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A Fully Flexible Valve Actuation System for internal combustion engines Zhao, Junfeng 2009-09-21

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A Fully Flexible Valve ActuationSystem For Internal CombustionEnginesbyJunfeng ZhaoB.A.Sc., Tsinghua University, 2007A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinThe College of Graduate Studies(Mechanical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)August 2009c© Junfeng Zhao 2009AbstractAir pollution, global warming, and rising gasoline prices have lead govern-ments, environmental organizations, and consumers to pressure the auto-motive industry to improve the fuel efficiency of cars.Since alternative fuels such as hydrogen are still quite far from beingcommercially viable, improving the existing internal combustion engine isstill an important priority. Traditional internal combustion engines use acamshaft to control valve timing. Since the camshaft is rigidly linked tothe crankshaft, engineers can optimize the camshaft only for one particularspeed torque combination. All other engine operating points will suffer froma suboptimal compromise of torque output, fuel efficiency, and emissions. Inan engine with a camless valve actuation system, valve events are controlledindependently of crankshaft rotation. As a result, fuel consumption andemissions may be reduced by 15% ∼ 20% and torque output is enhanced ina wide range of engine speeds.The Fully Flexible Valve Actuation (FFVA) system is our approach toconstructacamlessvalveactuationsystem. Withinthelimitsofthedynamicbandwidth of the system, it allows for fully user definable valve trajectoriesthat can be adapted to any need of the combustion process. The systemis able to achieve 8mm valve lift in 3.4ms, which is suitable for an engineoperating at 6000RPM. The valve seating velocity is similar to conventionalvalve trains that achieve 0.2m/s at high engine speeds and 0.05m/s at engineidle conditions. Finally, the energy consumption measured in an experimen-tal test bed matches the friction losses of conventional valve trains and itcan further be improved by using an optimized motor.This thesis describes the progress that has been made towards designingthis technology. A design methodology is derived and important operationfeatures of the mechanism are explained. Modeling and simulation resultsshow significant advantages of the FFVA over previously designed electro-magnetic engine valve drives.iiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiAcronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background and Motivation . . . . . . . . . . . . . . . . . . 21.2 Principles of Camless System . . . . . . . . . . . . . . . . . . 41.3 Current State of Research . . . . . . . . . . . . . . . . . . . . 72 FFVA System Overview . . . . . . . . . . . . . . . . . . . . . 122.1 Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Principles of Brushless DC Motor . . . . . . . . . . . . . . . 142.3 Valve Control Unit . . . . . . . . . . . . . . . . . . . . . . . 15iiiTable of Contents3 Actuator Design with a Stock Motor . . . . . . . . . . . . . 183.1 Mechanical Optimization . . . . . . . . . . . . . . . . . . . . 183.2 Motor Selection . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Trajectory Generation . . . . . . . . . . . . . . . . . . . . . . 223.4 Design Example . . . . . . . . . . . . . . . . . . . . . . . . . 264 Motor Optimization . . . . . . . . . . . . . . . . . . . . . . . . 304.1 Stator Saturation Constraint . . . . . . . . . . . . . . . . . . 304.2 Demagnetization Constraint . . . . . . . . . . . . . . . . . . 324.3 Linearity Constraint . . . . . . . . . . . . . . . . . . . . . . . 354.4 Energy Constraint . . . . . . . . . . . . . . . . . . . . . . . . 364.5 Motor Design Example . . . . . . . . . . . . . . . . . . . . . 385 Finite Element Analysis of DC Motor . . . . . . . . . . . . . 425.1 Brushless DC Motor Topology . . . . . . . . . . . . . . . . . 425.2 Maxwell Equations . . . . . . . . . . . . . . . . . . . . . . . 435.3 Governing Equations in 2D Electromagnetic Field . . . . . . 445.4 Finite Element Simulation for BLDC Motor . . . . . . . . . 465.5 Evaluation of Optimized Motor . . . . . . . . . . . . . . . . 496 Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 526.1 3 Phase Inverter . . . . . . . . . . . . . . . . . . . . . . . . . 536.2 Position (or PD) Controller . . . . . . . . . . . . . . . . . . . 546.3 States Observer . . . . . . . . . . . . . . . . . . . . . . . . . 547 System Simulation and Experimental Validation . . . . . . 617.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 617.2 Simulation of Transition Performance . . . . . . . . . . . . . 62ivTable of Contents7.3 Simulation of the Robustness Towards Parameter Variations 647.4 Simulation of Disturbance Rejection . . . . . . . . . . . . . . 667.5 Simulation of Low Resolution Sensor with a Kalman Filter . 667.6 Experimental Results . . . . . . . . . . . . . . . . . . . . . . 678 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 798.2 Suggestions for Future Works . . . . . . . . . . . . . . . . . . 80Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82vList of Tables3.1 Motor Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 275.1 Comparison of motor parameters . . . . . . . . . . . . . . . . 507.1 Motor Parameters . . . . . . . . . . . . . . . . . . . . . . . . 637.2 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657.3 Performance comparison . . . . . . . . . . . . . . . . . . . . . 68viList of Figures1.1 Powertrain evolution of EU standard . . . . . . . . . . . . . . 21.2 Key technologies . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Fuel economy solutions . . . . . . . . . . . . . . . . . . . . . . 41.4 Schematic p-V diagrams . . . . . . . . . . . . . . . . . . . . . 91.5 Honda VTEC mechanical valve actuation . . . . . . . . . . . 101.6 Hydraulic valve actuation . . . . . . . . . . . . . . . . . . . . 101.7 Solenoid valve actuation . . . . . . . . . . . . . . . . . . . . . 111.8 EMVD system . . . . . . . . . . . . . . . . . . . . . . . . . . 112.1 System structure . . . . . . . . . . . . . . . . . . . . . . . . . 122.2 Real object and 3D model of QB02302 . . . . . . . . . . . . . 132.3 Linkage structure between motor and valve . . . . . . . . . . 162.4 2D geometry of BLDC motor . . . . . . . . . . . . . . . . . . 173.1 Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Jerk limited smooth trajectory . . . . . . . . . . . . . . . . . 233.3 Winding variation for QB02302 . . . . . . . . . . . . . . . . . 294.1 Demagnetization curve . . . . . . . . . . . . . . . . . . . . . . 334.2 Flux density due to current and magnet . . . . . . . . . . . . 344.3 Diagram of optimization procedure . . . . . . . . . . . . . . . 41viiList of Figures5.1 QB02302 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 Optimized motor . . . . . . . . . . . . . . . . . . . . . . . . . 435.3 Mesh result . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.4 Flux density distribution of the optimized motor . . . . . . . 516.1 Diagram of control units . . . . . . . . . . . . . . . . . . . . . 526.2 Cascaded control structure . . . . . . . . . . . . . . . . . . . 586.3 Current controller . . . . . . . . . . . . . . . . . . . . . . . . 596.4 Position controller . . . . . . . . . . . . . . . . . . . . . . . . 607.1 System hardware . . . . . . . . . . . . . . . . . . . . . . . . . 627.2 Simulation of displacement trajectories . . . . . . . . . . . . . 707.3 Simulation of energy losses of different trajectories . . . . . . 717.4 Transition simulation of the optimized motor . . . . . . . . . 727.5 Simulation of parameter variations . . . . . . . . . . . . . . . 737.6 Simulations of disturbance rejection . . . . . . . . . . . . . . 747.7 Simulation of transition response with a 7 bit sensor and var-ious filtering strategies . . . . . . . . . . . . . . . . . . . . . . 757.8 Simulationsofmeasurementerrorusingdifferentfilteringstrate-gies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767.9 Experimental trajectory results using QB02302 . . . . . . . . 777.10 Experimental energy loss using QB02302 . . . . . . . . . . . . 78viiiAcronymsFFVA=Fully Flexible Valve ActuationVVT=Variable Valve TimingEIVC=Early Intake Valve ClosingLIVC=Late Intake Valve ClosingEMCV=Electromechanical Camless ValvetrainEMVD=Electromechanical Valve DriveNdFeB=Neodymium Iron BoronFEM=Finite Element MethodFEA=Finite Element AnalysisLPF=Low Pass FilterPWM=Pulse Width ModulationixNomenclaturer Rotor Radiushs Slot Heighthrs Thickness of Stator Backrsi Stator Inner Radiusrso Stator Outer Radiusl Motor Lengthlg Airgaplge Effective Airgaplm Magnet Thicknessβ Magnet Coverage Spanwt Tooth Widthws Slot WidthKT Motor Torque ConstantKB Back EMF ConstantR Motor Terminal ResistanceL Motor Terminal InductanceZ Total Number of ConductorsI Current in each ConductorItotal Total Current Itotal = ZIT Motor Torquera Length of Excenter ArmJm Motor Inertiam Valve MassJ Total Inertia J = Jm +mr2aα Angular Accelerationω Angular Velocityθ Rotation Anglea Linear Accelerationv Linear Velocitys Linear Displacementj Jerk(Derivative of a )xNomenclatureE Energy Lossρ Density of Core and MagnetBr Magnet Residual Flux DensityBc Flux Density in CoreBs Saturation Flux DensityBgo Airgap Flux Density Due to Magnet AloneBI Airgap Flux Density Due to Current AloneBg Airgap Flux Density Bg=Bgo +BIBD Demagnetization Flux Densitywp Width of Each Polewm Width of Each MagnetKs Linear Current Densityγ Angular Displacement Between the Fields Produced by the Magnet andthe Stator Currentkw Stator Length FactorAca Copper Area per SlotAslot Slot Areadw Wire Diameternw Number of Wires per Slotkfill Filling Factorp Number of Polesq Number of Slot per Pole per PhaseQ Total Number of Slot−→H Vector of Magnetizing Field−→D Vector of Electric Displacement−→J Vector of Free Current Density−→B Vector of Magnetic Field−→A Potential Vectorε Electric Permeabilityµ Magnetic Permeabilityσ Electric Conductivity−→n Normal Unit VectorPi Proportional Gain in PI ControllerKi Integral Gain in PI ControllerPd Proportional Gain in PD ControllerKd Derivative Gain in PD ControllerxiAcknowledgementsI would like to thank all people who have helped and inspired me during mymaster study.I especially want to thank my advisor, Prof. Rudolf Seethaler, for hisguidance during my research and study at University of British ColumbiaOkanagan. His perpetual energy and enthusiasm in research had motivatedme. In addition, he was always accessible and willing to help me with myresearch. As a result, research life became smooth and rewarding for me. Iam indebted to him more than he knows.Prof. Holzman, Prof. Najjaran, and Prof. Koch deserve a special thanksas my thesis committee members and advisors.Finally, I thank my family for supporting me throughout all my studiesat University of British Columbia Okanagan.xiiChapter 1IntroductionIn conventional Internal Combustion (IC) engines, the timing of intake andexhaust valves is controlled by the shape and phase angle of cams. Engineersneed to choose the best compromise timing among fuel economy, emissions,and torque, to design the shape of the cam. The optimization of cam shape ispossible only at one engine speed. But IC engines in automobile applicationoperate over speed and load ranges covering about an order of magnitudein each variable. This wide range of speeds and loads results in conflictingdemands for the design of the lift profiles for the valves.A fully flexible camless valve mechanism [1][2][3] allows controlling theengine load without a separate throttle and thereby avoids the associatedenergy loss, which will be discussed in next section. It is also known thatin a conventional engine the control of valve overlap, during which both theintake and exhaust valves are open, can affect the emissions, full load andidle performance. For example, to achieve high efficiency at high speed andhigh load, a large amount of overlap is desired, however, this will not allowthe engine to idle smoothly at low speed and low load because the residualfraction is excessive. Therefore, engine designers are starting to considercamless systems. The Fully Flexible Valve Actuation (FFVA) system in ourresearch is a very promising technology of its kind.Fully Flexible refers to the ability to control the duration (for how longthe valve is kept open or closed), the phase (when the valve should be openedor closed), and the lift (how far does the valve move). Many presentedsystems have only provided duration and phase control and they are referredto as Variable Valve Timing (VVT) systems [4][5].Flexible intake and exhaust valve mechanisms can greatly improve fueleconomy, emissions, and torque of the internal combustion engine. Fuelconsumption may be reduced by 15%−20% [6], torque output is enhancedin wide range of engine speed, and emissions may be decreased by the sameratio.11.1. Background and MotivationFigure 1.1: Powertrain evolution of EU standard [1]1.1 Background and MotivationThe emissions of automobiles are becoming a global problem. Many coun-tries and areas have been focusing on them and have set different standardsto regulate emissions and to improve the performance of engines. Emissionstandards are requirements that set specific limits to the amount of pollu-tants that are released into the environment. While emission performancestandards have been used to dictate limits for conventional pollutants suchas oxides of nitrogen NOx, this regulatory technique may also be used toregulate fuel consumption which is related to the emission of carbon dioxideCO2.Emissions are directly influenced by the combustion process. A fuel thatburns incompletely is obviously not being utilized efficiently, and unburntfuel remains as pollutants. In both gasoline and diesel engines, the fuel isatomized very finely to ensure good combustion. But that’s just one partof the story. The other is that the nature of the combustion process alsoinfluences pollutant emissions.To address the problem of global warming, emissions of exhaust pollu-21.1. Background and MotivationFigure 1.2: Key technologies [1]tants and greenhouse gas from motor vehicles must be reduced [7]. Fig-ure 1.1 shows the EU standard of powertrain evolution in the future forboth gasoline engines and diesel engines, which are represented by red andblack spots respectively in the picture. These objectives are challenging andconflict with each other. It can be seen that for both gasoline and dieselengines there is still a long way to go before they can meet the proposedstandard. In practice, if NOx emissions are reduced, the CO2 emissionsand fuel consumption inevitably rises. With the more stringent regulationsexpected, new engine technologies are urgently required.In Figure 1.2, key technologies for improving engine’s performance areshown. The circled camless system, is on a very promising place on the map.Also, it can be seen from Figure 1.3 that the camless technology is the mosteffective, since it can improve the fuel economy by 15% ∼ 20%.But a combination of different technologies needs to be developed, sinceno single one can fully satisfy the future standard. The large number of mu-tually interactive variables and sub-systems is a major engineering challenge,but it also provides the flexibility that is essential for converging to an op-timal solution. After all, a properly matched combination of fuel, injectionsystem, air management, and exhaust treatment should make it possible to31.2. Principles of Camless SystemFigure 1.3: Fuel economy solutions [1]create sufficiently stable operating conditions to meet prevailing regulatoryemission and fuel economy targets.Another advantage of camless technology is that it is compatible withall other energy saving solutions. Thus, the research on camless systems isnecessary and important for the evolution of engines.1.2 Principles of Camless SystemIn a conventional four stroke internal combustion engine, the operating cycletakes place over two revolutions of the crankshaft [9].In the first stroke, the piston of engine starts from top dead center(TDC). At the beginning of the movement, the intake valve is alreadyopened, which is called inlet valve opening (IVO), to let the fresh air orair-fuel mixture into the cylinder. Then after the piston has reached thebottom dead center (BDC), the intake valve is closed, which is called inletvalve closing (IVC).The second stroke from BDC to TDC is defined as a compression stroke,41.2. Principles of Camless Systemduring which both of the intake and exhaust valves are closed. Then themixture in the cylinder is compressed when the piston moves upwards. Ig-nition is started when the piston is close to the end of the stroke. Then thepressure in cylinder increases rapidly.The third stroke from TDC to BDC is defined as a power stroke. Whencombustion is completed, the pressure in the cylinder reaches a maximumvalue. Then the cylinder starts expanding, which pushes the piston to moveuntil the exhaust valve opens, which is called exhaust valve opening (EVO).Generally before BDC, the first portion of the burned gases is allowed to bedischarged.The fourth stroke from BDC to TDC is defined as an exhaust stroke, asthe piston pushes the remaining burned gases out. Near the TDC position,the intake valve opens again and the exhaust valve closes, which is calledexhaust valve closing (EVC). The timing is usually slightly after the TDCposition.Figure 1.4 shows schematic p-V diagrams of a four-stroke engine witha conventional mechanical valvetrain (plot 1) and a camless systems withearly intake valve closing (EIVC, plot 2) and late intake valve closing (LIVC,plot 3). The shadowed area corresponds to the work needed to induct andexpel gases. These losses are referred to as pumping losses.The pumping losses due to the throttling operation in a conventionalengine with a mechanical valvetrain are quite significant [10]. A challenge inimproving engine efficiency is to reduce the pumping losses while the frictionloss is not excessively increased. Two strategies are available for controllingthe amount of air drawn into the combustion chamber with variable valvetiming systems: Early intake valve closing (EIVC) and late intake valveclosing (LIVC). With EIVC, the engine load is controlled by closing theintake valve early to trap the desired amount of charge, instead of throttlingthe incoming charge conventionally by means of a throttle plate. Likewise,LIVC also controls engine load with reduced pumping loss, but in this caseby returning unwanted charge to the intake manifold.The comparison between pressure cycles clearly shows the advantagesobtainable by adopting a camless valve actuation system in the same enginedue to a significant reduction in pumping losses.No matter whether EIVC or LIVC is implemented in the combustionprocess, the full controllability of each valve must be obtained by replacingthe conventional valve system with a camless system, which must have some51.2. Principles of Camless Systemequivalent performance, while allowing the additional flexibility mentionedpreviously.First, a camless system must allow for fast valve transitions, where thetransition time refers to the time required to either open or close a valve.At an engine speed of 6000rpm, the nominal cycle time for a conventionalfour stroke engine is 20ms/cycle. Each cycle includes a closed-to-open tran-sition, an open-to-closed transition, and holding phases between the transi-tions. The valve should be open for about one third of the cycle. Thus, thetransition time at 6000rpm engine speed needs to be about 3.5ms [11].The second constraint is the valve seating velocity which is the valvespeed when the valve hits the cylinder head after the valve closing transition.In a typical IC engine, the seating velocity is usually less than 0.3m/s [12] athigh speed and less than 0.05m/s [13] at idle. Higher valve seating velocitieslead to excessive noise and potentially damage to the engine. Thus, ”softlanding” is an essential requirement for any valve actuation system.The third consideration is energy loss for each transition. In a typical2.0L, 16 valve, four stroke IC engine, the total energy loss of the valve trainat 6000rpm is about 2−3kW [14]. If only considering the eight intake valves(due to gas force, there is additional energy loss for each exhaust valve, butwe consider intake valves only here), the power loss for each intake valve isaround 1kW. Thus, at 6000rpm, and 20ms/cycle, the energy loss for eachintake valve is approximately 2.5J/cycle. Therefore, the average energy lossof each valve at 6000rpm is approximately 1.25J/transition. This assumesthat the power to keep the valve open or closed is minimal, which is the casefor all valve actuation systems proposed to date.The three constraints above are the main indicators of the system per-formance. Additional constraints (such as working temperature, appliedvoltage and system package size etc.) should be carefully considered beforea system can be put into practical application.Different vehicle engines run different temperatures at different condi-tions, but a fairly normal range is around 80oC to 140oC [15]. So thepractical system should be able to work at this temperature.Several voltage standards [16] currently exist for automotive applica-tions: most automobiles use 12V and trucks often use 24V. In order toreduce the size of the wire harnesses and reduce copper losses, a 42V stan-dard has been proposed but not implemented in production. In addition,Hybrid cars usually can provide approximately 200V onboard voltage. For61.3. Current State of Researchour investigation we will focus on 42V.1.3 Current State of ResearchIn recent years, some relatively basic variable valve actuation systems havebeen presented in publications or even introduced into production engines.These forms mainly use mechanical, electro-hydraulic or electromagneticvalve actuation technologies.The mechanical systems could be very simple in structure as in Fig-ure 1.5. The simplest ones, the cam phasers, change only valve timing.Other types, slightly more complex, can change the valve lift. These mech-anisms are quite simple and effective, and some of them are already on themarket. But the mechanical mechanisms can only provide limited flexibilityof the valve’s motion, and their dynamic response is too slow for guaran-teeing optimum valve timing for transient engine operations. The HondaVTEC mechanism [17] and the Toyota VVT-i system [18] are examples ofmechanical variable valve timing systems.Electro-hydraulic systems [21] [22] are conceptually quite simple. Theelectro-hydraulic camless systems proposed so far usually offer a contin-uously variable and independent control of all aspects of valve motion.Electro-hydraulic systems typically use piezo-actuated valves to control thehydraulic fluid flow that is used to displace the valve. Unfortunately, hy-draulic systems suffer from viscosity changes across the required temperaturerange, since engine oils are typically used as the hydraulic liquid. Thus, theperformance deteriorates at low temperatures. In addition, it is very dif-ficult to achieve good energy efficiency with hydraulic systems, since thereis no simple way to recover the kinetic energy of the valves when they areslowed down [23].Electromagnetic systems are characterized by a spring system that isused to accelerate and decelerate the valve. Magnets or motors are used tohold the valves in the end positions and to compensate for friction loss aswell as for combustion forces. Devices using solenoids such as in the oneshown Figure 1.7, are able to generate flexible valve phase and duration,however, high valve seating velocity is difficult to control and the valve liftis limited by the structure. Nevertheless, this is a very popular technologyand needs to be discussed in more detail.71.3. Current State of ResearchTypically, the solenoid actuator consists of a linear-moving armaturewith two coils and two preloaded springs. The springs can achieve rapidtransition times while minimizing electrical energy input and are essentialin overcoming the significant combustion pressures. The electromagnets arerequired for ”catching” the armature at either stroke bound. In addition,they are used to overcome friction and pressure disturbances. This deviceneeds only very little current to hold the valve at both ends. But since thereis a very nonlinear relationship between force, position and current, it isvery difficult to control the seating velocity when the armature approacheseither end [6].Figure 1.8 shows another electromagnetic system, in which a BLDC mo-tor is applied to drive the valve rather than solenoids. A number of differentconfigurations [14][25][26] exist for this design that all use springs to accel-erate and decelerate the valve and a motor driven pivoting cam to providetiming. Note that the cam has a constant radius at either end of the valvemotion. As a result, the motor can keep the valve at either end usingzero torque. The disadvantage of this system clearly is its relatively highmechanical complexity, and the inability to adjust valve lift continuously.Nevertheless, the EMVD system demonstrates good performance on bothtransient time and seating velocity.Since electromechanical systems provide better energy recovery poten-tial, they will be used as benchmarks for the proposed FFVA system. Itcombines advantages of the other electromechanical systems and avoids someof their inherent problems. Like EMVD, FFVA uses a BLDC motor to gen-erate shear force to drive the valve. This leads to a much simpler linearcontrol system than that for the EMCV system. In contrary to EMCV andEMVD, FFVA does not use springs, but energy recovery is provided by themotor that is able to electrically feed back the breaking energy to storagecapacitors. In the following sections, the system structure, design procedureand system performance are discussed in detail.81.3. Current State of ResearchFigure 1.4: Schematic p-V diagrams [8]91.3. Current State of ResearchFigure 1.5: Honda VTEC mechanical valve actuation [19]Figure 1.6: Hydraulic valve actuation [20]101.3. Current State of ResearchFigure 1.7: Solenoid valve actuation [24]Figure 1.8: EMVD system [14]11Chapter 2FFVA System OverviewA schematic of the FFVA system is shown in Figure 2.1. There are threemain parts: the actuation part, the valve control unit and the engine controlunit.Figure 2.1: System structureThe engine control unit controls the engine operation and provides therequired valve timing information to the valve control unit. The enginecontrol unit is designed separately, and not part of this research.122.1. ActuatorFigure 2.2: Real object and 3D model of QB02302The valve control unit receives the desired valve timing and lift from theengine control unit and uses this information together with measured valveposition and measured current in order to regulate the amount of voltageapplied to the actuator.The actuator consists of BLDC motor, a valve and a linkage structureconnecting the two. A state observer, including sensors and digital filters,is connected to the actuator and used to measure the valve motion, whichis then provided to the valve control unit.2.1 ActuatorFigure 2.3 shows a detailed picture of the linkage between motor and valve.An excenter arm of length, ra, is attached to the motor’s shaft, which in turnis connected to the valve through a small bracket. This structure transfersthe motor’s angular movement to the valve’s linear movement:a = αra (2.1)If the rotor angle is small, the relationship between lift and rotor anglecan be assumed linear. The excenter arm is made of aluminium and itsinertia can be neglected when compared to the rotor inertia and the valvemass. The motor torque T is used to accelerate the rotor with an inertia,Jm, and the valve with a reflected inertia mr2a, where m is the mass of thevalve:T = (Jm +mr2a)α (2.2)132.2. Principles of Brushless DC MotorThe figure also shows several parameters, which play an important rolein determining the system’s performance. These parameters, especially therotor angle θ and excenter arm length ra, will be discussed in the chapter ofoptimization.2.2 Principles of Brushless DC MotorAs shown above, a brushless DC motor is the key part of the FFVA system.The basic structure of a permanent magnet brushless DC motors has threeelements: a stator with windings, a rotor with permanent magnets attachedto it, and a sensor to measure the rotor position. A picture of QB02302 [27]and its 3D model is given in Figure 2.2.The motor’s torque constant and other properties are all related to thestructure and material of the motor. Figure 2.4 provides the dimensioningdetails of an interior rotor BLDC motor (2D geometry of motor QB02302).The rotorradiusr, the slotheighths andthe lengthofthemotorl aretreatedas variables for an optimized design goal in subsequent chapters. The airgaplg and magnet thickness lm are selected to give sufficient flux density in theairgap. Magnets are glued on the rotor surface. The coverage of the magnetson the rotor is called span, represented by β. In our application, the span isabout 0.8. Inside the stator, the tooth width wt and the slot width ws arealmost the same.To understand how these elements work as a motor, consider some ele-mentary magnetics [28]. When a current carrying wire is placed in a mag-netic field so that the current flow is perpendicular to the direction of thefield, a force is exerted between the field producing element and the wire.The electromagnetic model of the actuator is approximated by an equiv-alent linear single phase DC-motor model. The mathematical model of theBLDC motor is based on the following assumptions: 1) stator resistancesof all the three phases are equal and the self and mutual inductances areconstant; 2) the motor is operated within the rated condition and hence thesaturation effect due to current level is neglected; 3) iron losses are negligible.This approach is followed, since most motor specifications are based onthis model and we want to be able to select an optimum motor from themanufacturer’s motor specifications. The motor current I, is defined bya first order differential equation in terms of the applied voltage U, and142.3. Valve Control Unitthe back EMF voltage KBω, the winding resistance R, and the windinginductance L: dIdt =1L(U −KBω−IR) (2.3)The acceleration capability of the device is the torque T , which is pro-portional to the current I:T = KTI (2.4)The maximum or peak torque available for a particular motor is givenby:Tmax = KTImax (2.5)This is not the continuous torque available, which is usually constrainedby heat generation of the windings, but the value of torque that is con-strained by saturation of the core or demagnetization of the permanentmagnets on the rotor. It is important to recognize that actuating valvesis an intermittent operation in nature and requires large accelerations overshort periods of time. Thus, the performance is governed by the peak torqueand resistive copper losses of the motor rather than the continuous torquerating of the motor. For small automotive engines, the actuator motorshould consume less than 120W at 6000rpm and provide enough transienttorque in order to achieve valve openings or closings in 3.5ms. Chapter 3will show how to select a suitable stock motor for this application. Chapter4 provides a strategy to modify the stock motor in order to achieve optimumperformance.2.3 Valve Control UnitThe main function of the valve control unit is to move the valve from theclosed to the opened position (and vice-versa) avoiding noise, which is causedby nonzero seating velocity. This is achieved using a cascaded trackingcontroller with feed forward.In Chapter 3, valve trajectories for minimizing energy and maximizingacceleration will be derived, and in Chapter 6 the design of the trackingcontroller will be described.152.3. Valve Control UnitFigure 2.3: Linkage structure between motor and valve162.3. Valve Control UnitFigure 2.4: 2D geometry of BLDC motor17Chapter 3Actuator Design with aStock MotorThe FFVA system is a servo system that uses a lightweight mechanicallinkage structure to transfer the motor rotation to the valve translation.Typically, high speed servo systems operate at the accelerations less than40g. The application shown here requires acceleration in the order of 250g.At the same time, energy consumption needs to be minimized in order toensure that fuel consumption reductions gained through the introduction ofvariable valve control are not offset by the power consumption of the valveactuation system. To achieve these goals, the mechanical linkage, the electricmotor, and the valve trajectories are optimized in the following sections.3.1 Mechanical OptimizationIn the FFVA system, the motor’s rotation is converted to valve’s verticalmotion through an arm-like structure called the excenter arm. The lengthof the excenter arm, ra, plays an important role in the performance of theactuation system. This section outlines how the arm length can be optimizedto provide maximum acceleration and minimum energy consumption.Maximum power transfer will occur in a mechanical system if the inertiaof the load matches the inertia of the motor. That is, for a specific motor,if load inertia reflected to the motor shaft can be made to match the motorinertia, disregarding added inertia and inefficiency of the reducer, powertransfer will be optimized and maximum acceleration of the load will result.The proof for this is detailed [29].The motor torque, T, is used to accelerate the rotor with inertia, Jm,and the valve with a reflected inertia of mr2a, where m is the mass of the183.1. Mechanical Optimizationvalve:T = (Jm +mr2a)α (3.1)This equation can be rearranged to provide the rotor acceleration, α:α = TJm +mr2a(3.2)The valve acceleration is a = α · ra. Taking the derivative of a withrespect to ra results in:dadra =ddt(TraJm +mr2a) =T(Jm +mr2a)−2Tmr2a(Jm +mr2a)2 (3.3)By setting the derivative equal to zero, one finds the excenter arm lengththat provides maximum acceleration:ra =radicalbiggJmm (3.4)It will now be shown that the same excenter arm length also providesminimum energy consumption, given a desired valve acceleration profile.When the motor’s rotation angle, denoted as θ, is small enough, the valvemotion can be regarded as linear. Then the relationship between valve’slinear displacement s and motor’s rotational displacement θ can be expressedas:s = raθ (3.5)Thus,d2sdt2 = ra ·α (3.6)where α is angular acceleration. The torque that the motor provides is:T = Jα = Jrad2sdt2 (3.7)where J is the total inertia including motor inertia Jm and load inertia mr2a:J = Jm +mr2a (3.8)If the motor constant is KT , the current required is:I = TKT= JαKT= JKTrad2sdt2 (3.9)193.2. Motor SelectionNow consider the motor’s copper loss, which depends on current in theform of:E =integraldisplayI2Rdt = ( JKTra)2Rintegraldisplay(d2sdt2 )2dt = (Jm +mr2aKTra )2Rintegraldisplay(d2sdt2 )2dt(3.10)Take the derivatives on both sides:∂E∂ra =2RK2T (m−Jmr2a )(Jm +mr2aKTra )2Rintegraldisplay(d2sdt2 )2dt (3.11)Then the optimal arm length is found as:ra =radicalbiggJmm (3.12)which is exactly the same as the optimal arm length for maximum acceler-ation derived previously.This suggests that matching the inertia of the load with the inertia ofthe motor will simultaneously provide maximum acceleration and minimumenergy consumption.3.2 Motor SelectionFew off-the-shelf motors are designed for the highly dynamic operating con-ditions found in the FFVA system. However, it is very important for a suc-cessful implementation that the motor operates with high efficiency. Thus,using the findings from the mechanical optimizations, criteria for selectinga motor that provides maximum valve acceleration and minimum energyconsumption are derived in the following section.The mechanical optimization assumed that the rotor motion would besmall enough in order to ensure a linear relationship between valve andmotor motion. Using this assumption, the identical Equations 3.4 and 3.12describe the optimal excenter arm length. One can now go backwards anddescribe the minimum motor inertia required in order to achieve a rotorangle smaller than θmax, for a maximum valve motion, smax, and a valvemass, m:Jm greaterorequalslant m(smaxθmax)2 (3.13)203.2. Motor SelectionSince minimizing the size of the motor reduces cost and facilitates pack-aging the motor in the cylinder head, one would usually choose motors withinertia close to the linearity constraint.In addition to the linearity requirement, the motor is also required toprovide large acceleration. Substituting Equation 3.4 back into Equation 3.2provides an equation for the maximum valve acceleration in terms of motorand valve parameters:amax = TmaxraJm +mr2a= Tmax2√Jmm(3.14)This expression indicates that maximum acceleration is achieved by min-imizing the valve mass. It also shows that the ratio of maximum torque oversquare root of motor inertia should be maximized. The relationship can beused to compare and select stock motors from their specification data sheets.In addition to large accelerations, the motor also needs to minimize cop-per losses.If the optimal arm length is substituted back into Equation 3.10 forenergy consumption, the following equation is obtained:E = 4m× JmRK2T×integraldisplay(d2sdt2 )2dt (3.15)This equation indicates that there are three parts of the actuator thatneed to be optimized in order to minimize copper losses.• Energy consumption is directly related to valve mass m. A low massvalve will significantly reduce energy consumption.• The energy cost term of the motor consists of three parameters, themotor inertia multiplied by the electrical resistance divided by thesquare of the motor torque constant. The energy cost term providesa convenient guideline to compare and select stock motors using theirspecification data sheets. Chapter 4 will derive an optimum designprocedure for the motor.• The last term in Equation 3.15 is the integral of the acceleration tra-jectory of the valve. The next section will show how to design energyoptimal trajectories.213.3. Trajectory Generation3.3 Trajectory GenerationThe usual requirement for a valve trajectory is that the valve needs to travelthe desired lift within a prescribed transition time t4, which is given by theengine control unit. Both lift, and transition time will vary with changingengine speeds and engine torque requirements. Thus, a simple online al-gorithm that generates energy optimal valve trajectories is required. Theproblem can be solved by calculus of variations [30], which leads to thefollowing valve acceleration [31]:a(t) = amax(1− 2tt4) (3.16)where amax is the maximum acceleration required to achieve the desiredFigure 3.1: Trajectoriesvalve lift and transition time with minimum energy consumption. The waveform is shown as the plot of ”Optimal” in Figure 3.1 and the resistive copper223.3. Trajectory GenerationFigure 3.2: Jerk limited smooth trajectorylosses for this trajectory can be expressed as:Eopt =integraldisplayI2Rdt = 3s2max(Jm +mr2a)2R2t32r2aK2T (3.17)where smax is the maximum valve travel, and t2 = t4/2 is half the valvetravel time.In practice, the optimal trajectory suggested above is not feasible due totwo physical constraints.First, maximum current constrains the available acceleration for a motor233.3. Trajectory Generationwith constant KT [32]:a = TraJ = IKTraJ (3.18)Secondly, the ideal trajectory contains acceleration discontinuities, orinfinitejerkatthebeginningandattheendofthevalvemovement. However,jerk is limited by the driving voltage:j = KTraJL (Umax −KT vra−R aJKTra) (3.19)If the motor parameters are fixed, then the voltage becomes the limitingfactor for jerk. The optimal trajectory can be followed only when the motorcan provide infinite jerk, which requires infinite voltage.The remaining section then outlines a procedure for imposing a jerk lim-ited smooth trajectory. The kinematic profiles used in trajectory generationare illustrated in Figure 3.2. The suboptimal acceleration has a triangularprofile with maximum slopes (i.e. jerk values) at the start and at the endof the valve motion. It requires a slightly higher amax than the optimaltrajectory, which can be seen from Figure 3.1.Given a time t1 during which the initial maximum jerk j1 is applied, thevalue of this maximum jerk is defined as:j1 = 3smax2t2 −t1t1t2 (3.20)The energy lost in the copper windings during a single transition fromclosed to open or from open to closed, with the sub-optimal trajectory isgiven by:Esubopt =integraldisplayI2Rdt = 6s2maxJ2R2t2(t1 −t2)2r2aK2T (3.21)It is interesting to note the ratio of energies of the optimal to the sub-optimal trajectory. As expected the ratio increases for larger values of t1,which leads to the conclusion that a motor with rather small inductance isrequired in order to achieve good energy efficiency:EoptEsubopt =4t22(t1 −2t2)2 (3.22)We now aim our attention towards finding the minimum value for t1.Equation 3.19 indicates that during the initial period where j = j1, the243.3. Trajectory Generationvoltage must be continuously increasing, since the jerk is constant and bothvelocity and acceleration are increasing. Thereafter, the voltage decreases,since jerk is reversed. Thus, it is expected that the maximum voltage willtake place at t = t1. Equations 3.19 and 3.20 for t = t1 lead to a quadraticequation in terms of t1:(3K2Tsmax+2KTt2raU)t21+6smaxLJ+(6smaxRJ−4KTt22raU)t1 = 0 (3.23)The solution to this equation represents the minimum and maximumvalue for t1. The smaller of the two values is the minimum energy solutionfor the triangular trajectory. Note that the fastest trajectory possible witha given motor and fixed supply voltage is the one where the solution toEquation 3.22 reduces to a single real value. The solution to this problemis a quartic equation in terms of t2 that is difficult to solve analytically. Inpractice however, one usually is presented with the problem of finding j1 andt1 for a desired valve travel time. Having picked the largest possible value ofj1, one would usually check whether the required acceleration at time t = t1does not violate the torque constraint. If the required acceleration is toohigh, the transition time is too short or the valve lift is too high.Given that the initial displacement, velocity and acceleration are zero,and values for j1 and t1 from Equations 3.20 and 3.23, the acceleration a,velocity v, and displacement s profiles can be obtained by integrating thejerk profile:a(t) = a(ti)+integraldisplay ttij(t)dt;v(t) = a(ti)+integraldisplay ttia(t)dt;s(t) = v(ti)+integraldisplay ttiv(t)dtThe jerk profile in Figure 3.2 can be written as:j(τ) =j1 0 ≤ t < t1j2 t1 ≤ t < t3j1 t3 ≤ t < t4(3.24)where j1, j2 are the magnitudes of jerk in different regions. IntegratingEquation 3.25 with respect to time, and denoting the maximum acceleration253.4. Design Exampleand deceleration magnitudes with a1 and a2 respectively, the accelerationprofile can be expressed as:a(t) =j1(t−t1) 0 ≤ t < t1a1 +j2(t−t2) t1 ≤ t < t2j2(t−t3) t2 ≤ t < t3a2 +j1(t−t4) t3 ≤ t < t4(3.25)The same idea can be applied to the velocity and position profiles. Forconstant jerk, acceleration profiles are linear, velocity profiles are parabolicand displacement profiles are cubic. The advantage of using a jerk limitedprofile is that triangular acceleration profiled trajectories have smoothervelocity, acceleration and jerk characteristics compared to other profiledtrajectories. The control signals resulting from the utilization of such a ref-erence trajectory will also be smoother, hence reducing the risk of impactingthe drives, or exciting the machine’s structural dynamics.InthesimulationofFFVAsystem, aWaveformGeneratorisprogrammedto generate the reference trajectory. The transition timing and the displace-ment of the valve can be set.3.4 Design ExampleFrom the sections above, two important criteria for motor selection werederived which are summarized as follows:• amax = Tmax2√Jmm• E ∝ JmRK2TThe first criteria shows the maximum acceleration is constraint by twomotor parameters: The maximum torque, and the inertia of the motor. Theenergy consumption for a fixed trajectory and a fixed valve mass providesthe second rule to guide the motor selection process.In addition, energy consumption for a desired transition time with asuboptimal triangular trajectory can also be compared using Equation Design ExampleComparison with other proposed modelsMotor Name QB02302 119007 I2383092NCManufacturer Maccon[27] Pittman[33] MCG[34]Torque Constant KT [Nm/A] 0.076 0.0718 0.066Terminal Resistance R [Ω] 0.24 0.541 1.12Motor Inertia Jm [kg.m2] 2.3E-5 3.1E-5 1.7E-5Peak Torque Tmax [Nm] 7.6 2.19 1.235Acceleration Term Tmax√Jm1585 393 299Energy Cost Term JmRK2T9.56E-6 32.5E-6 43.7E-6Energy Cost E 2.68 9.12 12.3for 6000rpm [J/Cycle]Table 3.1: Motor SelectionIn Table 3.1, three candidates with similar size are listed. The size ischosen in order to provide the minimum inertia that fulfills the linearity con-straint between valve movement and motor movement. Since the QB02302series motor outperforms the other candidates in terms of energy consump-tion and acceleration, it is used in the experimental test bed in Chapter7.It should be pointed out that the QB02302 motor can be ordered withdifferent windings.To make a first approximation, changing the windings from N to N∗affects the motor parameters as follows:K∗T = N∗N KT,R∗ = (N∗N )2R,L∗ = (N∗N )2L (3.26)Note that the energy cost term is not affected by changing the numberof windings. Also, the maximum torque and thus, the available accelerationdoes not change, even though the current required to achieve this torque willbe altered, since the torque constant KT is linearly related to the numberof windings:Imax = NKTN∗Tmax (3.27)273.4. Design ExampleAnother interesting relationshipforthe FFVA system is the jerk availablefor a given maximum supply voltage Umax:j = KTraJL (Umax NN∗ − KTvra−R aJKTra) (3.28)Equation 3.28 indicates that the available jerk scales linearly with volt-age and the inverse of the winding ratio. In addition, the jerk is reducedonce the valve starts moving. To summarize, decreasing the number of wind-ings increases the available maximum jerk. However, the current required toachieve the maximum acceleration is increased at the same time. Selectingthe optimum number of windings then depends on the available voltage, cur-rent, and the type of trajectory chosen to reach the required valve dynamics.For our trajectories, a higher initial jerk leads to lower energy consumption.It is expected then, that a lower winding number improves efficiency at theexpense of higher currents.For the FFVA system with a QB02302 motor, Figure 3.3 shows a plot ofmaximum current, maximum torque and energy consumption vs. windingratio: This plot shows that fewer windings require moderately less energyand a slightly smaller maximum torque. However, these advantages areoffset by a large increase in required current. Note that there is a minimumvalue for maximum current and the winding ratio chosen for the FFVAsystem is close to that minimum value.Before presenting an implementation of a system with the stock QB02302motor, the following chapter derives how to design a custom motor for thisapplication.283.4. Design ExampleFigure 3.3: Winding variation for QB0230229Chapter 4Motor OptimizationThe last chapter showed that motor parameters play an important role inthe energy consumption and the acceleration capability of the FFVA sys-tem. Motor selection criteria were presented that can be used to choosethe best off-the-shelf motor. However, in the FFVA system, the motor isused for a transient application, while the majority of motors on the marketare designed for continuous application. Thus, off-the-shelf motors usuallydo not provide an optimal design for this application. This chapter thenattempts to provide an analytical method to design an optimum motor.Several critical constraints should be considered when such a BLDC motoris designed. First it will be demonstrated that the stator saturation deter-mines the thickness of the permanent magnets used on the rotor. Then aconstraint on magnet demagnetization will provide a relationship betweenthe acceleration of the actuator and the motor length. Thereafter, the needfor a linear relationship between rotor movement and valve movement will beused to define radius of the rotor. Finally, it will be shown, that a relation-ship between rotor and the stator radius governs the energy consumption ofthe actuator.4.1 Stator Saturation ConstraintThe iron core of the stator consists of teeth and slots. The slots are filledwith windings that create a stator field. The teeth are used to guide thestator field due to the current in the stator windings and the rotor field dueto permanent magnets on the rotor. In order to ensure efficient use of thestator material, the stator core should not be saturated. This section showsthat stator saturation can be used to determine an optimal thickness of thepermanent magnets on the rotor.A variety of magnet materials are available to provide the requiredrotating magnetic field in a brushless dc motor. The most popular are304.1. Stator Saturation Constraintneodymium-iron-boron (NdFeB) magnets, which are expensive but have thehighest B−H characteristic. The simplest form of brushless dc motor rotorconstruction uses a cylindrical shaft and a ferromagnetic rotating structurewith a surface on which magnets are affixed. The magnets are radiallymagnetized and the magnet outer surfaces are ground or preformed to beconcentric with the stator inside diameter. The magnets are held in place bya structural adhesive to prevent radial movement during operation. A mag-netic field is generated by the magnets and it passes through the magneticcircuit formed by different parts of the motor.The flux density in the airgap Bgo due to the magnet alone and theacceptable linear current load Ks are important factors in motor design.In this section, we will show how to choose the best value of Bgo. Thisis also called selecting the operating point of the magnet. If a magnet withradial thickness lm is selected, the flux density in the airgap can be expressedby the magnet residual flux density Br:Bgo = lmlgeBr (4.1)where lge is the effective length of the airgap including the distance fromthe stator teeth to the rotor iron core. Usually the effect of slotting is alsoincluded. Approximately, lge = lg +lm.Ideally speaking, reducing the airgap lg could obtain the same Bgo byusing less permanent magnet material. But in practice, the minimum valueof the airgap is set by mechanical considerations. The usual range of lg isabove 0.5mm.Choosingtheoperatingpointofthemagnettobeatthemaximumenergyproduct of the magnet material will result in minimum magnet volume andmagnet cost [35]. However, the resultant average air gap flux density will below (about one half of the magnet Br), and therefore the armature windingwill take a larger portion of the stator volume to provide the larger totalcurrent in order to generate the same torque.Using a thicker magnet results in a more expensive magnet, but increasesthe airgap flux density, reduces the armature current loading, and resultsin a better balance of stator lamination iron and stator copper. But theflux density in the iron core Bc should also be considered before decidingBgo. The maximum flux density in the iron core is usually limited in orderto avoid saturation. For the QB02302 motor, the material of the stator is314.2. Demagnetization Constraint”TRAFOPERM N3”, whose saturation point is about Bs = 2.03T. In orderto leave some margin, it is set conservatively to 1.8T, thus:Bc = wt +wswtBgo < 1.8T (4.2)where ws is the width of each slot and wt the width of each tooth. For mostmachines (including our motors), the slotting of the stator is usually madewt ≈ ws. Thus Bgo ≈ 0.9T is a reasonable choice.The next section shows how the demagnetization constraint affects theacceleration capabilities of the motor. This will lead to a discussion on howto choose the linear current load Ks.4.2 Demagnetization ConstraintThe performance of a BLDC motor used in transient application is mainlydetermined by the maximum acceleration it can provide, thus a high linearcurrent loading is desirable. But the current density in the stator must beconstrained not to demagnetize the permanent magnet. From a demagne-tization curve, a critical point (BD, HD) can be found, which should notbe exceeded if demagnetization is to be avoided. With currently availableNdFeB material, a value of about BD = −0.2T can be achieved below atemperature of 120oC.In a BLDC motor, the flux density is distributed as in Figure 4.2. Thefirst plot shows the geometry of a magnet on the rotor. wp is the width ofeach pole, wm is the span width of the magnet and lm is the thickness of themagnet. The second plot shows BI, which is the sinusoidally distributed fluxdensity created by the stator current. The last plot adds the flux density dueto the magnet alone, Bgo, and BI in order to obtain the total flux densityalong the airgap. Clearly, the flux density of any point on this curve shouldbe kept above BD. If β is the magnet span in mechanical degrees, or simplydefined as β = wm/wp, then:BI,peaksinβ ≤ Bgo −BD (4.3)Since the peak value of BI can be expressed as [36]:BI,peak = 2√2rµ0Ksplge (4.4)324.2. Demagnetization ConstraintFigure 4.1: Demagnetization curve [36]where Ks is the rms linear current density along the stator periphery. No-tation p represents the number of poles. So the demagnetization constraintis given by [36]:Ks ≤ plge(Bgo −BD)2√2rµ0sinβ(4.5)For a PM motor, the torque can be expressed as [36]:T = 2pir2lBg1Kssinγ (4.6)where γ is the angular displacement between the fields produced by themagnet and the stator current. The maximum value is found at sinγ = 1.Bg1 is the rms value of the fundamental space component of the air gap fluxdensity due to the magnet. It evaluates toBg1 = 2√2Bgosinβpi (4.7)Since we know the maximum linear current density Ks (see Equation334.2. Demagnetization ConstraintFigure 4.2: Flux density due to current and magnet [37]4.5), then the maximum torque of a 3-phase motor is given by:Tmax = 2rlplmBr(Bgo −BD)µ0(4.8)In practice the stator length l should be an effective length, thus a lengthfactor kw(since there are windings stretching out of the stator frame at bothends) should be added. Then the equation above turns into [38]:Tmax = 2rlplmBr(Bgo −BD)µ0kw (4.9)This equation does not include saturation of the iron core. Especially forsmall motors, this can lead to substantial errors. Substituting Equation 4.9344.3. Linearity Constraintand 3.12 into 3.14 provides an expression for maximum valve accelerationin terms of geometric dimensions and material properties (the expression ofJm can be found in next section) of the motor [38]:amax = Tmaxra2Jm=√2plmBr(Bgo −BD)kwµ0√piρm√lr (4.10)The equation above shows that the maximum acceleration is propor-tional to the number of pole pairs p:p = 2pir3q(ws +wt)(4.11)where q is the slot number per pole per phase. For small motors, q = 0.5is often used, because it provides a good torque to volume ratio. Thesemotors are called fractional-slot winding motors [39]. In practice, the mini-mum tooth and slot widths are limited because of manufacturing constraints.Thus, p is function of rotor radius r. Substituting Equation 4.11 into theequation above gives:amax =√2lmBr(Bg −BD)kwµ0√piρm√lr2pir3q(ws +wt) = Kα√l (4.12)From the equation above, it can be seen that the maximum accelerationis proportional to √l. Thus, for high acceleration requirements, the rotorlength should be chosen as large as possible, or if there is a constraint onmotor length, then the maximum acceleration available can be estimated.It needs to be pointed out that Equation 4.12 is based on a demag-netization constraint of the permanent magnets, rather than a saturationconstraint of the iron core. Thus, this equation does not provide good quan-titative information of the available acceleration, especially for small motors.It only provides the qualitative guideline that the acceleration is length de-pendent.The previous sections showed how to select the magnet thicknessand the rotor length. In the upcoming section, criteria for rotor radius areprovided.4.3 Linearity ConstraintThe mechanical optimizations shown in chapter 3 were based on the assump-tion that there is a linear relationship between valve and rotor motion. This354.4. Energy Constraintassumption requires that the rotor rotation is small. In practice, one wouldusually constrain the rotor rotation to a maximum value of θmax = 30o, thusthe length of the excenter arm is also constrained:ra =radicalbiggJmm greaterorequalslantsθmax (4.13)This defines the lower limit for the rotor’s inertia:Jm greaterorequalslant s2mθ2max (4.14)In practice, the density of the rotor core and the permanent magnetsattached to it, are very similar. Thus, the rotor can be assumed to be asolid cylinder with density, ρ, motor length, l, and rotor radius, r. Therotor’s inertia Jm can be expressed as:Jm = 12pir2lρr2 = 12pilρr4 (4.15)Substituting Equation 4.13 into Equation 4.15 we find:Jm = 12pilρr4 greaterorequalslant s2m2θ2max (4.16)So,r4l greaterorequalslant 2s2m2θ2maxpiρ (4.17)Since the length of the rotor has been determined by the accelerationrequirement of the application, Equation 4.17 provides a constraint for theminimum rotor radius. At this point the rotor dimensions are fully definedby the valve acceleration requirements, the constraints on stator saturation,and linearity between motor and valve motion. The following section showshow the stator diameter determines the energy consumption of the actuationdevice.4.4 Energy ConstraintIn the FFVA system, the energy loss should be less than 2.5J/cycle. Whenthe motor is designed, the index function JmRK2Tshould be taken into accountin order to minimize the energy loss.364.4. Energy ConstraintFrom above, we know the expression of Jm:Jm = 12pilρr4 (4.18)and the torque constant KT can be derived as [38]KT = TI = 13 ·(Z ·2r·l·Bgo)kw. (4.19)The motor’s terminal resistance R can be expressed by a function ofconductors, motor length, and copper area per slot, Aca:R = f(Z2lAca) (4.20)Then the energy cost term of motor parameter can be rewritten asJmRK2T =12pilρr4f(Z2lAca)19 ·(Z ·2r·l·Bgo ·kw)2∝ r2Aca, (4.21)which shows that the cost term is proportional to r2 and 1Aca, but is inde-pendent of the stator length l or number of conductors Z. If we want toreduce the energy loss, the radius of the rotor should be decreased or thecopper area in each slot increased. The minimum radius is constrained bythe linearity requirement from the previous section. The copper area is con-strained by the slot area and the ability to fill the slot area with copper. Theremainder of this section is then concerned with the relationship betweenstator geometry and copper area in each slot.The copper area in each slot is related to the wire diameter, dw, and thenumber of wires in each slot, nw:Aca = nwpi(dw2 )2 (4.22)The stator slot cannot be completely filled with conductors, since there isalways space left around the wires. The ratio of slot area, Aslot, to conductorarea, Aca, is defined as the filling factor, kfill:kfill = AcaAslot(4.23)374.5. Motor Design ExampleThe slot area is related to the number of slots, Q, the stator inner radius,rsi, the slot height, hs, and the tooth width, wt:Aslot ≈ piQ[(rsi +hs)2 −r2si]−wths (4.24)Then the outer radius of the stator is found as:rso = rsi +(hs +hrs) (4.25)where hrs is the required thickness of the stator back. In Figure 2.4, it canbe seen that the stator back must be larger than half the tooth thickness:hrs ≥ 12wt (4.26)4.5 Motor Design ExampleThe DC motor (QB02302) chosen for the FFVA system has the parametersshown in Table 7.1. This is a very good motor, but it was not specificallydesigned for our application. This section then shows how to optimize themotor for the FFVA system.1. Motor length l: The acceleration capability of the FFVA system is pri-marily determined by the length of the motor (see Equation 4.12). Forthe stock motor, the maximum valve acceleration can be determinedas: amax = Tmaxra2Jm = 6300m/s2. The ideal triangular trajectory shownin Section 3.3 for a lift of 8mm and an engine speed of 6000rpm is ap-proximately 2500m/s2. Clearly, the stock motor can provide higheraccelerations than necessary. By reducing the motor length to onehalf of its original length, the maximum possible acceleration reducesto 4400m/s2. This is still more than the ideal triangular trajectoryprescribes and it leaves room for the suboptimal performance to intro-duce more inductances.2. Rotor Radius r: In the last step, the length of the motor was decreased,thus the rotor inertia Jm becomes smaller. The linearity constraintneeds to be verified. Equation 4.17 can be rewritten as:r4 greaterorequalslant 2s2m2θ2maxpiρl384.5. Motor Design ExampleFor lift s = 8mm, valve’s mass m ≈ 40g, motor length l = 28mm thedensity of steel ρ = 7800kg/m3, and θmax = 30o, the limit of r is givenby:r greaterorequalslant 12.8mmThe rotor radius is kept at 14mm, still fulfills the linearity constraint.3. Slot Area Aslot: The two steps above are used to determine the rotorsize. Energy consumption determines the stator size. It was shownin Section 3.4 that the energy consumption of the stock system isexpected to be at least 7% larger than required. Thus, the goal of thisstep is to reduce the cost term JmRK2Tof the optimized motor to half ofthe value of the original QB02302 motor. The energy cost term has notbeen affected by the change in rotor length and the parameters left forus to manipulate are mainly the slot height hs and wire diameter dw.The number of conductors will be kept. Thus, since the rotor lengthwas cut in half, the inductance of the motor should also be halved.This should allow for more energy efficient trajectories.(a) First, the slot area and related parameters for the original mo-tor QB02302 are determined. The measured parameters are slotwidth ws = 5.1mm, tooth width wt = 5.0mm, number of wiresper slot nw = 72, stator inner radius rsi = 14.5mm, numberof slots Q = 9, airgap lg = 0.5mm, thickness of stator backhrs = 4.65mm. wire diameter dw = 0.723mm [40] (Gauge 21:constant maximum current is about 9A, transient maximum cur-rent is usually 6 ∼ 7 times of that, which is around 50A; theresistance is 42.0Ohm/km) and slot height hs = 8.5mm.According to Equation 4.22 the copper area of one slot is givenby:Aca = nwpi(dw2 )2 = 29.6mm2Thus, Equation 4.24 provides the expression for the slot area:Aslot = piQ[(rsi +hs)2 −r2si]−wths = 68.8mm2The fill factor can be calculated by using Equation 4.23:kfill = AcaAslot= 43%394.5. Motor Design ExampleThen outer radius of the stator is found as:rso = rsi +(hs +hrs) = 27.65mmAdditionally, the terminal resistance of the motor can be esti-mated by:R = 23 ×42.0Ohm/km×Zl ≈ 0.254Ohm (4.27)The first constant term 23 was applied because of the relation be-tween the total terminal resistance (or line resistance) and phaseresistance in the motor. It can be seen that the estimation isfairly close to the measured value given in Table 7.1, which is0.24Ohm.(b) In the next step, the wire diameter and the slot height are ad-justed in order to provide for lower energy consumption. The slotheight and the wire diameter are set to new values: hs = 14mm,dw = 1.15mm (Gauge 17: constant maximum current is about19A, transient maximum current is usually 6 ∼ 7 times of that,which is around 120A; the resistance is 16.6Ohm/km). Now fol-lowing the same calculation procedure.Aca = 74.8mm2Aslot = 140mm2kfill = 53%rso = 35mmThus, the copper cross section area and slot area have both in-creased. The filling factor becomes a little higher, but it is still ina reasonable range. The outer radius has increased by 7.35mm.Most importantly, the cost term JmRK2Thas decreased. From Equa-tion 4.21, we know the copper loss of the system for an FFVAsystem with constant rotor radius is inversely proportional to thecopper area:E ∝ JmRK2T∝ 1Aca(4.28)Which means theoretically, the copper loss now is 29.6mm274.8mm2 =39.6% of the value that QB02302 consumes.404.5. Motor Design ExampleAlso, the terminal resistance of the motor can be estimated byR = 23 ×16.6Ohm/km×Zl ≈ 0.050Ohm. (4.29)However, the end effect of winding becomes more dominant. Since themotor length is reduced, the portion of noneffective winding which isstretching out of the stator increases, which means the actual value ofterminal resistance will be bigger than the calculation.In this chapter, major constraints of designing an optimized motor forthe FFVA system were studied and a design procedure was presented. Theprocedure is systemically shown in the Figure 4.3.Figure 4.3: Diagram of optimization procedureThe derivation was verified by numerical calculation of the QB02302 pa-rameters. Finally, the parameters of the QB02302 motor were optimizedusing approximate analytical expressions in order to provide better perfor-mance and a shorter motor. In the next chapter, the predicted performanceof the optimized motor will be verified using finite element calculations.41Chapter 5Finite Element Analysis ofDC MotorIn the FFVA system, a brushless DC motor drives the mechanical partand its copper loss is responsible for most of the energy losses of the ac-tuation system. In a conventional internal combustion engine, the energyloss for each intake valve is about 2.5J/cycle. Right now, the experimentalFFVA platform using a stock QB02302 motor has an energy loss of about2.7J/cycle. In order to make the system compare favorably with the conven-tional ones, the energy loss must be reduced. According to the theoreticalderivation, the energy cost term JmRK2Tshould be minimized by optimizingmotor parameters. In the last chapter, an optimized motor was given byderivation and calculation. In this chapter, both the stock QB02302 mo-tor and the optimized motor are simulated using the finite element analysissoftware Maxwell SV. Then the parameters of the two models are compared.This chapter first introduces the different topologies of the motors. Thenthe theoretical background of the FEM calculation is briefly explained. Fi-nally the results of simulating the two motors are presented.5.1 Brushless DC Motor TopologyBecause of the motor’s symmetry along the axis of the shaft, a 2D modelis sufficient to analyze the important properties, while the complexity ofthe calculations are reduced. The transverse sections are given in Figure 5.1and Figure 5.2. The structures of both motors are also symmetrical by every120o, only one third of the layout is simulated, which is sufficient and concisefor the Finite Element Analysis. Comparing the two models, it can be seenthat the rotor structure is kept the same and the stator structure is changedby varying the slot height and outer diameter of the stator.425.2. Maxwell EquationsFigure 5.1: QB02302 Figure 5.2: Optimized motor5.2 Maxwell EquationsIn electromagnetism, Maxwell’s equations are a set of four partial differentialequations that describe the properties of the electric and magnetic fields.Here, one of them is mainly used, which is called Ampere’s circuital law:contintegraldisplayL−→Hd−→L = integraldisplayS−→J d−→S +integraldisplaySd−→Ddt d−→L (5.1)Here, −→H is the vector of the magnetizing field, −→J is the vector of the freecurrent density and −→D is the vector of the electric displacement field. Theconstitutive equations are as follows:−→D = ε−→E−→B = µ−→H−→J = σ−→Ewhere −→E is the vector of the electric field, −→B is the vector of the magneticfield, ε is the electric permeability, µ is the magnetic permeability and σ isthe electric conductivity.435.3. Governing Equations in 2D Electromagnetic Field5.3 Governing Equations in 2D ElectromagneticFieldFrom the equations given above, 2D electromagnetic field governing equation[41] can be derived:−→∇ ×(1µ−→B) = −→Jt (5.2)Or,∂∂x(1µ∂Ax∂x )+∂∂y(1µ∂Ay∂y )+Jz = 0 (5.3)where Jt is the total surface current while Jz is the component of Jt in thez-direction, and the flux density vector −→B is defined in terms of the potentialvector −→A using the auxiliary equation:−→∇ ×−→A = −→B (5.4)The boundary conditions areΓt : 1µ1∂−→A1−→n +1µ2∂−→A2−→n = JsΓu : −→A = −→A0(5.5)The natural boundary condition is represented by Γt while the essentialboundary condition is Γu. The equivalent surface current density Js equalsthe summation of change rate of the potential vector along the normal vectorto the interface of the two fields, while the subscript refers to different partson each side of the boundary. −→n is the normal unit vector. The potentialvector on the border equals to the prescribed value. As long as we have astrong form of the governing equations for the 2D electromagnetic field, theweak form can be derived by using the minimal potential energy principle orthe Galerkin method. Then, the weak form can be applied to each meshedelement to obtain the stiffness matrix and the damping matrix.So far, the general equations for a 2D electromagnetic field analysis havebeen defined. But for different parts of the BLDC motor, the forms of theequations are different.445.3. Governing Equations in 2D Electromagnetic FieldIn the laminated stator, the iron core and air gap areΩ1 : ∂∂x(1µ∂Ax∂x )+ ∂∂y(1µ∂Ay∂y ) = 0Γu : −→A = 0(5.6)Here, Ω1 represents the field in the stator. Jz becomes 0 since there isno free current going through the core and the eddy current can be omittedsince the core is formed by stacked silicon steel. Beyond the inner and outerboundary of the core, the potential vector is 0.In the rotor iron core,Ω2 : ∂∂x(1µ∂Ax∂x )+ ∂∂y(1µ∂Ay∂y ) = σ∂A∂tΓt1 : 1µcore∂−−−→Acore−→n +1µair∂−−→Aair−→n = Js1(5.7)The term σ∂A∂t exists in the solid rotor iron core where eddy currentscannot be ignored.There are two models which are commonly used to represent perma-nent magnets: the magnetization vector method and the equivalent currentsheet method. The magnetizing vector method is used in this model for thepermanent magnets:Ω3 : ∂∂x(1µ∂Ax∂x )+ ∂∂y(1µ∂Ay∂y ) = ∇×(1µBr)Γt2 : 1µPM∂−−−→APM−→n +1µair∂−−→Aair−→n = Js2(5.8)Here, the free current density is not 0 anymore, because there is inducedcurrent in the permanent magnet when the magnetic field is changing. Thelinear current density between air and the permanent magnet gives the nat-ural boundary condition.455.4. Finite Element Simulation for BLDC MotorIn the windings, the following conditions hold:Ω4 : ∂∂x(1µ∂Ax∂x )+ ∂∂y(1µ∂Ay∂y ) = −NISΩ5 : ∂∂x(1µ∂Ax∂x )+ ∂∂y(1µ∂Ay∂y ) = NISU = RI +Ldidt + NLS (−integraldisplayn∂A∂t dΩn +integraldisplayp∂A∂t dΩp)(5.9)Since there is free current going through the windings in the positiveor the negative direction, the current density can be expressed as the totalcurrent over area. The third equation is the coupling of the field and theexternal drive circuit. The boundary conditions were already given in theprevious three parts.These are governing equations for different parts of motors. They are notdirectly solved by the FEA software, because they are all partial differentialequations. They have to be transferred to a weak form, which then can besolved numerically by the software.5.4 Finite Element Simulation for BLDC MotorThe previous sections described the motor geometry, the governing equa-tions, and the boundary conditions of the motor. These models are imple-mented in Maxwell SV using Galerkin’s method for 3-node elements. Thissection describes the meshing process, the Galerkin’s formulations, and typ-ical plots of flux density and current density that are obtained with MaxwellSV.Mesh generation for the FEM should be simple and robust, and the rotormesh should be allowed to rotate easily. In this approach, the FEM mesh ofthe cross section of the BLDC motor is divided into three parts: the stator,the rotor and the magnet, with each including a part of the air gap. Whenthe rotor is rotated according to the time step, the shape of the mesh forboth the stator and rotor can be kept constant and only the coordinates ofthe rotor mesh and the periodic boundary condition on the interface needto change. Therefore, in this approach the stator mesh and the rotor meshare required only need to be generated once. This can greatly reduce thecomputing time required to generate the FEM mesh at each time step. A465.4. Finite Element Simulation for BLDC MotorFigure 5.3: Mesh resulttypical mesh for the stock QB02302 motor is shown in Figure 5.3. It isautomatically generated by the software, but a finer mesh along the air gapwas specified manually, because this is the most important part of the fluxdistribution. Additionally, the software checks for convergence and suggestsfiner meshes, if the convergence criteria are not met.Galerkin’s method is usually employed for the finite element formula-tion. This method uses particular weighted residuals for both the weightingfunctions and the shape functions.According to the Galerkin’s method, for a 3-node triangular element, themagnetic vector potential can be expressed as [42]A =3summationdisplayi=1NiAi (5.10)Here A is the function of the vector potential, Ni is the element shape475.4. Finite Element Simulation for BLDC Motorfunction and the Ai is the approximation of the vector potential at the nodesof the element.The Galerkins formulation of the laminated stator iron core and air gapintegraldisplayintegraldisplay(∂Ni∂x ∂∂x 1µ3summationdisplayj=1NjAj + ∂Ni∂y ∂∂y 1µ3summationdisplayj=1NjAj)dxdy = 0 (5.11)In matrix form, this turns into[1µ[G]{A}] = 0 (5.12)For the rotor iron core, the formulation isintegraldisplayintegraldisplay(∂Ni∂x ∂∂x 1µ3summationdisplayj=1NjAj + ∂Ni∂y ∂∂y 1µ3summationdisplayj=1NjAj +σNi∂Ai∂t )dxdy = 0 (5.13)In matrix form, this can be written as[1µ[G]{A}+σ[T]∂A∂t ] = 0 (5.14)For the permanent magnet, the formulation can be expressed asintegraldisplayintegraldisplay 1µ(∂A∂x∂Ni∂x +∂A∂y∂Ni∂y )dxdy =integraldisplayintegraldisplay µ0µ (Mx∂Ni∂y −My∂Ni∂x )dxdy (5.15)In matrix form[G]A = Brx[ci]−Bry[bi] (5.16)For the winding, the equation isintegraldisplayintegraldisplay(∂Ni∂x ∂∂x 1µ3summationdisplayj=1NjAj + ∂Ni∂y ∂∂y 1µ3summationdisplayj=1NjAj +NiNIS )dxdy = 0 (5.17)Again, the equation can be rewritten in matrix form:[1µ[G]{A}+{Q}NIS ] = 0 (5.18)485.5. Evaluation of Optimized MotorFor the circuit equationV = LS[integraldisplaynNi∂A∂t dΩn −integraldisplaypNi∂A∂t dΩp]+Ri+Ldidt (5.19)In matrix form:V = LS[({Q}{∂A∂t })n −({Q}{∂A∂t })p]+Ri+Ldidt (5.20)where,Tij =integraldisplayintegraldisplayNiNjdxdy =braceleftbigg∆e6 if i = j∆e12 if i negationslash= jQ =integraldisplayintegraldisplayNidxdy = ∆e3G =integraldisplayintegraldisplay(∂Ni∂x ∂Nj∂x + ∂Ni∂y ∂Nj∂y )dxdy = bibj +cicj4∆eand ∆eis the triangular area of the element.The field equations above and the circuit equation have to be solvedsimultaneously. Rotor movement has to be coupled. The coefficient matrixis symmetric.The computed steady-state flux distributions when maximum current100A is applied in the stator winding is shown in Figure 5.4 (QB02302),which indicates that the iron core is not saturated even maximum currentis applied. Forces and torques are calculated by integrating the Maxwell’sstress tensors along a closed path in the air gap.5.5 Evaluation of Optimized MotorThe simulations in the last section need to be compared to the analyticalderivations from Chapter 4. The properties of the stock and the optimizedmotors are shown as in Table 5.1. The parameters of the optimized mo-tor are given by both the FEM method and the analytical method. In thesimulation, eddy currents and displacement currents are neglected. Thepermeability is linear. The iron core material is homogeneous. These as-sumptions are widely used in modeling DC and AC machines, permanentmagnet devices, transformers and other electrical equipments [43]. In thetable, it can be seen that the optimized motor has a smaller energy cost495.5. Evaluation of Optimized MotorParameter QB02302 Optimized Optimized(FEM) (Theory)Outer Radius of Stator [mm] 27.65 35 35Length of stator core [mm] 56 28 28Wire Diameter [mm] 0.7229 1.15 1.15Torque Constant KT [Nm/A] 0.076 0.042 0.036Terminal Resistance Rc [Ohms] 0.24 0.067 0.050Motor Inertia Jm [kg.m2] 2.3E-5 1.5E-5∗ 1.5E-5Energy Cost Term JmRcK2T9.56E-6 5.60E-6 5.79E-6Table 5.1: Comparison of motor parametersterm, which means that it consumes less energy for completing the sametransition. Also, there is good agreement between the FEM simulation andthe analytical expressions. The parameters of size are inherently the samesince the models are identical. The difference of energy cost term betweenFEM and theory is mainly caused by two parameters: motor resistance andtorque constant. The motor resistance given by the software includes theextra windings stretching out of the stator, which is not estimated in ourtheocratical calculation. The torque constant in the analytical calculationis an estimated value, with some assumptions, such as the flux density inthe iron core is uniform and the magnet thickness is even. The FEM modelis likely closer to the true motor parameters.The value of the energy cost term in the optimized motor is almost halfof that of the stock QB02302. Thus, the energy loss for the same operation iscut down to half in theory. After optimizing the geometry of the stator, thequantity of material used in the laminated core is increased. Even thoughthe core loss has actually increased, it is relatively small comparing to thecopper loss. It can be seen that the overall performance of the optimizedmotor is far better than the stock motor QB02302.This chapter used a finite element simulation in order to validate thetheoretical predictions of the optimized motor. This was achieved by sim-ulating the original QB02302 motor and the new optimized motor. TheQB02302 motor compared well with the specification sheet and the opti-mized motor compares well with the theoretical predictions from Chapter4. The parameters obtained with the FEM model for the optimized motorwill be used in Chapter 7 in order to simulate the overall actuation system.505.5. Evaluation of Optimized MotorFigure 5.4: Flux density distribution of the optimized motor51Chapter 6Control StrategyIn this chapter, the technology for controlling the FFVA system is discussed.The main function of the control system is to move the valve from the closedto the opened position (and vice-versa) avoiding noise, which is caused bynonzero seating velocity. Similar to typical modern servo control systems, acascaded control architecture is employed (see Figure 6.1). A conventional 3phase inverter provides PI current control and commutation using measuredvalues of position and current as well as reference current. The referencecurrent is provided by a PD+Feedforward position controller that are im-plemented in a dSpace rapid prototyping system. The position controllerreceives its reference position from an energy minimized trajectory genera-tor that is also implemented in dSpace. The algorithms for the trajectorygenerator have been provided in Chapter 3. Positions measurements areprovided by an encoder. In order to minimize noise when deriving velocityfrom the position signal, a state observer is employed. A detailed descriptionof the different parts of the controller follows in this chapter.Figure 6.1: Diagram of control units526.1. 3 Phase Inverter6.1 3 Phase InverterThe 3 phase inverter provides commutation and current control. Commuta-tion is the process of switching current to generate a rotating magnetic field.In brushless systems, commutation is accomplished electronically using a ro-tor position feedback device. The rotor position sensors may be magnetic,optical, or any type of device that provides sufficiently accurate and reliableinformation on the motor position. In general, the best position for commu-tation is that point at which the back EMF waveform is ”centered” betweencommutation points.In addition to commutation, the 3 phase inverter also provides PI currentcontrol. Thus, to the outside the 3 phase inverter combined with the BLDCmotor looks like a single phase DC motor plus inverter, because the 3 phaseinverter takes on the function of the mechanical commutation device foundin a conventional single phase DC motor. It is thus possible to model the3 phase inverter and brushless DC motor as an equivalent single phase DCmotor. A block diagram of this representation together with the PD positioncontroller is shown in Figure 6.2. The position controller is built around thecurrent controller. Usually in cascaded control loops, the inner current loophas a bandwidth ωi, that is considerably higher than the bandwidth ωp, ofthe outer position control loop. This allows independent tuning of the twocontrol loops. Then, the current controller is shown in Figure 6.3:Ignoring the back EMF due to motor speed, the transfer function of thecurrent controller shown in Figure 6.3 can be written asI(s)Iref(s) =Pis+KiLs2 +s(R +Pi)+Ki =PiL s+KiLs2 +s(R+PiL )+ KiL (6.1)The proportional gain Pi and the integral gain Ki of the PI controllercan be derived from desired bandwidth of the current controller, ωi (usually,ζ is close to 1):ω2i = KiL ; 2ζωi = Pd +RLThen,Pi = 2ζωiL−R; Ki = ω2i LThe value of the ωi is usually selected to be approximately five timeshigher than the bandwidth of the position controller.536.2. Position (or PD) Controller6.2 Position (or PD) ControllerPosition control can be implemented in a variety of different ways. Typically,Either a Lead lag controller or a PD controller are used for this task. In ourcase we have chosen a PD controller because it provides a simple strategy toset bandwidth and damping for the position loop. It also does quite well inrejectingdisturbancesanditfairlyrobusttowardsmodeluncertainties. Oncethe gains of the PI controller are determined, the current can be regulatedfast and accurately. For the position controller, the current controller canbe idealized as the unit gain block shown in Figure 6.4.The transfer function (Bm can usually be neglected which reduces thecomplexity of the transfer function) for position control can be written asθ(s)θref(s) =Kds+PdJs2 +Kds+Kd =KdJ s+PdJs2 + KdJ s+ PdJ (6.2)The proportional gain Pd and the derivative gain Kd of PD controllercan be derived from the mechanical resonance frequency ωp (usually, ζ isclose to 1):ω2p = PdJ ; 2ζωp = KdJThen,Pd = ω2pJ; Kd = 2ζωpJThe value of ωp needs to be sufficiently high in order to allow tracking ofthe reference trajectory. For the FFVA system the trajectories at 6000rpmcontain a fundamental frequency component at approximately 100Hz withvery few harmonics. Thus it is sufficient to set the bandwidth of the positioncontroller to 350Hz or ωp = 700×pirad/sec.6.3 States ObserverThe PD position controller requires measured values of position and velocity.In commercial servo applications, resolvers or encoders are commonly usedfor measuring position. Velocity is either found by digitally differentiating546.3. States Observerthe position signal or by employing a tachometer. For the FFVA applicationin a real engine, encoders would not be suitable, because they are too ex-pensive and cannot withstand the extended temperature range found in thecylinder head. Inductive pickups or hall sensors are much likelier solutions.However, in the test bed used in this thesis, an encoder is used, because itis readily available and provides excellent position resolution as well as highbandwidth.The principal operation of the optical encoder is explained here. The en-coder consists of light sources, a slotted disk, photo detectors, a bearing-unitand signal processing circuits. After the signal light passes through the slitson the the rotating disk, it is captured by photo detectors, and transducedto an electronic signal. There are two types of disks, an incremental and anabsolute type disk. However, creating high resolution absolute encoders ismore difficult and most encoders are of the relative type.The encoder chosen for the FFVA test bed has a resolution of 20,000 linesper revolution, which provides a highly accurate measurement of position. InSimulink, this encoder can be modeled by a ”Quantizer” with a quantizationinterval of 2pi/80000.The PD controller requires a position and a velocity measurement. Toavoid additional hardware it is desirable to derive the velocity measurementfrom the position measurement. Even though the resolution of the directposition measurement is relatively high, the differentiation operator ampli-fies high frequency noise and reduces the resolution by the inverse of thesampling time:resolution(ω) = resolution(θ)SamplingTimeresolution(α) = resolution(ω)SamplingTimeSince the typical sampling time is 0.025ms, the resolution for velocityand acceleration using a simple backward difference operator deterioratesdrastically. The quantization noise on the measured velocity is small forthe encoder type chosen in the experimental setup. However, real sensorsin actual engine applications would usually provide a much lower resolutionthat would then lead to significant quantization errors in the derived velocitymeasurements. Alowpassfilter(LPF)canbeintroducedtoreducethisnoise556.3. States Observerand quantization errors, although it introduces a delay. The cutoff frequencyof the LPFs should be high compared to the bandwidth of the position loopsince this delay may deteriorate the performance of the control system.In order to get better velocity estimation, a Kalman filter can be used.The specific Kalman filter designed for FFVA application is shown here.The transfer function of a DC motor is generally described byθ(s)e(s) =KT(Jms+bm)(Ls+R)1+KB KT(Jms+bm)(Ls+R)1s (6.3)The numerical values for the parameters of the DC motor is given inTable 7.1.When we design a discrete Kalman Filter for the system, discretization[44] should be done. The state vector is defined as:q =θαωIf we set the sampling time at 0.25e−4ms, and use the parameters givenabove, the discrete state space can be calculated:A =1 0.001529 00 0.9794 00 121.9 0.9999 B = 1.0e−4000.001529C = bracketleftbig1 0 0bracketrightbig D = 0The predictor corrector type procedure of the Kalman filter can then bewritten asq(k) = ¯q(k)+G(k)[y(k)−C¯q(k))] (6.4)¯q(k +1) = Aq(k)+Bu(k) (6.5)G(k) = M(k)CT[CM(k)CT +Rv]−1 (6.6)P(k) = M(k)−G(k)CM(k) (6.7)M(k +1) = AP(k)AT +Rw (6.8)where ¯q(k) is the predicted state estimate at the sampling instant k, andq(k) is the actual state estimate. G(k) is the Kalman gain. M(k) is the566.3. States Observercovariance of the prediction errors. Matrices Rv and Rw are the covariancematrices of the observation noise, and disturbance signals respectively.The covariance of the input disturbance in a real engine cylinder are notestimated in our research. A large numerical value is used in order to ensurethat sufficient robustness towards disturbances is achieved. The actual valueof the covariance of the input disturbance was determined by observing thecontrol stability of the actuator when exposed to different types of frictionforces.Generally, the estimation of Rv is based on the assumption that it is truerandom noise with a Gaussian form and a standard deviation comparableto the size of the least significant bit of the sensor. Then the matrix has thefollowing form:Rv = cov(θ) = [E(θ2)] (6.9)For sensor quantization, the error probability for any one sample is uni-form within the region −0.5 to 0.5, and zero elsewhere. The covariance ofthe noise for one sample can be calculated as:Rv =integraldisplay ∞−∞integraldisplay ∞−∞xpθ(x)×xpθ(x)dxdx=integraldisplay 0.5−0.5integraldisplay 0.5−0.5xpθ(x)×xpθ(x)dxdx= 2(0.5)33 = 0.0833(6.10)where, pθ(x) is the function of probability.The Kalman Filter is simulated in Simulink together with other systemcomponents. Simulation results comparing the performance of different fil-tering techniques are given in chapter 7. They show the advantage of theKalman Filter over direct differentiation and low pass filtering.576.3. States ObserverFigure 6.2: Cascaded control structure586.3. States ObserverFigure 6.3: Current controller596.3. States ObserverFigure 6.4: Position controller60Chapter 7System Simulation andExperimental ValidationIn the previous chapters, two setups were introduced. The first setup usesa stock QB02302 motor, and the second setup uses an optimized custommotor that provides lower power consumption.The first part of this chapter describes the components of an experimen-tal test bed used in this study. The second part of this chapter comparesthe transition performance of the two motors using a Simulink simulationfor typical engine operating scenarios. The third part of this chapter looksat the robustness of the actuation system towards parameter variations ofthe mechanical design and variations of the motor parameters. The fourthpart of this section focusses on the ability of the control system to rejectexternal disturbances due to combustion pressures or friction. Finally, thefifth part of this chapter describes the experimental results obtained withthe stock QB02302 setup.7.1 Experimental SetupThe experimental test bed drives a single exhaust valve of a Honda cylinderhead (see Figure 7.1). A block diagram of the FFVA system is shown inFigure 6.1. It contains a dSpace1103 controller board that creates trajecto-ries and performs position control. For position measurements, a 20000 lineencoder from Quantum devices is used. The control board performs its tasksat 40kHz in order to match the PWM frequency of the subsequent 3 phaseinverter from Maccon GmbH. The inverter performs current control andcommutation using high speed PWM controlled power MOSFETs that canregulate up to 100A per phase. The inverter internally uses LEM modulesto feed the current controllers. In addition, three external LEM HTP100-617.2. Simulation of Transition PerformanceFigure 7.1: System hardwareP current probes are employed to measure and display currents with thedSpace system. The inverter drives a QB02302 motor that is mounted to asmall cylinder head from Honda. The light weight excenter arm is fabricatedin aluminum and has a length of 23mm in order to match the 37g valve tothe inertia of the motor. The excenter arm and the valve are joined using aconnecting rod made from 2mm piano wire. Table 7.1 lists the parameters(QB02302 with customized winding) of the FFVA system.7.2 Simulation of Transition PerformanceBefore building an experimental setup, the overall system is simulated usingSimulink. All mechanical, electrical and magnetic components of the systemare included in this simulation.627.2. Simulation of Transition PerformanceQB02302 with customized windingTorque Constant KT 0.056 VoltsBack EMF constant KB 0.056 V/rad/sPeak Current Ip 100 AmpereTerminal Resistance R 0.13 OhmsTerminal Inductance L 0.15 mHWire Diameter dw 0.7229 mmMotor Inertia Jm 2.3E-5 kg.m2Airgap Flux Density Bg ∼ 0.9 TeslaMagnet Thickness lm 3.5 mmEffective Airgap lge 4.05 mmStator Inner Radius rsi 14.5 mmStator Outer Radius rso 27.5 mmMotor Length l 56 mmNumber of Phases 3Number of Poles 6Number of Slots 9Number of Conductors per Slot 36Table 7.1: Motor ParametersTwoseparatesimulationsareperformed. First, thestockmotorQB02302system is simulated and its performance is estimated. Second, the optimizedmotor is simulated in order to compare its possible performance improve-ment with the predictions from the design procedure.The transition performance of the closed loop controlled system can bequantified by using the following three indices [45]:Transition Time: The time it takes for the valve to move from 5% of themaximum lift to 95% of the maximum lift.Valve Seating Velocity: The velocity of the valve when it contacts thevalve seats.Energy Loss: The copper loss per valve per transition.The initial simulation of the actuation system with the stock QB02302motor is based on the parameters listed in Table 7.1.A number of different operating conditions are simulated to demonstratethe flexibility and performance of the FFVA system. Figure 7.2 shows the637.3. Simulation of the Robustness Towards Parameter Variationssimulated valve lift curves and Figure 7.3 depicts the corresponding energyconsumptions.The dark blue curve shows a typical 8mm valve lift curve for 6000rpm,which corresponds to t2 = 2.4ms. As predicted in Section 3.4, this tra-jectory requires 1.35J/transition which is slightly more than the desired1.25J/transiton. This problem can be alleviated by reducing the lift. Atrajectory with half the lift and the same transition time is shown in greenand it requires approximately 0.35J which is less than a third of the energyconsumed for twice the lift.In practice, the required lift reduction would be much smaller in order toachieve the desired energy consumption. The red curve shows an 8mm liftcurve for 3000rpm. Since the additional valve open time was achieved byinserting extra time with the valve completely open, rather than reducingthe valve accelerations, the energy consumption is still approximately 1.35Jin every transition. In practice, one would likely reduce the acceleration inorder to find a compromise between engine performance and valve energyloss. The light blue curve represents a 4mm valve lift curve at 8000rpm.Compared to the case of 6000rpm with the same lift, this mode requiresalmost three times the energy. This highlights the nonlinear relationshipbetween energy consumption and transition time.Even though the setup with the stock QB02302 motor performs quitewell in the simulations, the energy consumption at high rpm is slightlylarger than desired. The optimized custom motor was designed to addressthis problem in Chapter 4. Figure 7.4 shows the displacement curves andenergy consumption for simulating the optimized motor at 6000rpm en-gine speed. The energy consumption for this setup has been reduced from1.35J/transtion to 0.66J/transition. This corresponds well with the pre-dictions shown in Table Simulation of the Robustness TowardsParameter VariationsThe system parameters such as valve mass m, excenter arm length ra, motortorque constant KT and winding resistance R can shift from the nominalvalues due to manufacture accuracy, abrasion, temperature or other factors.In the simulation, the values of the listed four parameters are all increased647.3. Simulation of the Robustness Towards Parameter Variationsby 30% from the nominal value. Each parameter is varied individually inone simulation.The results of these simulations are shown in Figure 7.5 and they demon-strate that the control system is able to compensate for a wide range ofparameter variations, since all the motion curves including position, veloc-ity and acceleration are still accurately following the reference trajectories.However, energy losses are different. The sensitivity of the energy con-sumption towards parameter variations can be estimated by taking partialderivatives of Equation 3.10 with respect to the parameters being varied.For the parameters studied here this leads to:δEE ≈∂E∂mδmE =δmm (7.1)δEE ≈∂E∂RδRE =δRR (7.2)δEE ≈∂E∂KtδmE = −2δKtKt (7.3)δEE ≈∂E∂raδraE = 0 (7.4)Note that since the optimum excenter arm length was chosen to provideminimum energy consumption, the derivative of the energy with respect toarm length and hence the sensitivity in Equation 7.4 need to be zero. It isparameter stationary estimated sensitivity simulatedpoint δEE sensitivityValve mass m 0.037g 30% 38%Motor resistance R 0.13Ohm 30% 31%Torque constant Kt 0.056Nm -60% -42%Excenter arm length ra 0.023m 0 10%Table 7.2: Sensitivityexpected that actual sensitivity values will differ from the nominal values,because large changes are made to the parameters and Equations 7.1 to 7.4provide only a linearized approximation. Table 7.2 shows a comparison ofthe estimated and the simulated sensitivity values. It demonstrates that thetorque constant, the resistance, and the valve mass have a large influence on657.4. Simulation of Disturbance Rejectionthe energy consumption, whereas the excenter arm length is not very sen-sitive. This lets us conclude, that manufacturing tolerances of the linkagesystem do not need to be very high in order to guarantee low energy con-sumption. On the other hand all the other parameters need to be designedcarefully.7.4 Simulation of Disturbance RejectionThe FFVA system is designed for intake valves where only moderate com-bustion pressure is expected on the valves. The shape of the pressure curveduring the opening or the closing transition is not well defined. Other distur-bances could include some degree of viscous damping or coulomb damping inthe motor or in the valve guides. In this investigation we attempt to combineall of these causes using disturbance torques on the motor that are modeledwith a viscous friction coefficient of 0.015Nms/rad and a coulomb coeffi-cient of approximately 1.15Nm. Each of the two parameters corresponds toan equivalent disturbance force of 50N on the valve.It should be pointed out, that the original controller was not designedto compensate for disturbances in the resting positions at either end ofthe valve motion. In order to achieve low steady state errors under thesecircumstances, the original PD position controller needs to be extended toa PID controller. The I term is used to reduce steady state error and thePD terms are defined in the same fashion as in the original design.Figure 7.6 shows simulation results that indicate that the system is ableto cope with significant disturbance forces. The additional energy requiredby the actuation system is very close to the energy dissipated in friction.We conclude, that the efficiency of the actuation system in the presence ofdisturbances is still close to optimal.7.5 Simulation of Low Resolution Sensor with aKalman FilterThe experimental system used in this thesis uses a very high resolution op-tical encoder. In a real engine, this is not a suitable sensor, because it istoo expensive and cannot withstand the harsh environmental conditions. Ahall sensor is a more likely candidate, and it would usually have a resolu-667.6. Experimental Resultstion somewhere between 7 and 10 bits. At the high sampling rates usedfor this system, the low resolution would lead to considerable quantizationerror, that would consequently introduce large noise in the position signal.For eliminating measurement noise we will now compare a low pass filterand a Kalman filter. The low pass filter is a simple backward differenceimplementation of a continuous first order lag with a break frequency thatis ten times higher than the position loop bandwidth. The Kalman filterimplementation and the selection of the covariances for the disturbancesand the measurement follow the guidelines shown in Chapter 6. Figure 7.7shows the systems response using an 7 bit sensor with 1 bit measurementnoise and different feedback strategies. When the sensor signal and a di-rect backwards differentiator are used, the system is unstable. When thesensor and the backwards differentiator are combined with low pass filterswith bandwidths at 10 times the bandwidth of the position controller, theoscillations are reduced but not eliminated. Only the Kalman filter, is ableto provide a stable response for the low resolution sensor.The reason for the difference in control performance can be found bycomparing position and velocity errors for the different feedback signals.Figure 7.8 then shows this comparison. As expected, the position error ofthe Kalman filter is slightly smaller than the actual sensor signal. However,the low pass filter demonstrates considerable phase lag which manifests itselfin a position error proportional to velocity. The velocity error of the directbackward difference differentiator is the same size as the full scale velocitymeasurement. This error is reduced considerably by both the low pass filterand the Kalman filter. However, the latter shows less than half the noiselevels of the low pass filter.In summary, for a low resolution sensor system, the Kalman filter is theonly approach investigated here that guarantees sufficient robustness.7.6 Experimental ResultsIn this section, the experimental system performance of the stock QB02302motoriscomparedwiththesimulationsandwithliteraturedatafromEMCVand EMVD systems. In these experiments, the valve opens 8mm in approx-imately 3.4ms, which corresponds to a typical valve motion at a 6000rpmengine speed.Figure 7.9 shows position, velocity and acceleration of the valve. Track-677.6. Experimental ResultsLift = 8mm EMCV1 EMCV2 EMVD FFVA[46] [47] [14]Transition 3.5 3.5 3.4 3.4Time [ms]Seating 0.3 0.1 0.15∼0.27 0.1∼ 0.25Velocity [m/s]Energy Loss 3.0∼5.2 - 1.4 1.35(QB02302)[J/transition] 0.66(Optimized)Voltage 100 42 42 42Source [V]Controllable Duration Duration Duration Fully VariableVariables & Phase & Phase & Phase & ProgrammableTable 7.3: Performance comparisoning performance is quite good. However, due to the flexibility in the linkagebetween valve and motor, mechanical vibrations are induced. This causewas determined by comparing the standard operation to a setup with anequivalent inertia mounted rigidly to the motor. With the rigid inertia,no noticeable vibration was observed. This leads to the conclusion thatthe rather rudimentary linkage implementation shown here needs to be re-designed to provide less flexibility in future setups. The velocity plot showsthat the mechanical vibrations due to the flexible link are primarily excitedduring the high jerk periods at the beginning and at the end of the motion.Consequently, the seating velocity at the end of the valve travel is ratherhigh. It should be noted that the transition time chosen here would be usedduring high rpm of the combustion engine. However, the low valve seatingvelocity of 0.05m/s is only required during engine idle, when the transitiontimes are much longer and the valve lift can be reduced significantly. Undersuch circumstances, the FFVA system will provide valve seating velocitieswell below the desired value.Phase current, total current, and energy loss are plotted in Figure 7.10.The motor draws approximately 100A during acceleration and 60A duringdeceleration. The unsymmetrical behavior and the large current oscilla-tions during accelerations are again attributed to the flexible linkage sys-tem, which has unsymmetrical damping elements for opening and closing.However, the energy consumption of 1.35J/transition in the experimentcorresponds well to the analytical predictions in Chapter 4. Table 7.3 shows687.6. Experimental Resultsa comparison of the performance characteristics of the FFVA system withthe EMVD and the EMCV system. For a similar transition time and lift,the FFVA system performs as good or better than the other two systems.However, the FFVA system provides not only variable valve timing but alsovariable lift. This additional flexibility leads to significant operating advan-tages for the combustion engine.697.6. Experimental ResultsFigure 7.2: Simulation of displacement trajectories707.6. Experimental ResultsFigure 7.3: Simulation of energy losses of different trajectories717.6. Experimental ResultsFigure 7.4: Transition simulation of the optimized motor727.6. Experimental ResultsFigure 7.5: Simulation of parameter variations737.6. Experimental ResultsFigure 7.6: Simulations of disturbance rejection747.6. Experimental ResultsFigure 7.7: Simulation of transition response with a 7 bit sensor and variousfiltering strategies757.6. Experimental ResultsFigure 7.8: Simulations of measurement error using different filtering strate-gies767.6. Experimental ResultsFigure 7.9: Experimental trajectory results using QB02302777.6. Experimental ResultsFigure 7.10: Experimental energy loss using QB0230278Chapter 8Conclusion8.1 SummaryIn this thesis, a Fully Flexible Valve Actuation system for the intake valvesof automotive internal combustion engines is demonstrated.After reviewing the need for electronic valve actuation and current imple-mentations of such systems, a direct drive system is proposed that providessix main advantages:• Fully flexible valve control• Simple mechanical layout• An effective control system• Good energy efficiency: 1.35J/transition using QB02302 (simulationresults show that the energy loss is only 0.66J/transition using anoptimized motor)• Fast transition: sufficient for the operation at 6000rpm engine speed• Relatively low seating velocity, which is regulated to about 0.2m/s at6000rpm and has the potential to be improved. Also, at engine idlethe system can provide the desired seating velocity of 0.05m/s.For a successful implementation, all aspects of the actuation system needto be optimized. This includes the mechanical portion, the electromag-798.2. Suggestions for Future Worksnetic portion, and the control algorithms of the actuation system. A designmethodology for an actuation system based on stock motors is proposedfirst. It provides guidelines how to select a good motor, how to design themechanical layout, and how to design an energy efficient control strategy. Inthe course of this work, analytical expressions were developed to predict thetransition performance and the energy efficiency of the actuation system. Inaddition, a lumped parameter model was developed to support the analyt-ical performance predictions. The lumped parameter model was also usedto study the influence of varying system parameters, the ability to rejectdisturbances, and effects of sensors with low resolution. Finally a test bedwas constructed that was used to validate the transition performance. Theseinvestigations show that the FFVA system based on stock motors performwell compared to other systems found in the literature.To further improve the performance of the FFVA system, an analyticaldesign methodology for modifying the stock motors is then proposed. AnFEM model is used to validate the motor optimization methodology andthe lumped parameter model is applied again in order to predict the systemperformance. This study shows that the modified motor should providesuperior energy efficiency without compromising transition speed.8.2 Suggestions for Future WorksEven though the current experimental setup performs well compared toother systems found in literature, there are still a number of areas of im-provement:As shown in Figure 7.9, the seating velocity is still relatively high. Thisis likely due to the elasticity of the connecting rod that causes a bouncewhen the valve comes to the end of a transition. A stiffer joint needs to bedesigned, or the control system needs to be refined in order to reduce theseating velocity.A second area of work is the experimental implementation of the op-timized custom motor. The theocratical derivation and simulation of theoptimized motor have been presented in this thesis, and this motor promisesto improve the performance of the actuation system significantly. However,the scope of the thesis did not allow for an experimental implementation.Finally, the current system is powered by a voltage source of 42V. For808.2. Suggestions for Future Worksbetter compatibility with current vehicles, the supply voltage needs to bedecreased to 12V. Further optimization has to be performed on the currentsystem structure to meet this requirement.81Bibliography[1] M. 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