RESTRICTED A.P. 3302, PART 1

SECTION 19

CHAPTER 2 SERVOMECHANISMS

ParaRraph Introduction 1 Speed Control of a D.C. Motor 6 Action of Human Operator 8 An Improved Method of Speed Control 9 Position Control Systems 14 Behaviour of a Simple Servomechanism 18 Response and Stability of Servomechanisms 20 Viscous Damping 23 Velocity Damping 26 Velocity Lag 32 Error-rate Damping 35 LJ,e of Stabilizing Networks 39 Transient Velocity Dam ping 42 Integral of Error Compensation 44 Summary of Stabilization Methods 48 Power Requirements of a Servomechanism 49 Components in a Servomechanism 52 Summary .. 55

A.L. 18 (Mar. 62) RESTRICTED

RESTRICTED

PART 1, SECTION 19, CHAPTER 2 SERVOMECHANISMS

Introduction Only an elementary outline of the basic 1. The discovery that heat (from coal or principles involved and a general idea of oil) can be converted into mechanical energy the purpose and applications of control brought about the industrial revolution systems can be attempted in this chapter. and which could use this energy t~ Further information is given in Part 3 of produce useful results were quickly invented these notes. and improved. By controlling such machines, man was able to release large quantities 4. Chapter 1 has shown that d.c. remote of energy with very little expenditure of indication and a.c. systems can energy on his own part. operate between shafts separated by a At first, machines were simple and a human considerable distance, but cannot supply being was quite capable of controlling in torque amplification: the torque delivered to detail the various operations that went to the load can never exceed the input torque. complete any process. But as time has For this reason, and because the error passed, machines and processes have become increases when large torques are transmitted, more complicated and results have had to remote indication and synchro systems are be produced more quickly and more accur­ employed to turn dials and pointers, to ately. Thus it has come about that in many move control valves or to actuate similar cases, man has proved to be an imperfect low-torque loads. controller of the machines he has created. Automatic control systems, on the other It is natural therefore that, wherever possible, hand, can supply the large torques required the human controller should be replaced to move heavy loads, and only a very small by some form of automatic controller. torque need be applied to the input shaft. Remote operation is not inherent in servo­ 2. Automatic control systems can include mechanisms but it can be obtained if synchro electron.ic, electro-mechanical, pneumatic, devices are made part of the system. hydraulic and mechanical devices. Such devices are used to perform diverse functions: 5. From any process there is an end-product f<_>r example, the automatic piloting of an which can be ca11ed the output. The pro­ aircraft, the control of a guided missile, duction of the output depends on the process, the movement of a radar aerial, keeping a and how the process is affected by the input. telescope trained on a star, and so on. A control system acts in such a way that the Nevertheless, regardless of the nature of the output can be controlled in the optimum quantities handled, the resulting arrange­ manner to give a desired result which bears ments have a strong family likeness to each a definite relationship to the input to the other and behave in very similar ways. A system. common theory is therefore applicable to all forms of automatic control. Speed Control of a D.C. Motor The title of this chapter is "Servomech­ 6. Fig. 1 shows an arrangement (known as anisms". A servomechanism, in fact, is the "Ward-Leonard" system) that is used merely a particular type of automatic control for controlling the speed of a d.c. motor system whose output is the position of a driving a load. shaft. It is however the most common The motor current is supplied type ?f control system in radio engineering, by a d.c. generator which, in turn, is driven and smce the theory which has been developed at constant speed. The d.c. motor is in its design is now used for all types of separately excited, the field current being control systems, it is convenient to confine held constant. The generator is also separ­ the discussion to servomechanisms. ately excited, but its field current can be varied by adjusting the controller potentio­ 3. A complete treatment of servomechanisms meter. Any variation in the generator is far beyond the scope of these notes. field current varies the generator output A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2

CONSTANT SPEED DRIVE GENERATOR SUPPLIES ~ G II c:::> lr MOTOR I I ARMATURE I I CURRENT I I CONTROLLER ~ I I',, CALIBRATED IN REVS/MIN. I I I' C~~ANTri__r-11! l ~ CO~~ANT ~ lllc VOLTAGE GENERATOR MOTOR FIELD FIELD VARIABLE. CONSTANT.

Fig. I. SIMPLE SPEED CONTROL OF A D.C. MOTOR voltage and hence the armature current Action of Human Operator to the motor: thus the speed of the motor 8. It is interesting to discuss at this point is varied. If the generator field current is the actions that a human operator would increased, the generated voltage increases, take to maintain a constant speed (Fig. 2). as does the armature current and hence the The first action of a human operator is to motor speed. Therefore the controller poten­ collect the information or data on which he is tiometer could be calibrated with a scale in to act. He has in mind a picture of the out­ revolutions per minute and set for whatever put speed required and at the same time he motor speed is required. notes the actual output speed. His sole With this arrangement, the speed of the function is to compare the two impressions output shaft represents the 'outpl!t': the and so to adjust the system as to reduce the 'input' is the setting of the potentt<;meter. difference, or error, between them: he does The input can therefore be set to gtve the this of course by adjusting the controller desired output which the system should hold potentiometer. He is thus, in this con­ constant. nection, primarily an error-measuring device, and the amount of error determines how he 7. In practice, however, speed is not held causes the motor to use energy from the exactly constant even though ideally the generator to produce the required output speed of a separately-excited .motor .is speed. Note that the human operator pro­ determined by the voltage applied to Its vides a feedback link between output and armature. Variations in speed arise from input. a variety of reasons. In particular, variations of load conditions will cause varying motor speeds and the output is no longer that An Improved Method of Speed Control demanded by the input. 9. In practice, a more effective and efficient This system is not good enough if speed control of output speed can be obtained by control to within a fraction of one per cent replacing the human operator with an auto­ is required. matic control system as shown by the arrange-

OPERATOR'S 1 AS Af'~ E~~L T OF CONTROLLED C~~['\R.Jv~G INPUT IMPRESSIONS I ACTUAL II OUTPUT · I ______yi~~_£.E.£p~A_EK_!:.!.N.f _____SP~ED j~ ACTUAL SPEED

Fig. 2. HOW A HUMAN OPERATOR CONTROLS MOTOR SPEED RESTRICTED RESTRICTED SERVOMECHANISMS

MOTOR CONSTANT SPEED ARMATURE DRIVE. CURRENT

II II ll %~~STANT Ill VOLTAGE CONSTANT DC MOTORe VOLTAGE · 0 FIELD (±) TACHO·GENERATOR VOLTAGE e t 8 2

APPLIED VOLTAGE e 1 Fig. 3. AN IMPROVED METHOD OF SPEED CONTROL ment of Fig. 3. The response of the auto­ by the tacho-generator decreases and the matic system is better than that of a human generator field current increases; the gener­ operator and the automatic arrangement ated voltage thus increases as does the is not subject to fatigue. motor armature current, and the motor speeds up until it reaches the demanded 10. Tachometer-generator. In Fig. 3, the speed. It follows that if for any reason actual motor speed is measured by connecting the load speed tends to change from that a device known as a tachometer-generator or demanded, the correct restoring action will tacho-generator to the output shaft: this automatically be taken. produces a voltage proportional to the speed at which it is driven, i.e. the actual output 12. The operations of the circuits shown speed. The tacho-generator in the circuit of in Fig. 1 and Fig. 3 differ considerably in Fig. 3 is a separately-excited d.c. generator detail. with a constant field and it is so constructed In Fig. 1 the· output depends primarily that it produces a generated e.m.f. which is on the input demand, but the accuracy of exactly proportional to the rotational speed control is limited because there are no means of its armature. On load, the terminal of controlling other factors that affect the voltage is still proportional to speed, pro­ output (such as variation in output load). vided the load current is small enough for The accuracy of control therefore depends armature reaction to have no effect. D.C. on the linearity of the system. Such systems tacho-generators usually have quite a small are referred to as open-loop control systems. maximum-load current, because the armature An open loop control system is characterized is wound with many turns of fine wire, and by the lack of error comparison; that is, the has a large number of there is no feedback of information from segments to ensure a relatively smooth d.c. output to input. Because of their limited output. accuracy, open loop systems are hardly ever used. 11. The output voltage from the tacho­ In Fig. 3, there is feedback of information generator representing the actual speed of from output to input so that the input the load is compared with the voltage across demand and the output can be compared. the controller potentiometer representing The feedback is in opposition to the input the demanded speed: the difference between and tends to reduce the net input to the these two causes the flow of generator system as the output follows the input field current. The connections are such demand more closely: it is therefore, negative that if the load speed is less than that de­ feedback. The system is automatically ad­ manded, the opposition voltage produced justed such as to reduce the error between A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2 the input demand and the output: it is proportional to the position of the shaft therefore an error-actuated device and is at any instant. This can be done by some referred to as a closed-loop control system: of the data devices discussed such systems are the only means of obtaining in Chapter 1. However, one of the easiest accurate and predictable control of output. ways in d.c. systems is to use a potentio­ Both the open-loop and the closed-loop meter as shown in Fig. 4. This method will systems discussed above are power ampli­ be assumed in subsequent paragraphs. fying; the energy expended in adjusting the controller to the desired output speed setting I 5. Consider Fig. 5 which shows in block is only a small fraction of that expended in form, the essential elements in a closed turning the load. The amplification comes loop system for position control. Com­ of course by choosing a motor that is power­ parison with Fig. 3 shows that the controller ful enough to drive the load. and are together equivalent to the potentiometer and generator in the Ward-Leonard system: the servomoter is 13. Note again the main features of a equivalent to the d.c. motor: and the output closed-loop control system: there is an potentiometer replaces the tacho-generator input demand and an output; there is negative because here position is being measured. feedback from the output which is compared The input is the angular position of the with the input demand; the resulting error input shaft and the output is the angular is amplified and used to control the power position of the output shaft connected to into a ; the servomotor turns the load. The requirement is that the the load in such a direction as to reduce the position of the output shaft should conform error and ensure that the output follows the with the input demand, i.e., that the output input demand. shaft follows precisely the movements of the input shaft. The input shaft controls a potentiometer Position Control Systems that provides a voltage proportional to the 14. For the closed loop speed control angle 8i of the input shaft. The output system, the quantity fed back and compared shaft similarly controls a potentiometer with the input demand is a voltage pro­ that provides a voltage proportional to the portional to the speed of the output shaft. angle 80 of the output shaft. The voltage

A more common type of control system proportional to 80 is fed back to an error­ of particular interest in radio engineering measuring device where it is compared with is one which controls the angular or trans­ the voltage proportional to 8i. The feed­ verse position of the output shaft. In closed back is such that it is in opposition to the loop position control systems therefore, input voltage (i.e., ) and the quantity to be fed back must be a measure the output from the error-measuring device of the output shaft position. One of the is an error voltage e proportional to the most convenient ways of providing this difference between 8i and 80: that is, e =

, feedback is to produce a voltage that is 8i - 00 and it can be positive or negative.

SHAFT -+-- ~ ANGULAR ~ -v1 +v 1 TRANSVERSE -v +v A POSITION

A In Each Case, The Potential Of 'A Relot1ve To Earth G1ves A Measure Of The Shaft Pos1l10n.

Fig. 4. PRODUCTION OF VOLTAGE PROPORTIONAL TO SHAFT POSITION RESTRICTED RESTRICTED SERVOMECHANISMS

VOLTAGE PROPORTIONAL TO -8-o

Fig. 5. CLOSED LOOP POSITION CONTROL SYSTEM

16. This error signal is amplified and net input voltage is an error voltage, and applied to the motor which then turns the not the simple voltage proportional to the in­ load in a direction depending on the sense put demand oi: this is the first improvement of the error signal. The direction of rotation of a servomechanism over an open loop is always such as to tend to reduce the error system. voltage to zero; that is, to drive the output A servomechanism has many applications. shaft into alignment with the input shaft. It is used, for example to make a search­

When the voltage proportional to 00 equals light follow its sighting mechanism, to rotate that due to Oi, the error signal is zero: the a radar scanner to a desired position, to motor stops at this point, with input and control aerodynamic surfaces in aircraft and output shafts aligned. missiles, and so on.

17. This particular type of closed loop automatic control system defines a true Behaviour of a Simple Servomechanism servomechanism-an error-actuated, power­ 18. Consider Fig. 6 which shows in block amplifying, position control system. For form the elements in a simple d.c. servo­ a servomechanism to fulfil its function it mechanism. It is assumed that the output must have "follow-up" properties, i.e., the shaft is driving a load, such as a radar output must be capable of following random scanner, and that it has taken up a position variations of input demand over a very which agrees with the position demanded by wide range. Note again that the final the input shaft, i.e., 00 = Oi. The resultant

INPUT SHAFT

Fig. 6. ELEMENTS IN A SIMPLE D.C. SERVOMECHANISM A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2 error signal ( e = 8i - 80 ) is zero and the one fixed value to another fixed value in a motor is stationary in a steady state condition. remote position control system can be Now suppose that the azimuth bearing represented by a "step input" as shown by the of the radar scanner is to be changed from graph of Fig. 7(a). its initial angle to another angle; then the As explained in the preceding paragraphs, input demand is suddenly changed. The initially the system is at rest with 80 = 8b output shaft cannot immediately follow this and at a 8i suddenly changes to a new value: change in demand because of the inertia 00 cannot follow immediately and the error of the load. There is therefore now a therefore, increases from zero to Oi (Fig. difference between 80 and 8i and the resulting 7(c)) and a large torque is applied to the error signal, after amplification, causes the load. As the load accelerates and 80 motor to accelerate in an attempt to bring increases, so the error and torque are reduced the output shaft to the new demanded posi­ until at b 00 reaches the required value and tion. they become zero.

As 00 approaches alignment with 8n However, unless special precautions are the error signal and the motor acceleration taken, a servomechanism will oscillate readily. are progressively reduced until the condition Thus, by the time 80 reaches the required is reached where 80 again equals Oi and the value at b, the load has acquired considerable error signal is zero: the motor then stops. momentum and consequently overshoots. This is the stable condition of the servo­ The error now increases in the opposite mechanism, with the output shaft in the sense and a reverse torque is applied which position required by the input demand. eventually brings the load to rest at c, and It obviously takes time. then accelerates it back again until once more it passes through the required position at d. 19. The period during which the output But again it has acquired kinetic energy in is changing in response to the change of the period c to d and another overshoot demand is called the transient period. When occurs at d. this period has been completed, the system is said to have reached a steady state. The 21. This process can continue indefinitely time taken by the system to reach a new if the frictional losses in the system are steady state after a change of demand (i.e., negligible, and the system oscillates con­ the time occupied by the transient period) tinuously, being unstable and useless: it is is called the response time or the time lag said to "hunt". of the servomechanism. Where there are frictional losses, a damped train of oscillations results as shown in Fig. Response and Stability of Servomechanisms 7(b): in this case, the output shaft oscillates 20. The change in the value of Oi if the several times about its new position before input demand changes instantaneously from coming to rest.

STEP INPUT (0)

.. TIME

(b)

+I

i 9,---b ~ - (C) e o'f-:----...laL------;b\-v--Jd;-___:\,.~;::--~fl"'.~'!llo-..----- ...~TIME.

c

Fig. 7. RESPONSE OF A SERVOMECHANISM TO A STEP INPUT RESTRICTED RESTRICTED SERVOMECHANISMS

TIME

eL SUDDENLY CHANGES_

a = -- =UNDER DAMPED. b = =REQUIRED DAMPING_ c • ---- =CRITICAL DAtviPING _ d ~ -- - =OVERDAMPED

Fig. 8. EFFECT OF DIFFERENT DEGREES OF DAMPING

To avoid oscillations and subsequent precisely and with minimum time lag. It hunti~g, friction or damping is necessary. has been shown that for a rapid response As will be seen later, the effect of frictional time the damping of the system should be damping can be given by electrical means; slightly less than critical damping. The hence damping is a more general term than frictional losses inherent in a servomechanism friction. produce some damping, but usually very much less than that required to ensure 22. Different degrees of damping produce a rapid response time and a short settling­ different response curves. Fig. 8 illustrates down period. It is therefore necessary typical response curves: where there is to introduce additional damping into the overshooting and transient oscillation, as system to obtain the required transient in (a), the system is under-damped: where performance. there is no overshooting or oscillation, as in (d), the system is over-damped: critical damping, as in (c), marks the boundary 24. One obvious method is to increase the between a non-oscillatory and an oscillatory friction in the system by inserting some form response. of brake on the output shaft, as indicated in The response reaches its final value more Fig. 9. This can be achieved either by quickly if there is under-damping: if there putting a mechanical friction plate device is too much under-damping, however, the on the motor shaft or by causing a copper response is oscillatory. For these reasons disc, mounted on the output shaft, to rotate practical servomechanisms are designed t~ between the poles of a horseshoe permanent have slightly less than critical damping (about (eddy current damping). 0 · 75 times critical damping): this is illustrated With a suitable amount of such damping in curve (b) which shows only one overshoot. the required response can be obtained; it is necessary, however, that the amount Viscous Damping of damping be accurately adjustable. 23. The main requirement in a remote position control (r.p.c.) system is that the 25. Viscous friction damping, as this method output shaft should follow the input demand is called, is not a good method and is used

Fig. 9. VISCOUS DAMPING A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2

POSITION FEEDBACK SIGNAL.

VELOCITY FEEDBACK SIGNAL

Fig. 10. ARRANGEMENT FOR VELOCITY FEEDBACK DAMPING only on very small servomechanisms. One power loss such as is obtained with viscous obvious disadvantage is that it dissipates damping. energy and therefore reduces the efficiency If the controller is skilful, the result is of the control system. Also, the energy that the load comes to rest just as it reaches absorbed by the viscous damper is dissipated the required position: overshooting with in the form of heat, and in large servo­ resultant instability is therefore prevented. mechanisms elaborate and expensive cooling arrangements would have to be provided to 28. In the case of the servomechanism, get rid of the heat from the brake. this behaviour is imitated by attaching a In fact any form of damping on the output tache-generator to the output shaft as in side of the control system has serious dis­ Fig. 10. advantages because of the much higher The tache-generator produces a voltage power levels at this end of the system. proportional to the angular velocity of Because of this it is usual to insert the the output shaft, and a suitable fraction of required damping on the input side of the this voltage is fed back to the input of the servomechanism. In this case, the damping amplifier in opposition to the error signal must be electrical in nature and takes the (negative feedback); this is known as velocity form of a modification to the error signal. feedback. Velocity Feedback Damping 29. It has been shown earlier that the error 26. Since a r.p.c. servomechanism is self signal e = cei - eo), where ei is a voltage correcting, it tends to remain quite stable proportional to the input demand and eo when the input shaft is stationary. Thus, is a voltage proportional to the output damping is required only during the transient shaft position. period which follows a change in input With velocity feedback, a voltage pro­ demand. As previously explained, the in­ portional to the speed of the output shaft stability is produced by the load's acquired is fed back to the input of the amplifier in momentum, resulting in an overshoot. opposition to the error signal. Thus, the net input to the amplifier is a voltage pro­ 27. It is interesting to see how a human portional to the error minus a voltage pro­ controller, faced with the same task of portional to the speed of the output shaft. causing a motor to move a load from one The aim with velocity feedback is to position to another, is able to do so without reduce the net input to the amplifier to causing instability or wasting energy. On zero and then to reverse it before the output receipt of his instructions, corresponding shaft reaches its final position: if the amount to a step input of position, the human of feedback is correctly adjusted the result controller will cause the driving motor to is that the momentum of the load, acting apply a torque accelerating the load. As the against the reversed torque, causes the load load gathers speed and approaches the to come to rest just as it reaches the required required position, the controller anticipates position: this obviously reduces the risk that it will overshoot and therefore reverses of overshooting and subsequent instability. the torque. Under this condition, the load is driving 30. This action is illustrated in Fig. 11. against the motor and no energy is being Initially, the error signal predominates and dissipated in the load: there is therefore no the load is accelerated. As the load velocity RESTRICTED RESTRICTED SERVOMECHANISMS

INPUT. ··~--- -~-----~----~TIME. (o.) 1 OUTPUT. 1----·,_i -~..,..- . ~0 OV=R~~-c:n_ \h)

ERROR.

LOAD VELOCITY. ld..J

...... ----LOAD ACCELERATING NET INPUT TO AMPLIFIER.

"-LOAD DECELERATING.

Fig. II. PRINCIPLE OF VELOCITY FEEDBACK DAMPING rises and the error falls (i.e., input and output velocity, i.e., oi increasing linearly with shafts coming into alignment), the net time. input to the amplifier drops rapidly and then increases in the opposite sense, so that a 33. For a servomechanism of this type, decelerating torque is applied to the load with velocity feedback, the transient period before it reaches the required position. is as already discussed. However the final result, after the initial transients have died 31. In addition to the advantage over a out, is that the output shaft rotates at the physical damping system of not causing a same speed as the input shaft but lags behind waste of energy, the velocity feedback it by some constant angle (see Fig. 12(b)). method of damping possesses the important practical advantage that the amount of voltage fed back, and hence the degree of (a) 9 damping, can be simply controlled by in­ '~--~=------R-AM_P_I_N_Pu-T.-;---- serting a potentiometer in the velocity feed­ - : - __J--:--TIME back path. This is a method of damping 1 e. - frequently used in r.p.c. systems. (b l I >----: :-----=:::::::::- Velocity Lag 32. Velocity feedback provides a satis- (c) e factory means of obtaining the required response in r.p.c. systems because in the ~ CHANGE IN steady state such systems are quite stable. INPUT DEMAND However, where the servomotor is required to rotate a load with a constant angular Fig. 12. RESPONSE OF A SERVOMECHANISM velocity, the disadvantage of velocity feed­ TO A RAMP INPUT back becomes apparent. Suppose the servomechanism load is a The resultant instantaneous positional error radar aerial that is required to rotate with between input and output shafts is known as a constant velocity. In such a system, a "velocity error" or "velocity lag". Its effect ramp function input is used as a means of can be quite serious; it can result, for investigating the servomechanism behaviour, instance, in wrong radar bearings of a target. in the same way that a step input is appro­ priate in r. p.c. systems. 34. In a velocity feedback system, velocity A ramp input is illustrated in Fig. 12(a): Jag arises in the following way. Since the it corresponds to the input shaft suddenly output shaft is rotating, the tacho-generator being rotated with a constant angular is producing a velocity feedback voltage A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2 input to the amplifier. On the other hand, isms required to rotate a load at constant since the load is being rotated with a con­ speed. stant velocity, it is neither being accelerated nor decelerated, so no torque is required from 36. Velocity lag is proportional to the the motor; that is, the net input to the speed of the output (and input) shaft. amplifier must be zero (neglecting friction Therefore, if some other signal proportional at bearings and wind resistance). to speed can be used to offset the velocity It has been shown that the net input, with feedback, the error can be made zero. velocity feedback, is a voltage proportional This could be done with the arrangement to the error minus a voltage proportional to shown in Fig. 13. the speed of the output shaft. Thus, if the One tache-generator is mounted on the net input is to be zero, and a voltage pro­ output shaft and produces a voltage pro­ portional to output speed is being fed back portional to the speed of this shaft. A from the tacho-generator in opposition to the second tache-generator mounted on the input, there must be a balancing error signal. input shaft produces a voltage proportional There is, therefore, always an error signal in to input speed. There are therefore three this system (and consequently an error) to input signals to the amplifier, and for the compensate for the velocity feedback signal. connections shown, the combined input is a The error signal, if it is to cancel that due to voltage proportional to error plus a voltage velocity feedback, must be proportional to proportional to input speed minus a voltage the speed of the output shaft, and so velocity proportional to output speed. lag is proportional to output velocity. In the steady state, the input and output shafts in a velocity feedback system rotate Error-rate Damping at the same speed, and in this condition the 35. It has been shown that viscous damping velocity lag is caused by the constant signal improves the transient response of servo­ produced by the output tache-generator. mechanisms, but because of power losses In the system of Fig. 13, this signal is exactly it is used only on small servo systems. cancelled in the steady state, by the signal Velocity feedback similarly improves the from the input tache-generator. Therefore transient response without introducing power since the net input to the amplifier is required losses and is, therefore, generally preferable to be zero, the error signal (e) itself can be in all but very small servo systems. zero; that is, the system will have zero In r. p.c. systems, either of these two forms velocity lag. of damping can produce the required result, because it is only the transient performance 37. The system outlined in para. 36 is not, that is important: the steady state error is in fact, a practicable proposition because of zero in any case. the difficulty of ensuring that the outputs However, in angular velocity control from the two tache-generators remain con­ systems, although velocity feedback improves stant with time. Fortunately, a simplifi­ the transient performance, it also unfortun­ cation is possible in which both tache­ ately gives rise to a steady state error known generators can be dispensed with. as velocity lag. Steps must therefore be For velocity damping of step position taken to reduce this error in servomechan- inputs, a feedback voltage proportional to

-e-i

~0 FEEDBACK -9o

VELOCITY FEEDBACK

Fig. 13. METHOD FOR REDUCING VELOCITY LAG RESTRICTED RESTRICTED SERVOMECHANISMS the speed of the output shaft is required. For a position control system, if the servo­ This, however, introduces velocity lag in mechanism is subjected to a step position servomechanisms required to rotate a load input, the error jumps immediately to its at constant speed, and to avoid or reduce maximum value, because the output shaft this form of error, a voltage proportional to momentarily will not move. Initially, there­ the speed of the input minus the speed of the fore, since the capacitor cannot charge output is required; that is, a voltage pro­ instantaneously, the full error voltage is portional to speed of (input-output) or developed across R 2 and applied to the proportional to speed of (error signal). amplifier, and the motor accelerates rapidly. In the same way as the velocity of the As the capacitor charges, the voltage across output shaft equals the rate of change of it rises and the input to the amplifier falls;

80 with time, so velocity of error equals rate the motor torque, therefore, also drops. of change of error with time. This is The effect of the network is initially to cause obtained by differentiating the error with the load to accelerate quickly. The resistor respect to time. R1 is inserted to allow C to discharge on a Thus by differentiating the error signal pre-arranged time constant. and combining the derivative with the actual error at the input to the amplifier, the net input to the amplifier is a voltage pro­ 40. As the load approaches the required portional to the error plus a voltage pro­ position, the error voltage falls. However, portional to speed of (input-output). This if the values of the components have been is the same form as that given in para. 36. correctly chosen, the charge acquired by the The result will therefore be the same, so capacitor during the initial period now that in the steady state the system has zero causes the voltage across it to exceed the velocity lag. error voltage. Thus the voltage applied to the amplifier is now negative even though the 38. An arrangement for providing this is error voltage is still slightly positive. In illustrated in Fig. 14. This method of other words, a retarding torque is applied to stabilization is called "derivative of error the load before it reaches the required compensation" or error-rate damping. position: overshooting is prevented and stability during the transient period con­ Use of Stabilizing Networks sequently improved. 39. Stabilization of a servomechanism to obtain a good transient response in a r. p.c. 41. For a ramp input, this system has system and a good steady state response in a almost zero error in the steady state: that velocity system can also be obtained by is, velocity lag has been virtually eliminated. inserting a suitable network in the input to In the steady state, zero torque is required the servo amplifier. A typical circuit, known (no acceleration or deceleration) and for as a phase-advance network, is illustrated in this condition to be satisfied, the input to Fig. 15. the amplifier must also be zero. The net_

VOLTAGE PROPORTIONAL TO SPEED OF (INPUT-OUTPUT) /

POSITION FEEDBACK 6o

NET INPUT TO AMPLIFIER IS A VOLTAGE PROPORTIONAL TO ERROR PLUS A VOLTAGE PROPORTIONAL TO SPEED OF (INPUT-OUTPUT) Fig. 14. ERROR-RATE DAMPING ARRANGEMENT A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2

-6-i

-&a

POSITION FEEDBACK -&0

r------, I I I I I I I I I I FROM ERROR -MEASURING-+ e R 2 ~~~~lED--+- AMP~~IER DEVICE 1 1 I I I I L------~ Fig. 15. USE OF STABILIZING NETWORK TO REDUCE VELOCITY LAG work however will only supply zero voltage would be no velocity feedback signal at the to the amplifier if the input to the network is amplifier input under conditions of steady zero, i.e., if the error is zero. rotation and no error signal would be required to offset it, i.e., the velocity lag Transient Velocity Damping would be zero (neglecting inherent friction). 42. In an angular velocity control system, velocity feedback is used to improve the 43. A simple method of achieving this is transient response: the only effect it has shown in Fig. 16. A voltage proportional once the steady state is reached, is to intro­ to the speed of the output shaft is produced duce velocity lag. During a state of steady by the tacho-generator and this is applied to a rotation, the velocity feedback signal, which CR network: that part of the velocity feed­ is the cause of velocity lag, is itself constant back signal appearing across R is applied to and therefore provides no damping. It is the amplifier input in opposition to the error only during the transient period that the signal. velocity feed back signal is changing and The time constant of the CR circuit is such therefore providing damping. that only variations of voltage applied across lf it were possible to use only the changing the combination are developed across R and part of the velocity feedback signal during applied to the amplifier. If the velocity the transient period and not the constant part feedback signal is constant (as it will be during steady rotation, velocity lag would be during steady rotation) then the voltage reduced. If this could be arranged, there across R falls to zero with a time constant

1-e-=_B.;....i-...B..;;;o___;+-ICON:~gLLE R - AMPLIFIER

POSITION FEEDBACK B-0

TRANSIENT/ VELOCITY FEEDBACK ~~~~~~~YK L------.. ..._ r PROPORTIONAL TO OUTPUT SPEED DIFFERENTIATING/ CIRCUIT.

Fig. 16. TRANSIENT VELOCITY FEEDBACK RESTRICTED RESTRICTED SERVOMECHANISMS

VOLTAGE PROPORTIONAL TO SPEED OF (INPUT.-OUTPUT).

POSITION FEEDBACK 9o

Fig. 17. INTEGRAL OF ERROR COMPENSATION of CR and the capacitor charges to this It is assumed that some inherent damping voltage. In other words, the tacho-generator is present on the output shaft but that it is output is differentiated by CR so that velocity insufficient to provide a correctly damped feedback damping is effective only during the response: error-rate damping is, therefore, time that the output velocity is changing, i.e., provided as well. To reduce the velocity during the transient period. This is the lag that results from the inherent frictional requirement. damping, the amplifier is also supplied with This method of stabilization is known as the integral of the error. transient velocity feedback damping: an alternative name is acceleration feedback 46. Neglecting the operation of the inte­ damping, because the damping is effective grator for the moment, it has been shown only when the load velocity is changing. earlier that in the steady state for a ramp input, there is a steady error known as Integral of Error Compensation 44. It has been assumed so far that the inherent damping and frictional losses in a servomechanism are so small that they can be neglected. Because of this, it was stated that in the steady state with a ramp input, no acceleration or deceleration was required and the input to the amplifier under such conditions was required to be zero. However, in practice, there will always '------~~~-·p ----- be a small amount of damping due to bearing and commutator friction; also in Fig. 18. PRINCIPLE OF INTEGRAL OF large aerials driven by a servomechanism ERROR COMPENSATION METHOD wind friction will introduce damping: the damping is quite insufficient to produce a stabilized performance and for this reason velocity lag due to the friction on the output additional damping, of one of the forms shaft. This is illustrated in Fig. 18. described in the preceding paragraphs, has Suppose now that the error signal is to be provided. applied to the integrator and that this circuit Nevertheless, the fact that there is inherent becomes effective at point P in Fig. 18. damping in these systems means that some The operation of the integrator is such that torque is required on the output shaft its output increases continuously in the even in the steady state for a ramp input, presence of an error. Thus the total input and a finite error will exist. to the amplifier starts to increase and the output torque consequently becomes greater 45. One method of reducing the steady than that absorbed by friction in the system: state error in a velocity control system is the excess torque accelerates the load and illustrated in Fig. 17. the output shaft starts to catch up on the A.L. 18 (Mar. 62)

54709-c RESTRICTED ..

RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2 input shaft. As it does so, the error is Power Requirements of a Servomechanism reduced and the integrator output increases 49. In the preceding paragraphs a broad more slowly with time. outline of the basic principles involved in Nevertheless, as long as there is a finite the operation of servomechanisms and of error, the integrator output continues to the steps taken to improve stability have increase with time. Thus equilibrium is been considered. To c0mplete the picture established and a steady state attained only it is necessary to have another look at the when the error signal has fallen to zero, at essential elements of a servomechanism so which point the integrator output remains that some idea of the range of applications constant at the required level. can be obtained. 47. This method of stabilization obviously 50. It has already been stated that in a has tremendous advantages, but unless the servomechanism much greater power is integrating circuit is carefully designed, associated with the output than is available over-correction can result and the error-rate from the source of the input signal: in this damping provided may be insufficient to sense therefore a servomechanism can be prevent oscillation. Under-correction is just looked upon as a power amplifier. as bad, because the effect then is that the The power requirements may be small or output shaft catches up on the input shaft may be very great, depending on the job only very slowly. Design is therefore very the servomechanism has to do. In what critical. may be termed 'instrument servos', the drive The integrator circuit commonly takes power required is only a few watts. In the form of a series CR network connected other systems that are required to control in a phase-lag circuit, the output being the movement of large radar scanners, the derived from the voltage across C. The output power required may be of the order time constant is very important. of kilowatts. 51. Some idea of this range of application is Summary of Stabilization Methods given in the illustration of Fig. 20. In (a) 48. The effects of the various methods the servomechanism is required to rotate used for obtaining stability in servomechan­ the large radar scanner: the size of the load isms are illustrated in Fig. 19. The approxi­ is such that the power output required is of mate response to step input and ramp input the order of 100 kilowatts. functions are shown and appropriate remarks In (b) on the other hand, the equipment are included. shown is carried in an aircraft and is used

METHOD OF DAMPING. RESPONSE TO STEP INPUT. RESPONSE TO RAMP INPUT.

~- fAST OSCILLATORY RESPONSE, INHERENT FRICTION. _ g; I .-V (CONSIDERABLE HUNTING): (UNDE RDM'\PED) TI~E e.i ..-c;~E SMALL VELOCITY LAG:

VISCOUS DAMPING

, _ .- FAST DAMPED RESPONSE: VELOCITY FEEDMCK e,l ~e;_--- LARGE VELOCITY LAG: DAMPING. e. a. & - - SATISFACTORY FOR MOST ~'k0: m'IE e. .- ..-- e. TIME R.P.C. SYSTEMS. 1 <' ERROR-RATE DAMPING. FAST DAMPED RESPONSE: PHASE -ADVANCE NETWORK. L~e~~ ~-- SMALL VELOCITY LAG: e,& ~ ~ ~ TRANSIENT VELOCITY e. t:} TIME 9,, ~ ~- TIME FEEDBACK DAMPING ~ ' / FAST DAMPED RESPONSE: o, I~ PRACTICALLY ZERO VELOCITY INTEGRAL OF ERROR. a. e. & _;.- LAG: t'~ TIME e. _-- a. TIME DIFFICULT TO MAINTAIN )' _.. STABILITY:

Fig. 19. COMPARISON OF DAMPING METHODS RESTRICTED RESTRICTED SERVOMECHANISMS

SERVOMOTOR.

MAP UNIT . DRIVE.

DRIVE ROLLER.

Fig. 20. RANGE OF APPLICATION OF SERVOMECHANISMS to produce a map of the ground over which each of these elements for varying appli­ the aircraft is flying: a servomechanism is cations and power requirements are given required to drive the roller at a speed pro­ in the following paragraphs. portional to the ground speed of the aircraft: it is a small mechanism, the power output 53. Error-measuring device. In d.c. systems, requirements being of the order of a few the input and output shafts are commonly watts. connected to potentiometer wipers that pick off d.c. voltages proportional to ei and eo Components in a Servomechanism respectively. The error-measuring device 52. Fig. 21 shows the essential elements in in this case is merely the arrangement of a r.p.c. servomechanism. Brief notes on the connections at the amplifier such that

-~~~~~~~~RNETWORK.

a POSITION FEEDBACK e. I ------~~------~ ERROR-MEASURING DEVICE. Fig. 21. ESSENTIAL ELEMENTS IN A R.P.C. SERVOMECHANISM A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2

SYNCHRO CONTROL SYNCHRO CONTROL TRANSMITTER. .

'-<- x-.9· c;:~ '" INPUT SHAFT. POSITIONAL FEEDBACK.

Fig. 22. A.C. ERROR-MEASURING DEVICE the input to the amplifier is the error voltage valve or magnetic : the amplified proportional to ei - eo. signal can then be applied to one of the In a.c. systems, a control synchro system field windings of the driving motor­ is usual as the error-measuring device. usually a two-phase (see This has been dealt with in Chapter 1 and a Sect. 5, Chap. 4). It will be remembered typical arrangement is illustrated in Fig. 22. that the magnitude and phase of the output This shows that the input to the amplifier is voltage from a control synchro depends an a.c. error signal proportional to ei - eo. on the magnitude and sense of the error and is either in phase or in anti-phase with the reference alternating voltage. If 54. Controller, amplifier and servomotor. the reference voltage is applied to one The components used in these stages, and d · their size and complexity, are determined by field winding of the two-phase in uctwn the power output requirements of the motor through a 90° phase shifting net- servomechanism. work, and the amplified error signal is applied to the quadrature field winding, (a) Low-power d.c. servos. In small d.c. the motor rotates. Since the field due to servomechanisms where the power output the error is now either 90° leading or 90° required is of the order of a few watts, lagging on the reference field, the speed the error signal is applied to a static d.c. and direction of rotation of the motor amplifier or several such amplifiers in depends on the magnitude and sense of cascade. Either thermionic hard valve the error. or magnetic amplifiers can be used and the An a.c. tacho-generator is used to give circuit will include the usual stabilizing velocity or transient velocity feedback. arrangements to ensure the required re- The a.c. tacho-generator produces an sponse. The d.c. output of the amplifier alternating voltage at a constant frequency, controls the armature current of a separ- but the magnitude of the generated voltage ately-excited d.c. motor, thereby con- is directly proportional to the speed at trolling the speed and direction of the out- which the generator is driven, i.e., the put load. Where velocity feedback or output speed of the servomechanism. transient velocity feedback is required, The is a 'drag-cup' or hollow brass the feedback voltage can be obtained cylinder, but the principles of operation from a small d.c. tacho-generator mounted can be more easily explained by considering on the output shaft which produces a a squirrel-cage rotor, i.e., made up of a voltage proportional to speed. In certain large number of uninsulated coils as cases, the back e.m.f. of the motor itself illustrated in Fig. 23(a). As the rotor can be utilized. rotates, voltages are induced in the coils by (b) Lower-power a.c. servos. In small a.c. interaction with the primary field: at any systems, the a.c. error signal from the instant, maximum e.m.f. is induced in the control synchro is amplified through hard coil passing through the primary axis, i.e., RESTRICTED RESTRICTED SERVOMECHANISMS systems where the power requirements are in excess of about 100 watts, a separ­ ately-excited d.c. motor is used to drive the load. The input to the system, on the other hand, is usually from a synchro control transformer and is therefore an a.c. error signal. There must then be con­ version from a.c. to d.c. in the servo­ mechanism. The small a.c. error signal is amplified in a static hard valve or magnetic amplifier and is then applied to a special type of rectifier known as a phase­ sensitive rectifier. It was noted earlier that the magnitude and phase of the voltage from a synchro control trans­ former depends on the magnitude and sense of the error. A simple rectifier takes no account of phase difference so that a rectifier circuit sensitive to phase is

INPUT D.C. OUTPUT TO SHAFT. POWER AMPLIFIERS.

e. POSITIONAL~ FEEDBACK.~

A.C. SUPPLY (REFERENCE) VOLTAGE. :F\f\Af\f\f\v •TIME (f:' ZERO ERROR :';

ERROf.~LTAGE ~ 'DEGREES Of ERROR, SYNCHRO. :r- vv(\ NOTE: CHANGE OF PHASE. 8 D.C.OUTPUT-GIVES NO OUTPUT FROM -A __ A- --~- - £INDICATION OF SENSE -u __ - - ~ OF ERROR. NORMAL RECTIFIE~r- _

tERROR OUTPUT FROM + -- f:\-- -~- PHASE-SENSITIVE 0 <"?'> L) {"'\ - RECTIFIER. \Z9-- ~-- Q....:::._POLARITY OF OUTPUT . V GIVES SENSE OF ERROR. . -ERROR. Fig. 24. OPERATION OF PHASE-SENSITIVE RECTIFIER

magnetic amplifier energises the field of a This system can be extended to produce

small exciter generator G1 which is capable outputs of the order of several hundreds of producing an output of, say, 100 watts. of kilowatts by connecting a number of This in turn is sufficient to energise the generators in cascade. It is, however,

field of the main generator G 2 which may more economical to group two or even produce an output of, say, 10 kilowatts three generators inside one casing. This to drive the separately-excited motor M. is the method adopted in the Power amplification has thus been achieved. and Metadyne generator systems.

CONSTANT SPEED CONSTANT DRIVE DC ----,------, VOLTAGE \ \ \ \ \ \

VALVE OR AND MAGNETIC SIGNAL POWER AMPLIFIER M~PLIFIER 11~11\ e. 10 w

POSITION FEEDBACK e.

Fig. 25. USE OF ROTARY POWER AMPLIFIERS RESTRICTED ..

RESTRICTED SERVOMECHANISMS

9; -=~= INPUT • ERROR e STATIC SIGNAL SEPARATELY MEASURING EXCITED SHAFT AND POWER CIRCUIT D.C. SERVO AMPLIFIE~S MOTOR '

POSITION FEEDBACK 9,

(OJ LOW-POWER D.C. SERVOMECHANISM

SIGNAL AND TWO-PHASE POWER INDS~;~~N F==:t===1 AMPLIFIERS MOTOR

... ERROR SIGNAL e ~ e1 -e,

(b) LOW- POWER A. C. SERVOMECHANISM

IU~~y ;:~~1;:======:=;-1

IYNCHRO ERROR RATE • MAGNETIC OR SEPARATELY DAMPING PHAS1- GAS FILLED EXCITED NETWORK AND ~ENSITIYE VALVE DC SERVO MOTOR SIGNAL AC RECTIFIER DC POWER DC ~~:tiSHAfT ~/~lT) AMPLIFIER L

(C) MODERATE- POWER SERVOMECHANISM

SYNCHRO ROTARY SEPARATELY CT SYNCHRO '""''~ .. ~:::~:~:~.~·:.J~~ .. -f •.·~:I~l·

i1\FORt-1ATION (d)HIGH-POWER SERVOMECHANISM ON OUTPUT ANGLE 6, ·~ TO Pt>·i·

Fig. 26. SOME TYPICAL SERVOMECHANISM ARRANGEMENTS

A.L. 18 (Mar. 62) RESTRICTED RESTRICTED A.P. 3302, PART 1, SECT. 19, CHAP. 2 Summary It should be noted however that there is considerable room for manreuvre on the 55. ~his chapter h~s considered briefly the operatiOn of a basic servomechanism and part of the designer within this broad area. Because of this, discussion has intentionally its b~haviour to step input and ramp input been kept at block diagram level. func~~ons: the stei?s taken to improve stablltty were also discussed. Mention was C~rcuit detai~s of servo amplifiers (in­ made of the range of applications of servo­ cludmg magnetic and thyratron amplifiers) mechanisms, and a general outline of the phas~-sensitive rectifiers and generator power~ amp~Ifier sys.tems of the Amplidyne type are ~ethods adopted ~o cover this range was given. These specimen methods are illus­ considered m the more appropriate part trated in the block diagrams of Fig. 26. of these notes-Part 3.

RESTRICTED