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UBC Theses and Dissertations

A programmable oceanographic winch controller Chaddock, Kenneth M. 1975

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A PROGRAMMABLE OCEANOGRAPHIC WINCH CONTROLLER by KENNETH M. CHADDOCK B.S.E.E., University of Alaska, 1972 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in; the Department of Electrical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA January 1975 In presenting th is thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make it f ree ly ava i l ab le for reference and study. I fur ther agree that permission for extensive copying of th is thes is for scho la r ly purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l ica t ion of th is thes is fo r f inanc ia l gain sha l l not be allowed without my wri t ten permission. Depa rtment The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Date 2^3 S 1-i ABSTRACT A position servo controller for an oceanographic winch is designed, implemented and tested. Depth, speed and acceleration of a payload are made programmable. Cable position and speed feedbacks are implemented to control the depth of the payload. Provision i s made to compensate for the wave-induced motions of the ship deck. For this purpose, the instantaneous vertical deck position i s determined using three orthogonal accelerometers fixed to the deck. Tests of the position servo system are successful, but limited by constraints of the hydraulic system used. Compensation for rapid deck motions is possible; however, compensation for slow deck motions causes noticeable drif t s in the payload depth due to integrating small errors i n the acceleration; signal. i i TABLE OF CONTENTS Page Abstract i i Table of Contents i i i List of Figures iv List of Tables v i Terminology v i i Acknowledgement i x I INTRODUCTION 1 II THREE MAJOR ASPECTS OF THE CONTROL UNIT 5 2.A. Programmability of Position, Speed and Acceleration 5 1) Position Programming wrt Zero Position 5 2) Speed Controller with Acceleration Adjustment 6 3) Operator Interfacing 8 2.B. Deck Position Instrumentation 10 1) Measurement of Vertical Deck Acceleration 10 2) Integrator 12 2. C. Control System 12 1) Hydraulic System 12 2) Cable Speed and Position Feedback Instrumentation 15 III TESTING, CALCULATIONS AND RESULTS 18 3. A. Programmability of Position, Speed and Acceleration 18 3.B. Position Error Analysis 19 1) Error Due to Deck Motion Instrumentation 19 a) Acceleration Error due to Noise 20 b) Systematic Error in Acceleration Measurement 22 c) Steady State Acceleration Error 27 2) Other Sources of Position Error 29 3.C. Hydraulic System Tests 30 IV CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK 33 Appendix A. Deck motions l i k e l y to occur. 35 Appendix B. Calculations for drifts of integrators. 38 Appendix C. System and circuit diagrams. 40 Appendix D. Alternate schemes for deck motion sensing. 50 REFERENCES 52 i i i LIST OF FIGURES Figure Page 1.1 General terminology. v i i 2.1 Depth comparison using input position counts. 6 2.2 Theoretical equivalent of speed controller. 7 2.3 Block diagram and operation sequence of speed 8 controller. 2.4 Sketch of hydraulic system. 13 2.5 System and feedbacks. 14 2.6 Four states of feedback signals sensed by tachometer. 15 2.7 Tachometer cir c u i t . 16 2.8 Count synchronizer. 17 2.9 Timing diagram for count synchronizer. 17 3.1 Depth and speed profiles. 18 3.2 Position error due to 100 ug step and pulse inputs to 19 the integrator. 3.3 Typical d r i f t waveform for single accelerometer input. 22 3.4 Error profile curves for t i l t i n g . 23 3.5 Average error versus maximum t i l t i n g angle for 26 different values of k x under stated assumptions. 3.6 Relative placement of accelerometers and pulley wheel. 28 3.7 System gain change due to payload. 30 3.8 System gain change due to drum diameter. 30 3.9 Output speed for two loop gain. 31 3.10 Single quadrant system gain characteristics. 31 iv A. l Terms and numbers used t o d e f i n e deck a c c e l e r a t i o n s . 35 B. l G e n e r a l i n t e g r a t o r c h a r a c t e r i s t i c f o r n p o l e s . 38 B.2 D r i f t s i n p o s i t i o n due to a 100 ug s t e p e r r o r i n 39 a c c e l e r a t i o n . B. 3 Peak d r i f t and phase e r r o r as a f f e c t e d by x. 39 C. l System components. 40 C.2 F r o n t view of main c h a s s i s w i t h p a n e l s removed. 41 C.3 I n s t r u m e n t a t i o n package. 41 C.4 B l o c k diagram of c i r c u i t s . 42 C.5 S e c t i o n of main c o n t r o l l o g i c . 43 C.6 Count s y n c h r o n i z e r and c o n t r o l l o g i c f o r c o u n t e r s . 44 C.7 Speed c o n t r o l l e r . 45 C.8 D i v i d e - b y - N and depth c o u n t e r s . 46 C.9 B l o c k diagram o f i n s t r u m e n t a t i o n c i r c u i t . 47 C.10 I n t e g r a t o r c i r c u i t . 48 C . l l B l o c k diagram of c o n t r o l c i r c u i t . 49 v LIST OF TABLES Table Page I Summary of the states at which the control unit 9 either ignores a command or orders a stop. II Manufacturer's specifications and data for the 20 vertical accelerometer. I l l Summary of peak deck motions. 37 v i TERMINOLOGY Fig 1.1 General terminology. Ship or Deck - Deck of the ship Ship Angle - T i l t of the ship from the angle i t would settle to in calm water (G i n figure 1.1) Static - No movement of the deck Pulley Wheel - Wheel over which cable rides Cable Angle - Angle that cable deviates from absolute vertical Payload - Object suspended on the cable Absolute Position - Position with respect to the earth Zero Position - Average position of the sea surface (neglecting tides) Symbols -z g or z g Q - ship position wrt zero position z^ or z^ Q - payload position wrt zero position z1 - payload position wrt ship position v i i desired payload position (input control signal) target position of the payload components of deck acceleration wrt earth (note that r.Z = - g .) total deck acceleration wrt earth total deck acceleration measurement vertical deck accleration measurement v i i i ACKNOWLEDGEMENT I w i s h t o thank my s u p e r v i s o r F r i t z Bowers f o r h i s c o n t i n u o u s i n t e r e s t , a d v i c e and many v a l u a b l e s u g g e s t i o n s throughout the t h e s i s work. S u g g e s t i o n s and comments from o t h e r f a c u l t y members and s t u d e n t s are a l s o a p p r e c i a t e d . Thanks i s extended t o t h e members o f the t e c h n i c a l s t a f f i n t h e department. I am g r a t e f u l t o Mr. E. P. F l e i s c h e r and Mr. Glenn May who ar r a n g e d the f a c i l i t i e s f o r t e s t s i n E s q u i m a l t . I would l i k e t o thank M i s s S h e i l a Lund f o r a s s i s t a n c e i n t y p i n g t h e t h e s i s . F i n a l l y , f i n a n c i a l a s s i s t a n c e from the N a t i o n a l R e search C o u n c i l i n t h e form o f s t u d e n t s u p p o r t and equipment funds i s g r a t e f u l l y acknowledged. Some equipment was a l s o p u r c h a s e d w i t h funds s u p p l i e d by t h e Department o f Oceanography. i x 1 I. INTRODUCTION A programmable winching system requiring a minimum amount of attention by an oceanographer is desired. The system should be able to change speeds or stop at a series of preset depths, while compensating for wave-induced deck motion. The cable suspending the payload i s assumed vertical where i t leaves the ship. Environmental conditions and deck motions are variable within limits of oceanographic research working conditions. The static speed must be within 10 per cent of that specified by the oceanographer. The position control should be as precise as the conventional depth measurement within ±1 foot and accurate enough to compensate for instantaneous vertical deck position within ±0.5 feet under most severe-working conditions. The static acceleration rate should be adjustable so the cable w i l l not slacken when payout i s begun. The main motives for deck motion©compensation are to (1) prevent adverse cable tensions, i.e., slackening and jerking as the deck plunges and heaves, and (2) enable control of the absolute position of the payload. Two typical uses of such a system are water bottle casts and STD (salinity, temperature with depth) recorder casts. Programmed stops at several depths are convenient for bottle casts where the bottles must be sequentially placed on an outgoing cable and removed one by one as the cable i s respooled. A programmed series of speed changes at preset depths would enable the oceanographer to lower an STD at different speeds, depending on the gradient of sea properties, to a maximum depth, and then have the instrument returned automatically to the deck. Wave motion compensating for STD casts would ensure the depth increases smoothly as the cast progresses, yielding more accurate recordings. 2 The general solution of the problem is restricted by certain constraints. Maximum absolute speed i s limited by the maximum speed;of the winch minus the vertical speed of the deck. Feedback from the pay-load cannot be used since only some cables have an insulated wire for data. Therefore, a l l measurements are limited to events within the reference frame of the ship: cable motion and tension, and deck motion. Instrumenting absolute deck motion requires either measuring relative motion to a fixed position or measuring i n e r t i a l effects. Since the objective is to effectively isolate the cable, which i s assumed vert i c a l , from the motion of the ship, only the vertical deck motion at the point where the cable leaves the ship need be known. Several possible schemes to measure the deck position were considered [Appendix D] but the one implemented was to measure accelerations ref-erenced to the deck and estimate the vertical component of the deck acceleration referenced to earth. Any type of servo w i l l perform a double integration when using the vertical deck acceleration to compensate for wave-induced motion. The continuous reeling in and out of cable should average to zero over long periods of time since the average absolute vertical position of the ship, neglecting tides, remains constant. Any integration, especially a double integration, w i l l d r i f t noticeable given enough time, even with the smallest input offset. Therefore, some position feedback is necessary to combat this d r i f t . In addition to limiting the d r i f t in position to ±1 foot, the absolute position of the payload from zero must be known. Previous approaches to this or related problems are not a l l published, making a complete survey of past work d i f f i c u l t . Of those 3 approaches found, a l l endeavour to keep the cable tension constant and to compensate for relative deck and load movement by adjusting the cable length. Constant tensioning systems are used mainly when the cable i s attached to some very heavy object, such as an undersea pipe [6] or another vessel [7,8,11], but can also be used to isolate the motion of the deck from the payload [4]. These systems can be "passive" or "active". Passive tensioning systems are essentially powered by varia-tions in cable tension. They store energy as cable tension increases and then use the same energy to keep the cable taut when the tension decreases. This energy balance i s convenient, since i t self-perpetuates deck motion compensation except for f r i c t i o n a l losses, but passive sys-tems can only be tuned to one ship frequency [4]. Active tensioning systems can work over the whole expected frequency range. They minimize variations in cable tension by continually adjusting the cable length. Another type of active system i s a velocity servo [16] in which the deck velocity is used as an input control signal to compensate for wave-induced ship motion. With this system, the cable tension fluctuates due to imperfect compensation depending on the drag and inertia of the load. These variations become small and unimportant with accurate enough compensation. The above mentioned systems require some form of position feedback to limit the pure integrating action of the winch. Since a pressure feedback from the payload i s not always possible, cable length must provide this information. A position servo is the simplest servo that w i l l keep tension virtually constant and display the depth of the payload and any 4 positional d r i f t directly. This is.because a high loop gain around the winch causes the output to track the input very closely. The input can be composed of two separate signals. One signal defines the depth. The other signal, deck position, is derived by double integration of the deck acceleration. Any drifts away from the desired depth can be seen by observing this latter signal. Cable speed, acceleration and tension, and vertical deck speed and acceleration are available to improve the basic servo performance. The object of the thesis work can be-divided into three major segments: i) Design a d i g i t a l c i r c u i t that is programmable for one depth and one speed at a time but is easily interfaceable to a memory that could store several depths and speeds. i i ) Find a way to produce instantaneous vertical deck position u t i l i z i n g simple accelerometers. i i i ) Using existing hydraulic systems found aboard local research vessels, i n s t a l l control and feedback transducers and confirm that the system works. 5 II. THREE MAJOR ASPECTS OF THE CONTROL UNIT 2.A. Programmability of Position, Speed and Acceleration A desired feature is to be able to predefine deveral depths where either speed changes or stops are to be performed. In the f i n a l design, a small memory would store the positions and speeds. In the prototype b u i l t , however, both position and speed ; are entered as BCD numbers on thumbwheel switches. Stopping at a preset position i s auto-matic; whereas, the speed change is manually toggled. To make the winch start and stop smoothly (like an elevator), variable control for accel-eration i s included. 1) Position Programming with respect to Zero Position In the automatic mode, the control unit reels cable in or out to a predefined position•[z^ f]. If the cable length [ z l g ] were used to stop the winch, an error would probably result since zT = z i s + z s • Instead, the input position [z-^] is continuously compared to the f i n a l position [z^f] and a stop signal i s generated when equals z ^ . However, the cable takes a distance to stop, depending on the maximum speed and the deceleration rate. In the prototype, the acceleration rate and the deceleration rate are made exactly equal, and the depth counter is incremented twice per input control count while accelerating and disabled while decelerating. As a result, the depth where the winch can stop is displayed, rather than the actual depth, and the payload i s slowed to a halt at z ^ . Position feedback, taken from the cable, i s sensed as N pulses per meter. The cable rotates a measurement wheel whose circumference determines N. Since the circumference of this wheel may diffe r between various winches, a divide-by-N counter was designed to produce a count of 6 one meter per N counts of the input. This counter i s bi-directional so that reversing the direction of the payload w i l l cause no positional error. Figure 2.1 illu s t r a t e s the method of depth comparison using the input position signal. Accel + Decel Accel Decel 'If => Depth . Comparator ~7S B Input 2* n 0 N Depth Counts Counter *• to Input Control Signal Fig 2.1 Depth comparison using input position counts A = B 'Zlf = Zli 2) Speed Controller with Acceleration Adjustment The speed controller, upon entry of a speed change command, w i l l cause the winch to accelerate at a constant rate to a preset speed. Both the acceleration rate and speed are preset by the operator who also toggles in a speed change. When a stopping condition occurs, the preset speed i s automatically reduced to zero and the winch decelerates at the same rate at which i t accelerated. At a l l times, the speed controller signals the main control logic whether i t i s stopped, accelerating, de-celerating or at constant speed. The main control logic i s then able to run the depth counter accordingly. The output of the speed controller i s continually compared to the preset speed. When a speed change is commanded, the speech approaches the desired speed, quickly or slowly, depending on the rate of acceleration. In figure 2.2 this rate i s represented by the magnitude of the limits i n the non-linearity. When the desired speed i s reached, the controller holds speed constant and cannot change speed again u n t i l i t receives another speed change command. The deadzone in figure 2.2 illustrates this state. Input Speed Fig 2.2 Theoretical equivalent of speed controller. The acceleration signal i s a square wave from a voltage con-trolled o s c i l l a t o r , whose frequency i s set by a potentiometer adjustment. The 1 -> 0 transition of the acceleration rate signal begins the sequence lis t e d i n figure 2.3. Since a stop command arrives anytime, a few posi-tion counts are li k e l y to occur before deceleration begins. The depth counter registers these counts, however, and i f the control unit i s i n the automatic mode, i t causes the winch to creep slowly back through this overshoot distance (at most a small fraction of a meter) u n t i l the exact meter distance desired i s reached. 8 Measurement 2048 hz Acceleration nn 9 to 250 hz Control Logic Preset . Speed (BCD) Down Counter Stop, Chge Speed Accel, Decel (2) Speed Comparison Stop Ack Main Control Logic Speed Reg n_n_n (J) ^ Input Speed Operation Sequence Wait for 1 •+ 0 transition of Acceleration rate. (1) When 1 -> 0 transition occurs, increment speed i f a speed change i s allowed. Measure actual speed and compare i t to desired speed. (2) When 0 -*- 1 transition occurs, latch the speed comparison. If Accel or Decel has gone from 1 0, inhibit any speed change u n t i l another speed change request is made. Fig 2.3 Block diagram and operation sequence of speed controller. 3) Operator Interfacing Since the operator i s confronted with an array of switches, i t is very l i k e l y that he w i l l eventually make an error that would ordinarily cause the winch to suddenly stop or change direction. When any such error i s made, the control logic either ignores i t or issues a stop command, thereby slowing the winch gently to a halt. A summary of the states in which the control unit either ignores a command or orders a stop is contained in Table I. 9 Manual Controls Signals in Main Control Logic Ignored Inputs for Certain Conditions Stops Due to Operator Error Normal Stops , Auto Mode ,., Man Auto(=Man) 1 1 0 0 1 Change Mode A Mode 1 Auto Dir lg Man Dir A Auto Dir lg 1 jjr „ . OUt Man Dir T In Man Dir lg Auto Dir Change Dir A Man Dir lg 1 Run Stop Run(=Stop) 1 1 0 Stop!Run Chg Sp Speed Chg Request lg Reset Diff C Reset^ lg 0 Reset Depth Reset2 lg lg Pos A c k ( s t ^ d 1 0 1 0 0 !Oj[ l O f 1 Table I. Summary of the states at which the control unit either ignores a command or orders a stop. Blanks are don't care states, lg implies ignored. In the automatic mode, the direction and stop command are auto-matically defined; whereas, in the manual mode, the operator must set the direction and the stop command. Of a l l the controls, only the manual stop i s unconditionally effective. In both modes, manual starting i s only allowed when the winch i s stopped (i.e., Pos Ack=l). No controls are effective after a stop command has been issued u n t i l the winch i s com-pletely stopped (i.e., Stop Command=l, Pos Ack=0). 10 2.B. Deck Position Instrumentation 1) Measurement of Vertical Deck Acceleration The object i s to measure the absolute vertical acceleration and subtract the acceleration due to gravity, g, to yield [ z = A - g ]. sm zm Two main characteristics of deck motions make an accurate measurement d i f f i c u l t , namely: i) t i l t i n g of the deck, and i i ) transverse as well as vertical accelerations. A single accelerometer perpendicular to the deck measures A z only i f the ship does not r o l l or pitch. T i l t i n g of the ship is inevitable, however, and causes an intolerable error due mainly to the term [ g cos 6 - g ], in equation 2.1, where 9 is the ship angle. z = z cos 6 - x sin 9 + g cos 9 - g (2.1) s m s s A study showed that the total acceleration vector of the deck [Aj,] i s very nearly vertical [Appendix A], Therefore, an accurate estimate of z's can be made i f i t i s calculated as [ ATJ - g ]. Since 1/2 A_ = (A 2 + A 2 + A 2)' T z y x = A 1/2 (2.2) error terms error w i l l arise in two manners: a bias or offset, and a distortion of the vertical acceleration signal. The method of measurement described below was implemented to compensate in part for these effects. Three orthogonal accelerometers, one vertical and two hori-zontal to the deck, measure three components of the total acceleration vector [ A_ ]. From Appendix A, A »|A |>|A |, so that the major portion of the signal [ A ^ ] w i l l come from the vertical accelerometer. There-fore, not squaring the vertical accelerometer signal [.a ] avoids possible 11 error due to inaccuracies in multiplying and taking the square root to produce A p m , which i s given by = a 1/2 With r A | - i | , £ By Taylor expansion, ^m * a z [ 1 + r + s ] 1/2 (2.3) A T m - az[ 1 + | r (1-. -|r +...) + | s ( l - |s +...) ] 1/2 First order approximation yields A ^ = a + — af- + - — a^ z 2a z y 2a x z approximation of a z = g yields = a + a2 + ^ £ a2 z 2g y 2g x (2.4) From Appendix A, at most severe conditions, a = g ± yg. A further (2.5) where k^ and k x are gain adjustments very close to 1. The circuit that implements this function (in Appendix C) requires only two squaring operations and two gain adjustments. The vertical deck acceleration is calculated by subtracting 1 g, hence, = a + 3m JL a2 + _x „2 _ 2 g a y + 2 g a x S (2.6) A complete position error analysis i s given in Section 3.B. 12 2) Integrator Any realizable integrator drif t s proportionally with time [t] due to an input offset. The problem i s compounded with double integration, since the d r i f t is proportional to t 2 . For example, a 10 ug offset w i l l cause a d r i f t of 1 foot after 2.25 minutes and 16 feet after 9 minutes. Since the zero shift in the accelerometers chosen is typically 300 ug/°F and the operating temperature range is 32°F to 100°F, some method of removing or counteracting an offset must be employed. It is impossible for an operator to zero the acceleration signal on a moving deck so any offsets or very slow changes in the acceleration signal must be f i l t e r e d out. Therefore the integrator circuit chosen [Appendix B] takes the form of a bandpass f i l t e r with a maximum gain of 9.11x10^ at a frequency of 0.53 miilihertz (~2 cycles/hour) and a predominantly integrating char-acteristic at operating frequencies. The choice of f i l t e r parameters is based on a compromise between drift s in the deck position signal and the quality of the integration. A complete analysis relating f i l t e r parameters to position error is discussed in Section 3.B. 2.C. Control System 1) Hydraulic System A p i c t o r i a l representation of the hydraulic system chosen appears in figure 2.4. An electro-hydraulic valve is driven by an electric current, varying the valve spool position and therefore the winch speed. In the figure, the hydraulic motor and winch i s depicted as a symmetrical jack with limitless travel. When the valve spool i s moved to the right, flow from the pressure source travels through A pushing the jack and causing f l u i d on the opposite side out B through E to the sump. The pressure across the jack [P T] w i l l depend on the balance of force with the load. 13 Motor and Winch -ff-Input Spool Position II fan r—2-f B # D j To Sump Constant Pressure Source 1 r El \ Electro~hydraulic Valve Pulley Wheel Q Payload To Sump Fig 2.4 Sketch of hydraulic system. A detailed mathematical analysis of the hydraulic system was derived but evaluation of a l l the parameters to predict the system res-ponse was not attempted since the same hydraulic system was not contin-uously available. Instead, the valve properties and a f i r s t order approximation of the winch were used to determine the control scheme. The equations of flow through the valve are Irl * x or, in general, Q = 0 v Q = k r/PA-P_ x v v 0 L Q v = f< r« P0» PL> ' r * x (2.7) The spool displacement of the valve i s a nonlinear function of the input current. From the manufacturer's specification sheet, these are related as ,2 r = k r e (2.8) The frequency characteristics of the valve show that i t i s a second order device with a r o l l - o f f frequency that is largely dependent upon the system pressure. Thus, r = f ( i , P Q) P >P 0 C (2.9) 14 such that the valve response i s faster at higher system pressures and i s impractically slow for pressures below P^ ,, the low pressure specification set by the manufacturer. A constant pressure source is therefore required. Constant pressure hydraulic sources are achieved most simply in one of two ways. One i s a constant displacement pump with a r e l i e f valve which sets the system pressure, and the other i s a pressure-com-pensated variable displacement pump. Both methods are susceptible to saturation, i.e., a substantial loss i s pressure at high flow rates. Therefore, the pump must have a large enough displacement to avoid saturation at a l l times. The winch can be modelled as a simple integrator, i f compression and leakage of the hydraulic f l u i d are ignored. The control scheme chosen i s a position servo with total input of [z1 - z ]. Velocity feedback i s included to help eliminate any gear backlash, i f that i s a problem. Optional lowpass f i l t e r i n g of the error signal i s also implemented. As can be expected from figure 2.5, vi r t u a l l y a l l control loop problems originate with the valve. These problems are discussed i n Section 3.C. fe Fig 2.5 System and feedbacks. 15 The generation of the input signals [z...] and [z ] have been previously discussed, z is an auxiliary signal from the integrating c i r c u i t . Measurement of the feedback signals [z^g] a n (^ ^ l s ^ f ° ± i O W S ^ n the next section. 2) Cable Speed and Position Feedback Instrumentation Both cable speed and position are derived from one transducer. The transducer i s a zero-velocity magnetic pickup which produces a two-bi t Gray code as gear teeth rotate past i t . A tachometer c i r c u i t decodes the b i t sequences to i) produce positive or negative direction pulses of equal width for velocity feedback, and i i ) synchronize the direction of the cable and the position feedback signal.. To produce directional pulses, the tachometer compares the previous and present states of the Gray code, as illustrated in figure 2.6. The directional pulses also set an R-S f l i p - f l o p for the position-feedback direction signal. The logic expressions, P = aAbB + aAbB + aAbB + aAbB N = aAbB + aAbB + aAbB + aAbB Simplify to (2.10) P = XY N = XY for X = A © b Y - a © B (2.11) Gear Teeth Gray Code Four States per Tooth y' \o i 1 1 , 0 i 7 17 l 1 I 0 0 A B a ,A b,B Fig 2.6 Four states of feedback signals sensed by tachometer. a,b i s the previous state. A,B is the present state. 16 / Position Feedback (I2) A —\D 0 Q B - D Q B D T2 Fig 2.7 Tachometer c i r c u i t . and T2 are alternating timing pulses as defined in f i g 2 . 9 . The input signal [z-^] a n d the feedback signal [z^ g] are each composed of a square wave representing speed and a logic level representing direction. Since the signals arrive at random- times, a c i r c u i t was designed to output clocking pulses for every 0 -*• 1 and 1 -> 0 transition of the two signals, synchronized with their directions. A pulse on every transition i s necessary to ensure that no systematic error occurs in the measurement of the cable position. The pulses are counted d i f f e r e n t i a l l y by a 12-bit up-down binary counter and then converted to an analog quantity [ z ^ - z^ ] which i s used i n forming the control signal. 17 Or V2 Timing Signals 1 S2-Count Pulse Fig 2.8 Count synchronizer. Outputs clocking pulses of the input signals 1^ and I 2 synchronized with their directions and S2. v2 W, j~ i r J i i—\—T~L h'H h'H h'H h'H Fig 2.9 Timing diagram for count synchronizer. Processing of I-L and 1~ i s switched back and forth at frequencies much higher than those of the highest speeds. 18 III. TESTING, CALCULATIONS AND RESULTS 3.A. Programmability of Position, Speed and Acceleration Figure 3.1 ill u s t r a t e s the programmability of the input control signal. The upper profile i s depth [z.^] and the lower profile i s speed [ z ^ ] • After starting (point 1), the speed i s changed twice (points 2 and 3). A stop command occurs when the depth counter reaches (point 4), and causes the speed to return to zero. After stopping, z^ i s set to zero by the operator, and the acceleration rate i s decreased to i l l u s t r a t e i t s effect. Upon restarting (point 5), the speed increases but does not " reach the preset speed before the depth counter reaches zero and a stop command i s again issued (point 6). As i s usually the case with any target position, a small overshoot in position results. After a f u l l stop, this overshoot i s corrected for by creeping back towards zero (point 7 to point 8). When the depth counter i s exactly zero the creeping ceases. Fig 3.1 Depth and speed profiles. 19 3.B. Position Error Analysis, 1) Error Due to Deck Motion Instrumentation The worst errors in measuring deck position are due to double integration of a) uncontrollable noise in the acceleration signal b) systematic errors in the acceleration measurement. From Appendix B, the integrating c i r c u i t i s really a bandpass f i l t e r with the gain characteristic f t Pos _ , q o * m 6 (s300)- _Accel " 1 U (l+s300)5 g (3.1) -1 At maximum gain, when s i s 1/300 sec (period 31.4 minutes), an rats noise of 7.7 pg yields an uncertainty of ±1 foot. Also for these characteristics, 1 foot peak d r i f t results from a sustained 4.5 ug error or a 1 minute 13.1 ug pulse. Figure 3.2 illustrates the resulting d r i f t s in position for a 100 ug step and 100 ug 1 minute pulse. -20 f Time (Min) Fig.3.2 Position error due to 100 ug step and pulse inputs to the integrator. 20 Now that the d r i f t in position due to an acceleration signal error has been established, the sources of error are studied in detail, a) Acceleration Error due to Noise Noise due to either random noise or temperature changes, orig-inates mainly in the i ) vertical accelerometer, or the i i ) t i l t compensation ci r c u i t . The accelerometers are high accuracy, non-pendulous servo-accelerometers. Nevertheless, their specifications are limiting factors in this application. Pertinent characteristics of the vertical acceler-ometer are list e d in Table II. Sources of Error Specification Data Noise: DC to 1 Hz 5 yg rms Zero shifts with voltage Sensitivity 2 regulator temperature1 4.5 yg/°F supply 0.5 yg/°F . ° supply Zero shifts with transducer Sensitivity temperature 300 yg/°F 20 yg/°F 200 yg/°F ? Table II. Manufacturer's specifications and data for the vertical accelerometer. The data is taken from the manufacturer's calibration certificate. ^he voltage regulator specification i s about 1 mv/°F maximum. 2Error due to sensitivity shift is calculated for a signal of 1 g. The 5 yg rms noise alone can cause an uncertainty of ±0.65 feet. The temperature of the voltage regulator supplying the instrumentation could possibly change a degree or so, causing ±0.58 feet uncertainty. Most serious, however, i s the temperature shift of the accelerometer i t s e l f , since a sudden change of only 1°F would result in a substantial 21 position error. (It should be noted in Table II that the maximum specified zero shift was 300 yg/°F, but on the performance certificate accompanying the accelerometer, actual shift was only 20 yg/°F. This implies that the actual sensitivity shift could be lower than the maximum 200 yg/°F specified by the manufacturer.) To reduce sudden temperature changes, the accelerometers were placed in an insulated, airtight box which was wrapped in t i n f o i l in order to reflect sunlight. It was expected that any sudden external temperature changes would be thus thermally delayed sufficiently for the f i l t e r i n g action of the integrator to prevent a serious position error. The t i l t compensation ci r c u i t , also contained in the insulated box, contributes noise and d r i f t due to the multipliers and the -1 g bias. The multipliers contribute an rms noise of about 3.4 yg but have a cal-culated temperature coefficient of less than 1 yg/°F. The -1 g bias, which i s zener referenced, is calculated to have an effective temperature coefficient of 26 yg/°F. Input offset voltages of the integrator op amps, in the main chassis, contribute at most by calculation, 0.2 yg/°F and by testing, an rms noise of 0.62 yg. Laboratory tests were performed at room temperatures (which fluctuate slightly) with various inputs to the integrator. In a l l mea-surements, the insulated box containing the accelerometers and t i l t compensation circuit was sealed. Output d r i f t s , after the integrator stabilized, show strong^frequency components with a period of about 30 minutes (Figure 3.3). 22 +/foot Fig 3.3 Typical d r i f t waveform for single accelerometer input. b) Systematic Error in Acceleration Measurement Systematic error in the acceleration measurement arises from three causes: (1) imperfect t i l t i n g compensation (2) transverse acceleration, excluding vibration (3) deck vibration Errors (1) and (2) are interrelated, while (3) is a separate problem. These errors appear as a very small offset i n acceleration. For any given deck motion this offset i s constant, but a change i n deck motion shifts this offset. The same phenomenon occurs for vibrations varying in intensity. This offset can be analyzed from the equation for the calculation of ve r t i c a l deck acceleration. k k . y 2 i x 2 z = a +-^-a^-+-^— a ^ - g sm z 2g y 2g x 6 (2.6) Considering for simplicity two dimensions only (cross-section of ship), the accelerometer signals are a = A cos 0 - A sin 9 + a (vib) z z X z a = A sin 6 + A cos 9 + a (vib) x z x x N (3.2) where [A - g] and [A ] are the deck accelerations referenced to the Z X . earth and 9 i s the deck angle. (1) Error due to imperfect t i l t i n g compensation only T i l t i n g the accelerometers slowly through angles -10 23 to +10 degrees so that the only acceleration measured i s g, illus t r a t e s the origin and character of the systematic measurement error. As the ship r o l l s from side to side, the error w i l l not average to zero but to some offset which becomes more severe for higher t i l t i n g angles. Figure 3.4 il l u s t r a t e s that by varying k slightly, the error can be reduced. X TiltC) kx = 1.0077 increasing slightly k =1.0000 Fig 3.4 Error profile curves for t i l t i n g . Computation was made to find the equivalent offset in acceler-ation due to t i l t i n g the accelerometers. sinusoidally between maximum (3.3) angles of 1 to 10 degrees. The equivalent offset errors, . l 2 * eA = ~ / z* dt - 2ir k = 27 { [ g " c o s 9 i + l | ( g s l n 0 i ) 2 ~ g ] d t where Q± = (i) sin t for i = 1,2,...,10° are approximately 1/3 the absolute errors in figure 3.4 . (2) Error due to transverse accelerations (no vibration) The equivalent error due to transverse accelerations [A x] i s far greater in magnitude than the t i l t i n g error. In this 24 calculation no t i l t i n g i s assumed, but the same transverse accelerations which would arise from the ship ro l l i n g back and forth between-angles 1 to 10 degrees are used. Furthermore, i t i s assumed that a l l transverse accelerations w i l l be proportional to the maximum deck r o l l angle, since the ship w i l l not have purely translational accelerations without roll i n g . The equivalent errors under these assumptions are 1 2 * eA__ = ^rr f z dt 3m zm 2ir o s n 2TT -k , 2TT" k = ^  / S ~ (A ) 2 dt . 2ir o 2g x 7 Substituting A = (100 mg) (9./0.1745) sin to t at to = 1, X 1 s s yields ix X eA = ~ (100 mg)2 (6 /0.1745)2  zm ^ ftS 1 = k x (6 i/0.1745) 2 2500 yg. (3.5) These errors, about f i f t y times greater than those due to static t i l t i n g , can be largely counteracted by varying k^. Considering the t i l t i n g only case again, i t i s seen that k eA = g cos 0 + — g sin 29 - g zm z 9 2 k x o • ( i - f + -f e 2 - l) g = f 2 ( k x - i ) g . The average error, - 6? ^ m ± " -T ( kx - » « - (k - 1)(6,/0.1745) 2 7610 ug, (3.6) is also dependent largely on the maximum t i l t i n g angle. This implies that both effects should cancel for a properly chosen k^. 25 The calculation of-k x is complicated by the fact that the ship w i l l r o l l due to transverse accelerations. The complete measurement equation (without pitching) becomes k z = A cos 6 - A sin 0 + -r*- [A sin 9 + A cos 9] 2 - g (3.7) s m z x 2g z x Since the object is to vary k^ to minimize the error function, (from equation 3.4) eA = f ( z ,x ,9,k ) , (3.8) zm s s x any terms which w i l l average to zero for back and forth r o l l i n g of the deck can be omitted. Physically speaking, this assumes that a l l actual accelerations w i l l average to l g , meaning the average deck position w i l l not change in t i l t , height, or lateral displacement. Therefore, 1 n T 9 - i // z cos 9 dt , T = — nT o s ' t o u s - nT — / 2z sin 29 dt , and (3.9) nT o s ' v ' 1 * T sin 29 . — J x z — dt nT o s s 2 9 2 are considered negligible. With the approximations, cos 9 = 1 - , and sin 20 sin 0 = 0 , for eeA = 0, k becomes z m ' x T / (0 2 + 2x 0) dt k - 0 x ' T (3.10) / [(l+z 2-x 2)0 2+ii 0+x2] dt 0 s s s s Since [z 2 - x 2] « 1, s s J ' T / (0 2 + 2x 0) dt V = Q '. § x T , (3.11) / (0 2 + x 0 + x 2) dt 0 s s' which should be nearly constant i f x\ i s closely related to 0. 26 To calculate a meaningful value for k , more complete data about typical ship motions is required, such as what correlations, i f any, may exist between the components of deck accelerations and the deck angle. To establish what accuracies might be achieved by this method, curves of average error versus maximum r o l l angles for different values of k x were computed for an assumed pattern of deck motion. The assumptions are 6 = e . s in u>t, a) =1, 0,=(1,2 10)(0.01745) X S S X z = 0.25(e./O.1745)sin io t (3.12) S X s x = 0.10(0./0.1745)sin 0) t S X & These assumptions imply a l l aspects of the motion are in phase and the magnitudes of the acceleration components are linearly related to the maximum deck angle. Thus equations 3.9 are a l l zero. The results of the computation are shown in figure 3.5. Average I Fig 3.5 Average error versus maximum ti l t ing angle for different values of k under stated assumptions. For these assumed deck motions, operation up to a maximum t i l t i n g of about 7.5 degrees for k = 1.117 keeps the average error X within about ±40 yg. In general, i t appears that a suitable k x can be chosen to keep the average error low over a limited range of maximum angles. (3) Error from deck vibration .Accelerations from vibration w i l l cause error not only due to being squared by the t i l t compensation ci r c u i t , but also because the acclerometers produce offsets of 1 mg per g of transverse vibration. Transverse vibration, therefore, must be attenuated to about 2 mg peak by placing the accelerometers on structural isolator mounts. The alter-native of f i l t e r i n g to attenuate the x and y accelerometer signals cannot be used, as i t would destroy the measurement accuracy which is sensitive to changes in k and k . ° x y c) Steady State Acceleration Error Even i f the drifting problem of the position output i s solved, there are s t i l l errors associated with the instantaneous position output which are due to: i) slight distortions of the ver t i c a l acceleration signal, i i ) not measuring the acceleration at the pulley, wheel, and i i i ) phase error due to imperfect double integration. Slight distortions are minimal, as shown by the preceding dis-cussion, and are certainly less than 1000 yg which causes a maximum error of 0.33 feet with a 20 second wave. The accelerometers are highly sensitive to shock, so they should be fixed to the deck and not the pulley wheel. Error can amount to over 1 foot when the deck t i l t s , i f the relative position of the 28 accelerometers to the pulley wheel i s poorly chosen. (See figure 3.6 and equation 3.13) Pulley Accelerometers e = r 6 cos 6 - r 8 cos 9 pm p p m m = (r cos 0 - r cos 6 )(0.1745) p p . m m (3.13) Fig 3.6 Relative placement of accelerometers and pulley wheel. Phase error due to imperfect integration i s the most important of these errors, since i t i s this error which largely determines the time constants of the integrator. From Appendix A, the largest anti-cipated deck rise w i l l be 20 feet. The maximum phase shift allowable is then d> = sin * ~ V~ or about 3 degrees lag for a 1 foot error at max 20 f t the zero crossing of the deck position. The integrator function shows that for small <(>, the time constant, T , i s T = - tan(90°-5<j>) (3.14) s For a phase lag of 3 degrees at to =0.316 sec T must be 300 seconds. s At higher frequencies this error decreases to a negligible amount. For example, a ± 8 foot deck movement at u>g=l sec 1 would cause a ± 0.14 foot error. The choice of T i s based on a compromise between i t s effect on i) d r i f t in position due to either random noise or systematic acceleration measurement errors, and i i ) the quality of the integration. 29 From Appendix B i t is evident that halving x halves the quality of integration but quarters the d r i f t in position. Hence, i t is possible, for certain ranges of deck motion, to decrease x sufficiently so that d r i f t i s not a problem and the integration is s t i l l adequate. For example, i f to =1 sec 1 a l l the time, x could be lowered to 1/4 i t s s present value, thereby decreasing the sensitivity to d r i f t by a factor of 1/16 but s t i l l maintaining a reasonable ± 0.53 foot position error for a ± 8 foot deck movement. 2) Other Sources of Position Error i) One extra count per start and stop of the winch can occur due to the d i g i t a l circuits that generate the input signal. ( 0.014 feet in the test system) i i ) The magnetic pickup produces a two-bit Gray code from a gear rotating on the shaft of a wheel that is driven by cable f r i c t i o n . Any slippage w i l l cause an incorrect position sensing. Also the diameter of the cable must be the correct one for the wheel diameter. i i i ) If the cable arcs under the sea surface, the position read-out w i l l not be the actual depth'of the payload. iv) Tracking error for a system gain [K g]» without deadzone, for an input [A sin oo t] is approximately — cos « t, and for an input S K S * sys . . A . [At] i s '.-- The system gain depends on the payload and i t s position.-- sys the payload,is lowered, the wire becomes a part of the dead weight of the load, which changes P . Also, the winch drum diameter decreases as l i the payload i s reeled out. Figures 3.7 and 3.8 il l u s t r a t e these effects on system gain for a linear valve characteristic. Deadzone of the valve causes an offset error i n position that can be limited by increasing the electronic gain; during testing this error was less than 0.07 feet. 30 A / / . / ' // r // s / / / ' / / / / / nominal -system gain Fig 3.7 System gain change due to payload. Fig 3.8 System gain change due to drum diameter. 3.C. Hydraulic System Tests Three different hydraulic systems were implemented in Esquimalt for these tests. The f i r s t and second, implemented on research vessels, were only available for two or three days each before being dismantled due to other p r i o r i t i e s . The actual testing time during these days was further limited by mechanical problems unique to each system. In the third system, implemented on shore, a failure of the valve ended the testing, but data acquired shows the valve characteristics were a major obstacle to achieving good system performance. Testing was carried out under stat i c conditions to determine i f the system could accurately track any typical input, which would imply that the system could then track an accurate deck position input and thus compensate wave-induced motion. Under closed loop operation with low gain, the system followed inputs for raising or lowering (parabolic start and stop) after a mild starting jerk. (Figure 3.9) Excessive jerking when starting resulted with a high system gain. The jerking was more severe for lowering than for raising the payload due to a combination of stiction and mechanical looseness of the winch spool. The i n i t i a l jerk was severe enough to 31 backlash Fig 3.9 Output speed for low loop gain. cause the cable to momentarily slacken on the wheel from which feedback i s taken, which resulted i n a faulty feedback signal, and continued jerking. Manual braking increased the system damping and removed this i n s t a b i l i t y . Nevertheless, the open loop gain characteristic (Figure 3.10), which i s largely dependent upon the valve, proved unsatisfactory for closed loop operation, and testing was halted. Normalized Speed LO 0.5 hysteresis s tic tion 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 J.O Normalized Input Fig 3.10 'Single quadrant system gain characteristics. 32 The valve was chosen under two basic assumptions: i) a pump with a high enough displacement to avoid saturation would be readily available, and i i ) at maximum flow rates, a small pressure drop across the valve ensures that enough power i s available to drive larger payloads at the speeds anticipated. The valve required a constant pressure source, but the sources invariably lost pressure at higher flows, thereby seriously degrading the response of the valve at higher winch speeds. This loss of pressure, combined with the high flow capability of the valve, resulted in a small latitude of control over the speed range for which PQ>P^; i.e., a small range of input caused the speed to go from zero to maximum. A different valve might have proven better for this project. For example, a valve with a lower flow capability would have allowed more of a latitude in control, but at a loss in power available to drive the payload. A valve made for use with a constant displacement pump might have been better. This approach would require an external pilot pressure supplied by a secondary source. Such a valve had been ordered but was found to be out of production for six months. Either valve should have no dead zone, since the winch is continually changing direction when i t i s correcting for deck motion. An underlapped valve has no dead zone (the valve purchased was overlapped); there are a few of these on the market without the additional nonlinearity which relates the input current and the spool position (eq 2.8), as with the present valve. Neither of these was purchased since their flow capacity was either too low, or else their price was three times the price of the valve used. 33 IV. CONCLUSIONS AND-RE COMMENDATIONS - FOR FUTURE WORK Programmability.of the absolute position, speed and accleration operates properly. Cable position and speed are accurately measured provided there is no slippage of the cable on the wheel assembly from which the feedback is taken. An accurate measurement of absolute vertical deck acceleration is possible without a gyro-stabilized platform. However, more data on complete ship motions is needed to determine whether or not this method is accurate enough to keep the drift s of position within design speci-fications with the double integration method used. A less noisy ve r t i c a l accelerometer is required i f the same integrator is to be used. Closed loop performance of the hydraulic systems implemented was limited by the non-linear characteristics of the valve and mechanical constraints of the available systems. The basic control concept i s satisfactory, but a more complete control scheme may be necessary to implement a f i n a l working system. Complete programmability is possible with a 16 x 16 b i t shift register memory and some additional control logic. Microinstructions can be entered on a thumbwheel switch in the f i r s t three bits of the most significant depth digit. The deepest programmable depth would then be 1999 meters. MSD Firs t 3 When restart pulse Depth bits arrives use 0,1 000 Allow manual thumbwheel speed Bottle casts restart after 2,3 001 Pos Ack memory speed Stop 4,-5 010 Restart when thumbwheel speed STD casts and Stop Ack 6,7 011 memory speed 'Other work 8,9 100 Change Speed Only 34 A method of integrating.the acceleration signal that does not require such a high peak gain would remove the excessive drifting prob-lems. Some form of d i g i t a l f i l t e r i n g i s probably necessary to implement such a scheme. One hydraulic system w i l l have to be continuously available for a more complete analysis of the control problem to be undertaken. Compensation for changing drum size and valve gain with payload depth could be accomplished within the limits of valve travel by varying electronic gain accordingly. A control strategy to minimize (P 2) for a Li constant speed of the payload would effectively minimize changes in cable tension. This approach could be extended for any cable angle. Several nonlinearities such as stiction, backlash, valve gain, maximum flowrates, and variations in cable tension which result,-..from imperfect wave motion compensation, w i l l have to be considered. 35 APPENDIX A. Deck motions l i k e l y to occur under working conditions. While on station, only ocean waves and wind w i l l affect the motion of the ship. Wind, under oceanographic research conditions, has negligible effect and the ocean waves are the main source of motion. Ocean waves contain a pseudorandom mixture of sine waves ranging in fre-quency (tides neglected) from 0.05 hertz for the longest swells to above 10 hertz for tiny ripples [17]. The hu l l of the ship severely attenuates the higher frequencies above 0.2 hertz to a negligible amplitude. For short periods of time, the motion of the deck is approximately sinusoidal and hence, a l l motions w i l l be considered sinusoidal for ease of calculation. Roll f r r = 20 ft I = 120 ft 9 =45° Fig A.1 Terms and numbers used to define deck accelerations. For the Endeavour, a research vessel on which the system might be used, three aspects of deck motion are available. At the stern (point P^ in diagram A.1), maximum accelerations are about ± |g at higher ship frequencies, typically to = 1 sec and maximum deck speed i s about 6 at frequencies possibly as low as t o g = 0.316 sec * [16]. Maximum 36 deck t i l t occurs at higher frequencies and oceanographic work is post-poned when rol l i n g is greater than ± 10° (± 0.1745 rad)[15]. Due to a sinusoidal r o l l i n g motion, that i s , 9 = 0.1745 sin to t, where to = 1 sec s s 0 t o 2r cos 0n transverse accelerations at the height of P, of about x = 1 s g or 77 mg peak can be expected. An additive effect i s transverse movement of the whole ship as i t rises on a wave striking broadside. A 1 foot movement would imply about 31 mg peak. Phase relationships of the above accelerations are not known, so the most severe conditions (to = 1 sec' 1) s at P^ are considered to be approximately 0 = 0.1745 sin ( t o t-<f>_ ) s 0z x = 100 mg sin ( to t-<f> ) (A.l) s s xz z = 250 mg sin OJ t . • s s At P2 similar conditions may cause .7 z = 300 mg sin to t (A. 2) s s due to rolling of the ship. Maximum pitch angle of the ship at this frequency should be no more than 5°, giving y g = 5 mg sin(togt-<}>yz) . (A. 3) At the lower end of the frequency range (to =0.316 sec 1) , the accelerations s and t i l t i n g angles are generally smaller but the displacements can be larger because of the lower frequency. At a maximum anticipated angle of 5°, transverse accelerations w i l l be at most x = 3 mg sin(0.316t-<|> ) S X Z (A.4) y g = 0.5 mg sin(0.316t-<}>yz) The maximum vertical speed i s 6 •g-^- , which implies that the peak dis-placement is about 20 feet and the peak acceleration i s 63 mg. The smallest vertical acceleration considered w i l l arise from 37 a vertical displacement of 1 foot in a long swell under which conditions transverse accelerations are negligible. A more subtle form of deck acceleration w i l l be vibration. Frequencies range from 0 -> 33 hertz and approximate peak amplitudes vary from 0.01 to 0.02 inches. Since structural isolators are usually chosen with a resonant frequency of 6 hertz, this frequency w i l l be chosen to define worst case acceleration due to vibration. Absolute Quantities Most Severe (co = l.sec"') Deep Swell (to =0.316 sec - 1) s Slightest (OJ =0.316 sec - 1) s A =-x x s 100 mg + a ^ 3 m g + a v i b x a v i b x A = y y J 8 5 m g + a v i b y 1 1 1 8 + a V i b y a v i b y A =l+z z s 1+250 mg+a v i b z 1 + 63 mg + a v . b z 1 + 3 mg + a v ± b z e 10° 5° -D z 8 f t 20 f t 1 f t Table III. Summary of peak deck motions. (a ., = 75 mg.) 38 APPENDIX B. Calculations for d r i f t s for different integrators. In general the integrator must have i) a DC blocking capability, i i ) an output of 1 volt per 4 f t deck ri s e , and i i i ) 3° phase error at us =0.316 s e c - 1 (-20 second swell). 6 Accelerationy Position Fig B.l General integrator characteristic for n poles, 1^ i s electronic gain. The calculations in this appendix determine the d r i f t in position due to a 100 yg average error in acceleration for f i l t e r s of 1 to 5 zeroes. The state equation approach is used. The equation, 0.5 K (ST ) y_ _ n n u = (1 + ST ) N n n-2 x = 60n for 3° lag, n can be converted to x. = X i + i + V n x «= b .u - I a. ,x. n n i - l i i = l,2,...,n-l u = 100 yg where a = x m n and a m -n _ m-n m (n + 1 - k\ " Tn k=l U + 1 - kj also, b. = 8 = 0 ' i Mn m = 0 m = l,2,...,n—1 i = 0 and b. = g - Z a .b. . n-i j = 1 n-j i - j where a l l 8 . = 0 ^n-i and 3 o'- 32f1 * M n " 2 V Tn / i = 1,2,...,n i = 1,2,...,n—3,n-lj A computer program produced the solutions y = x^ for n = [3,8]. 39 The value of T which affects the quality of integration at the operating frequencies, was also varied slightly. Electronic gain and other f i l t e r data were also calculated for comparison. The program was modified to output responses to a 100 yg pulse input for the integrator that was implemented (i.e., n = 5, T = 300). A l l results are condensed in figures B.2 and B.3. Fig B.3 Peak d r i f t and phase error as affected by T, for n = 5. r Accelerometers 6 Instrumentation C i r cu i t (analog) INSTRUMENTATION PACKAGE 1 Constant Pressure Hydraulic Source 3 Electro-hydraul ic Valve Control Signal MECHANICAL SYSTEM Ampli f i e r (ana log) Programmable Inputs & Feedback (d ig i ta l ) Integrator (analog) Power Suppl y Motor I ^ j Winch, Cable & Payload F r i c t ion Drive Zero-veloci ty Magnet i c Pi ckup rGear> IWheelJ 90 * 120 vac @ 60 Hz MAIN CHASSIS Fig C. l System Components. Fig. C.l Front view of main chassis with panels removed. F i g . C.3 I n s t r u m e n t a t i o n Package. The p r i n t e d c i r c u i t , o f f t o the s i d e , i s n o r m a l l y h e l d i n the co n n e c t o r b l o c k i n s i d e the box. 42 0 o r M Mode Han 01 r Han Han Rese t A u t o Han In Out Run Pause R e s t a r t o r Chge Speed OPERATOR INTERFACE T l Stop Command Speed Change Command SPEED CONTROLLER i P r o o f IngJ A c c e l Dece l S t o p Ack A l l o w Speed Change Reset 0/N Count BI -OtRECTIOHAl N COUNTER D/N E n a b l e Depth Count DEPTH COUNTER Reset I n h i b i t Depth Count > DEPTH DISPLAY DEPTH COMPARATOR . D e s ! r e d Depth Auto DI r Depth A - B MAIN CONTROL LOGIC Pos Ack Input Count Feedback Count C l o c k i n g S i g n a l s COUNT SYNCHRONIZER S , s ' S 2 s ' l » Reset D l f f C D i f f Count DIFFERENTIAL COUNTER D/A CONVERTER FEEDBACK TRANSDUCER A TACHOMETER D i r e c t i o n P u l s e s CONTROL CIRCUIT 5 ^ E l e c t r o - h y d r a u l V a l v e INSTRUMENTATION V INTEGRATOR zs-zs / I n t e r f a c i n g - Pos Ack s i g n i f i e s u n i t Is ready to r e c e i v e a new d e s i r e d d e p t h . A l l o w Speed Change s i g n i f i e s u n i t has reached the p r e v i o u s d e s i r e d s p e e d . A new speed can be e n t e r e d by a speed change command p u l s e . Fig Ch Block diagram of c i r c u i t s . 0/N state 0000 0001 0/H Count (Auto)(Depth A=B) x_TL AX. T (3) +5 (5)5 00 Stop Command Zero Depth C (Reset.)( leset,) Reset D/N ' (I) to (4) These signals are formed as shown In the inserts. (5) These capacitors i n i t i a l i z e the unit when power is switched on. * Unsynchronized signals are subscripted "n" . Signals synchronized to T. are subscripted " s " . Fig C 5 Section of Main Control Logic which screens commands from the operator and defines stop, star t and d i rect ion s igna ls . The timing c i r c u i t outputs clocking signals which act ivate the tachometer and count synchronizer. Resets and d i rec t ion changes are allowed ^ only when Pos Ack=l. w Stop A c k n Stop Command Auto node Run (Pause) 0 or N (from 0/M) Pos Ack, 'In Accel Double Count* Accel Accel Reset Diff C— Count Direction Di fferenti al Counter 12-bit COUNT SYNCHRONIZER In i t ia l ized at 1000 1000 0000 * Accel Double Count Is generated by the timing c i rcu i t and lags Wj by 90°. • • ' Fig C.6 Count synchronizer and control log ic for the divide-by-N and d i f f e r e n t i a l counters. Stop Command Desired Speed 8 - b i t BCD SD ' 1 ^ 512 I. 512 I. Enable • Down Counter EnabTJ XR-2556CN A c c e l e r a t i o n Rate Sampl Ing C i r c u i t XR-2307CN"! Load ;D Q P" c Ql Up-Down Counter - Stop Ack XR-2307CN new J " A c c e l — ' ' — A l l o w Sp Chg T.Accel + 512 'In A l»0 change In A c c e l n e w or D e c e l n e w I n h i b i t s a f u r t h e r change In speed A c c e l A l l o w Sp Chg Decel JAccel Speed Change Command X S t o p Command X(J"Accel) C D Q Accel J | f " " ' « J L J T J 1 _ J L J T _ J 1 _ J I ^ ^ lO-Accel) Enab leJ JAccel~]T" I 2 T A c c e l ; ; IT J L XU"Accel)_ T C l A c c e l ) For easy I n t e r f a c i n g , a speed change command Is retarded one c y c l e [ ( I ) to CO] so a new de s i r e d speed can be entered w i t h a speed change command pulse. This allows measurement and comparison o f the a c t u a l and d e s i r e d speed before the speed change commences. (I) Sampled WO t r a n s i t i o n of Accel begins c y c l e . D e s i r e d down counter. S^2SQ IS made f a l l of the previous 1-0 t r a n s i t i o n speed Is toaded i n t o Z i s l s e . Accel and Decel new new are l a t c h e d . (2) I f a speed change Is allowed, the speed Is incremented. (2) t o (3) The down counter counts 512 I , . (3) Fig C7 Speed Cont ro l le r . V5D VSD Conclusion at (3) New Di rect ion 1 0 VSD A c c e l e r a t e 0 0 SA" SD Hold 1 1 VSD Decelerate -t>-(it) iCcIT and Decel are' formed and compared t o new new latched values. I f a 1-0 change has oc c u r r e d In a l f h a r f u r t h e r r h a n r l A t n ttn»»d I* I n h i b i t t # d - -Stop Command N _ _ Comparator Up-Down Counter < Reset D/N > \ " i — y (Out NL=0) ( I n NL-N) In D/N Count D/N Counter n ' 9 h I deceleration begins n — u — L T — u — L l Ll 2 | I PN I N-1 | ti-2 Out Out Auto Stop Cond , o w | deceleration begins U — U — H — l l Li U In Auto Stop Cond - - -I Counts missed before . I Counts missed before H -2 | N-1 fo I 1 I 2 0 or N Inhibi t Cepth Count To correct for counts missed, creeping begins in S i s direct ion and continues unti l D/N counter Is 0 or N. S j t Zero Depth Counter Depth Counter Counted Depth Depth . Comparator Decoder/Drivers LED Display Fig C.8 Divide-by-N and Depth Counters. The divide-by-N counter is 8-bit b inary, al lowing N to be any value from 2 to 256. The depth counter, comparator and display are 4-digi t BCD. ©-Accelerometers Zener-Referenced Bias -g Fig C.9 Block diagram of instrumentation c i r c u i t . -t-Integrator —|(-AA LH0022C High performance FET Input Op-amp C - 6.8uf Blocking AmplIfler (inverting) R 50 k LrlOCMC Low Cost FET Input op-amp K z sm INTEGRATOR INTEGRATOR Blocking Amp (inv) Blocking Amp (non-1 nv) LM307N Fig C.10 Integrator c i r c u i t . 'z + offset Di f ferent i al Counter Output 12 b i ts / test i nput Tachometer Pulses Di fference Ampl i f i e r & Cal ib ra t ion 1 volt l i " *Vs" 160 counts 'Is 1 6 Q counts sec Fig C . l l Block diagram of control c i r c u i t . 50 APPENDIX D. Alternate schemes considered for deck motion sensing. 1) Position Measurement i) Sonar signals reflected from the ocean floor would have large time delays and would be inconsistent for certain shapes of the floor surface. i i ) Sonar from one or several semi-buoyant submerged platforms could remove the lag but with any sonar sensing, the pulley wheel move-ment must be derived from the h u l l movement. 2) Velocity Measurement i) Vertical velocity derived from the earth magnetic f i e l d i s susceptible to distortion by the ship and must be adjusted for different locations on the globe. i i ) A shaft pivoted near the pulley wheel and hanging into the water with a propeller on i t s lower end, must be deep enough so that the effect of the waves produces no error. Any such shaft could become tangled with the cable and payload. 3) Acceleration Measurement with one accelerometer placed on various platforms designed not to t i l t with the deck. i) A gyroscopically stabilized platform. This i s possible but expensive. i i ) A platform stabilized by reference to the sun, stars or shore lights. This could only be used under suitable weather conditions. i i i ) A pendulum. Transverse accelerations would cause too much swinging. iv) A hanging shaft, pivoted at the pulley wheel. This would have to be very long and could become tangled with the cable. 51 4) Acceleration Measurement with more than one accelerometer. Any scheme of measuring acceleration at two different points the deck is not accurate enough due either to transverse accelerations else too large a distance between the measurement point and the pulley. 52 REFERENCES [1] J. R. Buck, H. W. S t o l l , Jr., "Investigation of a Method to Provide Motion Synchronization During Submersible Retrieval",Naval Eng. Journal, Dec. 1969, 65. [2] L. H. Copeland, "Servo-controlled Winch uses Two Motors", Hydraulics and Pneumatics, 24, 1971, 10. [3] R. R. H i l l , "Air/Oil Servo Maintains Constant Coll Tension", Hydraulics and Pneumatics, 20, 1967, 81. [4] B.C'G. Keefer,"A Design Approach to Hydropneumatic Tensioning Systems for Marine Applications", Lockheed Petroleum Services Ltd., and Dept. of Physics, U.B.C, 1971. [5] W. H. Luehrman, "Shipboard Commander Marine Streamer Depth Controllers", Geophysics, 36, 1971, 1269. [6] H. A. McKenna, "Giant New Winch to Pull Undersea Pipe", Undersea Technology, 10, Sept. 1969, 40-42.. [7] K..TJ. Mitchell, D. J. Strong,"Replenishment-at Sea",Naval Eng. Journal, 82, Aug.' 1970, 52-62. [8] K. J. Mitchell, D. J. Strong, "Replenishment of Ships While Underway", Journal of Science and Technology, 37, 1970, 103-114. [9] S. M. Shinners, Modern Control System Theory and Application, Addison-Wesley Publishing Company, Reading, Mass., 1972, 122-128. [10] A. E. Snyder, J. C. Jerabek, and C. A. Whitney, "Constant Tension Oceanographic Winch", American Society of Mechanical Eng., paper 63-WA-335, 1963. [11] A. Southerland, Jr., "Mechanical Systems for Ocean Engineers", Naval Eng. Journal, 82, Oct. 1970, 63-74. [12] R. E. Wall, M. ,E. Wing, "Tension Recorder for Deep-Sea Winches", Deep Sea Research, 14, 1967, 321. [13] R. Walters, Hydraulic and Electro-Hydraulic Servo Systems, J. W. Arrowsmith Ltd., Bristol 3, England, 1967. Other Sources Conversations with [14] B. G. Keefer, Research Engineer, B. C. Research, Vancouver. [15] G. Pickard, Head, Oceanography Dept., U.B.C, Vancouver. 53 [16] J. Smith, Engineer, Defense Research Establishment Pacific, Esquimalt, B.C. [17] Handbook of Tables for Applied Engineering Science, Chemical Rubber Company, Cleveland, Ohio, 1970, 495, 539-540. [18] Instruction Manual for Obtaining Oceanographic Data, U.S. Naval Oceanographic Office, Pub. No. 607, U.S. Government Printing Office, Washington, D.C, 1970, B-9 to B-12. 

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