 10 -10 -20 Real Model 0.18s arx(2 1 10), 72.518 4.0015 + 436.5 5 2 + 25.735 + 66.8-time(s) Figure 53: Pump step input 75-62.5% -20 Real versus Modelled Response Real Model 0.22s arx(2 1 12), 68.353 2.6095 + 284.1 " 5 2 + 25.125 + 54.71 " 10 time(s) 15 Figure 54: Pump step input 62.5-50% 108 60 50 40 => 30 a . "O 0) 20 CD E o z Real versus Modelled Response 10 -10 -20 Real Model arx(2 1 12), 74.157 3.5715 + 391.9 s2 +27.575 + 83.27 10 15 time(s) Figure 55: Pump step input 50-37.5% 60 50 40 => 30 Q . o I 20 CO E I 10 -10 -20 Real versus Modelled Response Real Model 0.225 arx(2 1 12), 76.519-3.0525 + 335.3 _ 5 2 + 27.735 + 71.91 10 15 time(s) Figure 56: Pump step input 37.5-25% 109 60 Real versus Modelled Response Real Model 50 arx(2 1 10), 81.816 _ _ 0. 1 8 5 3.875s + 428.4 40 s 2 + 29.58s + 85.28 " "3 Q . 30 lized Oi CO E k_ 20 -o Z 10 0 - A -10 ( t * V v v u 5 10 time(s) 15 Figure 57: Pump step input 25-12.5% 150 Real versus Modelled Response i I Real Model arx(2 1 6), 76.865 100 _o.105 3.4665 + 361.1 6 s2 +12.235 + 26.71 Q . lized Ou o -CO E i _ I; o z \ 0 -l H = -50 ( 1 i 5 10 time(s) 15 Figure 58: Pump step input 12.5-0% 110 M O T O R - Increasing Input 10 T J 0) -5 . N 15 E 1 o 2 Real versus Modelled Response arx(2 1 58), 55.000 9.6615 + 1106 5 2 +44.995 + 809.3 10 15 time(s) Figure 59: Motor step input 0-12.5% 20 10 o J -20 co E $ -30 -40 -50 -60 Real versus Modelled Response arx(2 1 21), 80.873 • -0.405 18.165 + 2099 5 2 +44.985 + 488.2 10 15 time(s) Figure 60: Motor step input 12.5-25% Real versus Modelled Response arx(2 1 30), 8.796 0 5 10 15 time(s) Figure 61: Motor step input 25-37.5% Real versus Modelled Response 0 5 10 15 time(s) Figure 62: Motor step input 37.5-50% 112 20 10 -10 Real versus Modelled Response 3 S- -20 1 -30 co E -50 -60 -70 -80 -0.28s arx(2 1 15), 85.706 17.02s+ 2005 s 2 +48.77^ + 351.9 10 time(s) 15 Figure 63: Motor step input 50-62.5% 20 -20 3 o S -40 o z -60 -100 Real versus Modelled Response Real Model -0.18s arx(2 1 10), 87.205 14.76s+ 1780 -s 2 + 53.79s+ 208.5 10 15 time(s) Figure 64: Motor step input 62.5-75% 113 50 r Real versus Modelled Response 3 o "co E o z -100 Real Model 0.165 arx(2 1 9), 86.796 13.66s+ 1602 s2+ 4 5 . 9 k + 138.2 10 time(s) 15 Figure 65: Motor step input 75-87.5% 50 r Real versus Modelled Response & -501-O XI cu . N "co | -100r -1 SOr-Real Model arx(2 1 12), 87.732 23.235 + 2759 _ 5 2 +49.625 + 176.7 -200 L 10 15 time(s) Figure 66: Motor step input 87.5-100% 114 M O T O R - Decreasing Input 500 Real versus Modelled Response — Real Model 400 arx(2 1 12), 85.776 _ 0 2 2 s 34.74s + 4047 Q. 300 6 s2 + 43.92s + 115.9 -lized Oi 200 CD E o z 100 0 -100 ( I I ) 5 10 time(s) 15 Figure 67: Motor step input 100-87.5% Real versus Modelled Response 1 Real 1 Model arx(2 1 9), 88.800 c _ o . , 6 i 19.07s+ 2275 - 1 6 s 2 + 50.71s + 185" i 5 10 1 time(s) Figure 68: Motor step input 87.5-75% 115 Real versus Modelled Response 120 -20 ' 1 1 0 5 10 15 time(s) Figure 69: Motor step input 75-62.5% 100 Real versus Modelled Response i Real Model 80 arx(2 1 11), 87.394 _0.2o, 13.385 + 1625 60 6 s2 +55.685 + 231.7 "3 Q . lized Ou 40 CO E o z 20 0 -20 C i i ) 5 10 time(s) 15 Figure 70: Motor step input 62.5-50% 116 80 r 70 h -20 Real versus Modelled Response Real Model -0.14s arx(2 1 8), 84.118] 10.675 + 1278 s 2 +52.335 + 252.2 10 time(s) 15 Figure 71: Motor step input 50-37.5% 60 r 50 40 h o I 20r E I 10r -10r -20 Real versus Modelled Response Real Model -0.34s arx(2 1 18), 80.569-16.695 + 1957 5 2 +48.515 + 460.9 10 time(s) 15 Figure 72: Motor step input 37.5-25% 117 15r Real versus Modelled Response - 1 0 L Real Model 0.185 arx(2 1 10), 27.757 6.2625 + 677.4 -s2 +33.635 + 1217 10 time(s) 15 Figure 73: Motor step input 25-12.5% 40 r 35 h 30 25 F 3- 20h 3 o CD E - 1 0 L Real versus Modelled Response Real Model -0.345 arx(2 1 18), 71.838 18.495 + 2041 -5 2 +36.415 + 913.8 -15 Figure 74: Motor step input 12.5-0% 118 APPENDIX E A brief description of the Routh-Hurwitz stability analysis is given in this appendix. For a PI controller design, the values for the PI gains that ensure system stability are calculated using the Routh-Hurwitz criteria. 119 First-order system 1 i + y /T Second-order system 2 s +2£cons + con PI Controller C = K i ^ = K P S + K I P s s Routh-Hurwitz The characteristic equation: 1 + CG = 0 First-order Analysis ) \+ca =i+ Kps + K, V 1 V \+S/ = 0=^1 + T J (Kps + KA { T ) V s J [S + TJ = 0 => ^  + r)+T(KPS + Kf)=0=>s2 +T(\ + Kp)S + K/T = 0 =^s2 + r(l + Kp)s + KIT = 0 s2 1 K,T sx r(l + Kp) 0 s° c, Stability Criteria 1. T(1 + Kp)>0=>KP > - l 2. q = iC 7r > 0 => iC 7 > 0 1. Kp has to be greater than -1. 2. K/ has to be greater than 0, since r is greater than 0. For all positive values of the PI controller gains, the first-order system remains stable. 120 Second-order Analysis The characteristic equation: 1 + CG, = 1 + co„ s +2£a>ns + con = 0 => s(s2 + 2^cons + con2)+ CO 2{KPS + K,)=0 =>s3+ (2^con )s2 + co 2 (l + Kp)s + K.co2 = 0 1 con2{\ + KP) s2 (2Ca>„) K,con2 sl b, 0 1 lK,a>K2 -co2{\ + KpX2Cco„pa^i + Kj-^K, c, =K,con Stability Criteria 1. bx = co2{\ + Kp)-^K, >0^K, <2£con(\ + Kp) 2. OR KD > EL. 2 £ » . -1 3. c, =KjC02 >0^>KI >0 1. Ki has to be less than 2£con (Kp +1) K, 2. KP has to be greater than 2<X 1. 3. Ki has to be greater than 0. When KP is equal to zero, Ki has to be less than 2C,con. Increasing Kp does not cause system instability. Using the selected transfer function for the pump model, ignoring the delay and the zero and normalizing with con , it can be seen that when KP = 0, Kj < 46.46 for system stability. 297.2 'PUMP s2 +46.46^ + 297.2 121 References [1] Murphy, P; Design and Development of an L H D for Narrow-Reef Mining, Canadian Institute for Mining, Metallurgy and Petroleum, Montreal, 2003. [2] Thoma, J; Hydrostatic Power Transmission, Trade and Technical Press Limited. Morden, Surrey, England, 1964. [3] Betz, M ; The Productive and Efficient Hydrostatic Transmission, Agriculture Engineering, pp. 12-15, July 1990. [4] Huhtala, K ; Modelling of Hydrostatic Transmission - Steady State, Linear and Non-Linear Models, Acta Polytechnica Scandinavica, Mechanical Engineering Series No. 123, Helsinki 1996. [5] Kodkani, S; New Generation Hydrostatic Drives, Chemical Engineering World, Volume XXXIII , No. 5, pp. 53-55, May 1998. 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