Low-cost microprocessor-based system forteaching the c.a.d.of control systems

P. Atkinson B.Sc. (Eng.), A.C.G.I., C. Eng., M.I.E.E., M.I.E.R.E., andA.J. Allen B.Sc. (Eng.), M.Phil., C.Eng., M.I.E.E.

Indexing terms:

Abstract: A low cost system ('Cycloid') has been developed for the teaching of the c.a.d. of control systems.It is based on the Research Machines 380 Z microcomputing system with a coarse-graphics interactive tele-vision display. The software which has been developed is written in Basic and is briefly described in thepaper. The application of the design suite in the teaching environment is illustrated by reference to a particu-lar example. The low cost and high reliability of the system should make it particularly attractive to teachingestablishments and small industry as an alternative to expensive time-shared and minicomputer systems.

1 Introduction

It is now recognised that control system design is best per-formed using interactive c.a.d.1'2> 3 in which the designerchooses the strategy, and the computer performs the rou-tine calculations and controls a graphical display. There aretwo approaches to providing a c.a.d. facility for many users;one is to use a large central processor with a number ofgraphics terminals,4's>6 and the other is to use a number ofsmaller dedicated machines, each with its own graphics. Theadvantage of the time-shared system is that very sophisti-cated programs can be made available; the disadvantage isthat the waiting time increases with the number of usersand a processor crash will disrupt the work of many people.The use of several smaller dedicated machines will increasethe reliability of the overall computing facility and willnormally allow design to proceed at a faster rate; moreover,although the programs will in general be less sophisticated,the software can justifiably be tailored to suit an individualuser. Small minicomputor-based systems7 have been usedsuccessfully both in industrial consultancy and the teachingenvironment. However, such systems are rather expensiveand the hardware costs of a minicomputer with goodgraphics has never been less than about £10k. The adventof very low cost microprocessor-based computers withcheap television graphics has altered the situation consider-ably. It is now possible to buy five or six small systemscapable of running the program described in this paper for asimilar figure. It is likely that the price per machine will falleven further in the future as the trend towards personalcomputing gathers momentum.

In the teaching environment, postgraduate studentsworking in large university departments have usually hadaccess to good interactive c.a.d. facilities, but it has seldombeen economically possible to give undergraduates anyexperience. The ready availability of the new machinesshould alleviate this difficulty, and it is the object of thispaper to show how is has been done is a small universitydepartment with limited funds.

Paper 565A, received 14th August 1979Mr Atkinson and Mr Allen are with the Department of Cybernetics,University of Reading, 3, Early Gate, Whiteknights, ReadingRG6 2AL, England

IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

2 The new microprocessor-based system

2.1 'Cycloid'

The new c.a.d. system is based on the Zilog Z80 micro-processor, developed into a computer system by ResearchMachines Ltd. (UK) and termed the 380 Z. The softwarehas been specially developed at the University of Readingand is written in Basic. It allows the designer to obtainnumerical and graphical data on a v.d.u. showing thebehaviour of the control system in response to variousinputs and disturbances. The program has a 'commandstructure' in which the designer is usually confronted bythe prompt 'What next?'. The designer can obtain a list ofacceptable replies by simply keying the word HELP. Con-sequently, no manual of operating instructions or lecturesare necessary before the designer can begin to use thesystem. The system (known as 'Cycloid') is thus a systemfor the 'cybernetic computerised learning of interactivedesign.' The program allows the designer to design single-input/single-output control systems in the frequencydomain using Nyquist and inverse Nyquist diagrams and tocheck the time-domain and disturbance responses.

2.2 Control system structure

A block diagram (see Fig. 1) showing the general controlsystem structure can be obtained by keying the commandSYSTEM.

The general control-system structure has been keptfairly simple so that it can be used quickly by undergradu-ates to study a limited set of design problems. The blockdiagram includes

(i) a 'plant' of general transfer function

T2s)(l + T3s)

The structure of the plant can be adjusted by making anyparameter 71, 77, 73, Td equal to zero. The value of NImust be chosen as an integer 0, 1 or 2;

(ii) a 'series compensator' which can be set up to giveany subset of the general compensator transfer function

Tas

111

0143-702X180/020111 +8 $01-50/0

5VSTEH STRUCTURE

d D P r o g r a m s t o r D e s i g n us i rigy q u i s t & I n v e r s e Nyq . D i a g r o o s ;' • h F r e q u e n c y & T ime D o o a i n C h e c k - O u t sh a t n e x t •> |

Fig. 1 Block diagram showing general structure

(iii) a 'parallel compensator' which can be set up to givevelocity feedback having a transfer function

Kcp(s) = KvsThe signals appearing on the block diagram are

(i) the input di(ii) the output 0O

(iii) the error Er(iv) the disturbance input 6d.

When Cycloid is first loaded from cassette, the 'defaultvalues' can be read off by typing LIST.

2.3 The cybernetic interface

To avoid the need for the designers to continuously refer toan instruction manual a simple command language has beendeveloped which allows him to demand graphical and otherinformation by use of a short set of key words. Thesewords are listed below together with an abbreviated state-ment of the computer responses.

In reply to the prompt, 'What next?' a selection of theanswers obeyed are as follows:CHANGE XY (where XY may be K\, K2, Kp, Kv, NI, T\,72, 73, Te, Ta, Td). The computer responds with, say 'XYnow = 1-25 new = ?', reminding you of the present valueof XY and requiring you to type in the new value inresponse to the query. The computer prompt then becomes'Change which param. next?' which only needs a reply ofXY as above in order to change the value of XY.NONE: in reply to 'Change which Param. next?' returnsprompt to 'What next?'.LIST: The computer produces a list of the current par-ameter values.NYQUIST: The computer clears the screen, draws appropri-ate axes and a section of M = 1 -3 circle8 with — 1 + /0point marked, computes reasonable starting frequency andstepping ratio and then calculates, stores and displayspoints on the Nyquist diagram. At the end of the calcu-lation, the values of Mpf and cjrf are displayed where Misthe closed-loop modulus, Mpf its maximum value and ojrfthe angular frequency at which the maximum occurs.INV. NYQ: Similar to NYQUIST but displays an inverseNyquist diagram with an inverse M circle.MOD, DISTF, STEP, RAMPO, RAMPE and DIST clears thescreen, produces scaled graphs of closed-loop frequencymodulus |0o/0il versus frequency, |0o/0dl versus frequency,step response, ramp output response, ramp error response

and step disturbance response, respectively, and displaysrelevant data for each.AUTO: The computer reproduces the last response on axeswith better scales, leaving the relevant data on the screen.CONT: This reply is a request to see the end or tail of aresponse beyond the axes drawn. It is intended to mean'continue calculating'. The graph is superimposed on theprevious part of the response.CLEAR: This will clear the screen.DRAW: This will draw the graph of the last set of resultsobtained but should normally only be used after CLEAR.IDENTIFY: This allows the user to identify a point onthe presently displayed frequency response characteristic(e.g. on the Nyquist diagram) and is followed by a prompt'Ang. Freq. = ?'. If the angular frequency of the requiredpoint to be identified is then keyed in, relevant informationis displayed, e.g. for a Nyquist diagram the reply is

Op/ErMag. = rAng. Freq. = ?

= a+jbAng. =

To escape from the IDENTIFY mode, 0 (zero) must bekeyed to return to the prompt 'What next?'.SUPER: This can be used for superimposing any new fre-quency domain graph (e.g. a Nyquist diagram) on top of anexisting frequency domain graph of the same kind.TYPE: This clears the screen and tabulates appropriate cal-culated values stored during the last test.EXIT from Cycloid; enters Basic prompted by READY(RUN returns to Cycloid with default values reset).

In the event of an illegal combination being keyed in,the computer responds with 'Type HELP if you need it!!'followed by the request 'What next?'.

The system is initialised with default parameters suchthat

1

HC8{s) = 1

and

Hcp(s) = 0

2.4 Cycloid software

The software has to accept and decode commands and thenproduce the desired response (which is often in the form ofa graph with some written statements) before returning tothe standard prompt 'What next?'. These actions are facili-tated by the dual operational modes of the v.d.u. When along list is required, e.g. in response to HELP or TYPE, thescreen is cleared and then operated in scroll mode with 24lines of script. For other responses the bottom four linesremain in scroll while the top space is available for graphicaldisplay. Access to this area is achieved by Basic coding usingthe instruction PLOT X, Y, Z in which Y and X define thepositions of a symbol in a 48 by 80 matrix, and Z definesthe symbol required (e.g. Z = 2 defines a white square asused in Cycloid graph-plotting subroutines).

In order to speed up the interaction between the designerand the machine, the software is arranged to make goodestimates of the scales required for the graphs before thecalculations begin. The graphs can then be plotted as thepoints are calculated, so that the designer is made aware asquickly as possible of the shape of the developing response

112 IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

curve. The CONTINUE facility allows him to extend theresponse for longer time periods or frequency ranges.

Similarly, if the designer feels that the amplitude responseis too big or too small, he may use the AUTO facility whichclears the screen, searches the array of stored points for themaximum and minimum values, evaluates appropriate scalesand offsets, and rapidly replots the graph.

The core of the software contains the simulation sub-routines which must use the data associated with thestructural block diagram (Fig. 1) to compute the requiredresponse curves.

The major design graphs are the Nyquist and inverseNyquist diagram with their associated M and inverse-Mcircles. These are initially presented with fixed scales butcan be suitably rescaled by means of the AUTO facility.Points on the relevant locus are computed from the trans-fer functions using geometric steps in frequency, and ateach frequency these are stored and plotted. These graphs,together with the other frequency response data requiredfor displays of closed-loop modulus, disturbance response,and identification are computed by means of a commonsubroutine. For a given angular frequency this subroutineevaluates a complex number for each block and combinesthem to form

and then the overall open-loop inverse transfer function!

The open-loop transfer function H(j'co) is then calculatedby inversion.

The closed-loop modulus Mis determined from

\H(fcS){l+H{fcS)Yl\

and the disturbance response \60f9d\ from

For time domain response the overall structure is simulateddigitally by breaking it down into a number of basic ele-ments which can produce

(i) the weighted sum of a number of signals(ii) the time-integral of a signal(iii) the time-derivative of a signal(iv) a time-delayed version of a signal.

Each block can be represented by one or a few lines ofBasic coding using well-established numerical techniques.9

3 Applications of Cycloid

3.1 General undergraduate use

Cycloid is used in undergraduate courses at the Universityof Reading on a number of 'paper' design exercises, andalso in conjunction with formal practical work and projectwork in the control engineering laboratory.

There are five paper design exercises requiring the studentto ensure that specifications are met. In each problem thestudent is given the plant transfer function together with aspecification. In the earlier exercises the designs are routineand the student is given considerable guidance on the con-trol strategy to use; having completed his design he is thenrequired to check several responses, and so note the generalbehaviour of the system he has designed. In the later exer-cises he is given a plant together with a comprehensive

specification but no guidance on either the control strategyor the detailed design methodology.

In formal, practical work students use frequency response(or suitable alternative methods) to identify a linear modelof a plant and then proceed to use Cycloid to design a com-pensator so that the overall system will meet a given speci-fication. They then build the hardware (or program themicroprocessor controller) to implement the required com-pensator and proceed to test the complete system. Theactual performance is then compared with the computedperformance in fine detail.

In project work students are encouraged to use theexisting programs in their designs, but more often to writetheir own special purpose programs to match their ownparticular problem, incorporating the effects of nonlinear-ities and alternative design aids.

3.2 Illustrative example

3.2.1 The problem: In order to illustrate the use of Cycloidin the teaching situation we will consider an abstract designexample having a detailed and fairly stringent specification.

The plant to be controlled has a transfer function of theform

K

where K has a nominal value of unity with an uncertaintyof ±10%.

The overall design specifications are as follows:Step response: rise time to maximum 0-5 ± 0 1 s with anovershoot of (25 ± 5)%;Ramp response: zero steady-state error; maximum unitramp peak error 0-2 occurring at a time of less than 0-4 s,settling to 0 01 in less than 3 s;Disturbance response: must be zero at zero frequency andnot exceed 0-1 per unit disturbance at any frequency;Controller gain at high frequency: the controller gain athigh frequency must not exceed 200;Acceleration error constant: must be at least 4 s~2.

3.2.2 The design: It is immediately evident from the dis-turbance response specification and the ramp responsespecification that these cannot be met by the use of eitherproportional control, or series phase-lead compensation. Tomeet the zero steady-state requirements it is necessary tointroduce integral action; this will make the system absol-ultely unstable unless a proportional term is also introduced.Hence the first control possibility is to use a conventionalP +1 controller having a transfer function

Hc(s) =K2 (1 + Tes)

A useful starting point in the design is to choose Te to beabout ten times the sum of the lags and to adjust K2iteratively using the Nyquist diagram until the peak closed-loop modulus Mpf is 1-3. Thus choosing Te to be 11 secondsand K2 to be 0-2 we obtain the fatter of the two Nyquistdiagrams superimposed in Fig. 2. Several iterations leadto the thinner of the two diagrams with MPf =1-3 andoorf = 0-574 rad/s for A"2= 0-068. The step response forthis system is now checked, leading to Fig. 3, showing arise time of 4-5 s and an overshoot of 28%. Although theovershoot is within specification, the rise time is so long

IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980 113

Fig. 2 Superimposed Nyquist diagrams for P + I control alone

Fig. 3 Step response for P +1 control alone

that it is inconceivable that further changes in the par-ameters of the P + / controller will produce the desiredresults.

The next strategic move in the design process is to intro-duce a phase-lead compensator in addition to the existingP +1 controller; the overall series compensator now has atransfer function of form

This transfer function can be rewritten in the form

The time constant Te can be chosen as 1 s to cancel thelarge plant lag and Ta can be chosen as 0 1 s giving anextreme phase-lead network. The ratio KI/K2 can nowbe chosen to give ten times the sum of the residual lags(i.e. K1/K2 = 2s) while K2 can be iteratively adjusted togive Mpf = 1-3. The value of K2 required is 0-7 giving K\equal to 1-4; the associated value of corf is about 0-8 rad/s(cf. 0-574 rad/s for P + I control). This minor improvementin resonant frequency is insufficient to make it worthwhileproceeding with further parametric changes or even bother-ing to find the step response. Furthermore the accelerationerror constant (K2 in this case) is only 0-7 s~2, which iswell below the specification of at least 4 s~2.

The only other strategy available to the designer usingthis suite is to use local 'velocity' feedback in order to'speed up' the plant dynamics. This will have the additionaladvantages of reducing the response to disturbances and thesensitivity to changes in plant parameters. The equivalentblock design for the plant with velocity feedback is shownin Fig. 4.

nominal plant

Kv

Fig. 4 Equivalent block diagram of plant with velocity feedback

The local loop has a second order characteristic equationof the form

(1 + 01s)(l +s) + Kv = 0

or

s2 +lls+10(l+Kv) = 0

To reduce the sensitivity to changes in plant gain anddisturbances it is necessary to make Kv as large as possible;however, making Kv very large will tend to impair the minorloop stability so that some compromise is essential. A valueof Kv equal to 4 gives an oscillatory minor loop mode witha damping ratio of 0-78, which represents a reasonabledegree of damping.

We can again use a P + / controller with phase lead sothat the series compensator again has a transfer function ofthe form

K2(Kl/K2)s+1

Tes

Tas

The specified rise time in response to a step imput is 0-5 s,implying by second-order correlation a value of corf equalto about 6 rad/s. Thus the first design iteration should beaimed at producing sufficient total phase lead in the com-pensator to allow contact with the relevant Af-circle at6 rad/s. Use of the IDENTITY facility shows that the phaselag of the plant with the minor-loop is 168°. Thus assumingthat contact with the relevant M-circle will occur at approxi-mately — 135°, the net phase lead </> required to be pro-duced by the controller is 33° at 6 rad/s.

If we make Te/Ta a factor of 10, then the angle of leadproduced by the phase lead network will be 55° when6 Te = VlO; thus Te = 0-53 s and Ta = 0053 s. The 90° lagproduced by the pure integration of the P +1 unit will thengive a net lag of 35° so that the lead term will now have toproduce a lead of 35° + 33°, i.e. 68° at 6rad/s. Thus

K\tan 68° = 6—

or

K\

114 IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980

Table 1 : System test results with varying Kp values

Kp0 91 01-1Specification

Stepresponse

Tp0-490-460-430-5 + 0-1

% overshoot28282825 ± 5

Ramp response

Tp0-330-310-29

<0-40

Rpe0 200-190-18

<0-20

Ts2-202-252-30

<300

Peakdisturbancefrequency response

Mpd0 0460 0450044

<0-10

Accelerationerrorconstant

5 095-205-30

>400

Now K2 can be chosen initially to give an overall acceler-ation error constant of 4 (in accordance with the minimumspecified value). The plant with the minor loop contributesa component of 1/(1 + Kv), i.e. 0-2. Thus

0-2 £2 = 4

so

andK2 = 20

K\ = 20 x 0-41

= 8-2

The Nyquist diagram for this system is shown in Fig. 5. Thevalue of Afpf(l-27) and ojrf (l-58rad/s) are both low andcan be increased by raising K2 iteratively while keepingKI/K2 at 0 4 1 . Trial and error led to rounded values ofTe = 0-5, Ta = 005, K2 = 26 and ATI = 13 which gives aNyquist diagram as shown in Fig. 6 withAfp/ = 1-36 andcjrf = 7-5rad/s.

The acceleration constant is K2/(l + Kv) i.e. 5-2s~2

(cf. the specification 4s~2) and the high frequency gain ofthe controller is (K\ x Te)/Ta, i.e. 130 (cf. 200). The stepresponse is shown in Fig. 7 giving a rise time to the firstmaximum 0-46 s (cf. 0-5 ± 0-1 s) and overshoot 28% (cf30 ± 5%). The ramp error response is shown in Fig. 8 witha peak error of 019 (cf. 0-2) occurring at a time 0-31 s(cf 0-4s), settling to 0-01 within 2-25 s (cf 3 s). Thedisturbance frequency response is shown in Fig. 9 and hasa peak of 0045 (cf. 0-1). Thus for the nominal plant gainKp=l, the system is wholly within specification. Thesystem must now be tested over the envelope of plant gainsKp = 0-9 through to Kp = 1-1. The essential results of thistest are shown in Table 1.Table 1 shows that the specification has been met on allcounts over the envelope of plant parameters. The final

Nyqui*' B

C. L.Mpf m 1 . 2 6 9 3 4 a t Wr< • I 3 8 4 5 9

What n t x t ? |

Fig. 5 Initial Nyquist diagram of system with P +1, phase lead,and local velocity feedback

IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

set of system parameters can be called up by using thecommand LIST (see Fig. 10).

This example is a good illustration of the power ofclassical design methods when they are supported by aca.d. suite with interactive graphics. Although it cannot beclaimed that the design is optimum in any sense, a fairlystringent set of specifications have been met, and the result-ant series controller and minor loop could physically berealised very simply. It is doubtful whether either Truxall'sdirect transfer function synthesis10 or Towill's low-ordermodel/coefficient plane technique11 would yield simplercontrollers or any improvement in any other performanceindex. Thus it has been demonstrated that this simple ca.d.program can be used by undergraduates at an early stage intheir course to solve a design problem of some considerabledifficulty. At the same time students are made aware of thelimitations of simpler control strategies and become morefamiliar with system dynamics in general.

C . L . H p * « 1 . 3 6 3 6 8 a t \iri « 7 . 5 1 1 7 9

Fig. 6 Final Nyquist diagram of system with P + I, phase lead,and local velocity feedback

Fig. 7 Step response of final system

115

Fig. 8 Ramp error response of final system Fig. 9 Disturbance frequency response of final system

4 Extensions of Cycloid

4.1 Non-linear systems

In practice all systems contain nonlinearities such as hyster-esis, backlash, nonlinear friction, dead zone, curvature andsaturation, but it is standard practice to reduce the worsteffects of most of these by the use of high-gain local feed-back loops. Design is therefore usually based on linearsystems theory, whether this is classical or modern. Finaldesign checks must then be performed using simulationtechniques involving a special purpose simulation.

Students are encouraged to add the few extra lines ofBasic programming to incorporate typical nonlinearities andto test their effects on the time-domain' behaviour of thesystems they have designed. However, plant input satu-ration is inevitable in all control systems and its effectscannot be circumvented by any means. Thus, as an essentialextension of Cycloid, a symmetrical plant input saturationelement is included with controllable saturation level. Itseffects are incorporated into all the time-domain simu-lations but not into the frequency-domain responses.

The saturation level is set to 1017 by default; however, ifthe command SATURATION is made in reply to theprompt 'What next?' the present value of the saturationlevel is displayed and the new value is requested. An inter-esting example of the use of this facility can be coupledwith the solution of the design problem solved in Section3.2.2.

The minimum reasonable level of input plant saturationmust be selected so that the system can follow the maxi-mum ramp rate input with zero error under steady-stateconditions. Of course, under transient conditions the per-formance of the system will deteriorate compared with thelinear system, and it is here that the use of time-domainsimulation is absolutely essential for determining the min-mum actual saturation level for which the specification willbe met on all counts. In the specification, the steady-stateunit ramp error must be zero, implying that the value ofplant saturation which could meet this condition must begreater than unity. It is not a simple matter to predictanalytically the peak value of plant input when respondinglinearly to a unit ramp, and there are two alternativemethods of using Cycloid to determine this value. Eitherthe saturation level can be altered iteratively until the speci-fication for the ramp response is just no longer met, or theprogram can be modified slightly by changing one variablename in three lines of coding so that the plant input is dis-116

played in place of the ramp error. These tests showed thatin this design, the saturation level must be at least 7; other-wise the system will not meet the ramp specification.

The next study will be the step response test for differ-ent sizes of input signal. Cycloid has been designed to workalways with a unit step input. However, the relative effectof different size steps can be determined conveniently byadjusting the saturation level instead of the signal level. Theresults of these tests are shown in Table 2, giving in thefirst three columns the step input level, the percentage over-shoot and the rise time to the maximum.

For low levels of signal (i.e. those for which the initialrise does not cause the plant to saturate) the system respondsas for the linear system. As the signal grows larger the over-shoot initially becomes less, and the time to maximumbecomes rather longer; this is exactly what one expects forany saturating system. However, as the signal changes from0-1 to 0-2 we observe that the rise time has increased greatly.This is due to the fact that the system contains two oscil-latory modes; for low signal levels the effective system gain ishigh at the linearly designed level, and it is the higher fre-quency mode which dominates the step response. When thesystem is saturated for an appreciable portion of theresponse time, the effective gain is much lower and the lowfrequency mode then dominates the step response with aconsequent increase in time to the maximum.

For the very large signals the time to the maximumbecomes progressively longer and the overshoot becomesunacceptably large. This is due to 'integral wind-up' caused

What next ? LIST

Plant Parameters.

Gain Kp = 1No.of Integrations HI = 1Exponential Lags Tl = 1T2 = . 1

Velocity F-Bk. Kv =

Controller Parameters

Proportional Coef. kl •Integral Coef. k2 = 26Deri vat i ve Tin* Te * . '„Exponential Lag Ta • .03

Fig. 10 Display of final system parameters produced by thecommand LIST

IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

Table 2: Step response test for different sizes of input signal

Level ofinput step

0 0 50-10-20-51 02 03 0

With integral windup

Percentageovershoot

28212127346078

Time tomaximum (Tp)

s0-460-491-241-331-431-511-97

With limited integral action

Percentageovershoot

282121272110

7

Time tomaximum (Tp)

s0-460-441-241-331-522 072-42

by the integral of error term increasing while the error ispositive, even though the effect of it is limited by plantinput saturation; subsequently the error signal has to gonegative and remain so for a long period of time while theintegral term is reduced before the plant input signal canfall below its saturation level. This effect was studied indetail for the simple servomechanism many years ago12 andhas been recognised in the process control field, especiallywith the increasing use of direct digital control in whichthere is no natural limit to which the integral term can windup. In a practical implementation it is always essential toplace a limitation on the value to which the integral termcan rise and this feature has been included as an additionaloption on the Cycloid saturation command. By default theintegral term can wind up to 1017 or alternatively it will belimited to a value which will produce the plant saturationlevel. Table 2 includes in its fourth and fifth columns theresulting percentage overshoot and time to first maximumwhen the integral action is limited. The dominant feature ofthis effect is that the overshoot for very large signals isreduced, although the time to the maximum is of courselengthened.

The disturbance response is unaffected by plant satu-ration for disturbance of less than one and a half times thesaturation level of the plant. For disturbances larger thanthis level, the step disturbance response is more sluggishwith larger transient variations in the output.

4.2 Further extensions

With the advent of low-cost microprocessors, sampled-datasystems are becoming increasingly important so that anysuite of c.a.d. programs should incorporate a sampled-datadesign program. The authors wrote such a program13 severalyears ago for use on a PDP8 computer. Again the designstrategy was based on frequency response methods usinglinvil's approximation with a time domain checkout.

Cycloid is currently being updated to incorporate theseprograms and also to allow the user to investigate theeffects of limited word-length of the kind which occurwhen integer arithmetic is used in controllers based onmachine-code software.

It is emphasised, however, that sampled-data systemsusing adequate sampling rates (i.e. not less than ten timesthe frequency of the dominant oscillatory mode of theclosed-loop system) can be designed and checked with quitegood accuracy using ordinary linear theory based on theassumption that a sample and zero-order hold merely intro-duces a pure time delay of half a sampling period. ThusCycloid can be used directly to investigate the behaviour ofsystems with fast sampling rates in which the controllerscontain simple algorithms for proportional, two or threeterm control. However, when z-filters are used as control

IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980

elements it is necessary to use the more complicated andslower-running sampled-data programs mentioned above.

5 Concluding remarks

Cycloid is a control systems classical design system writtenfor use on a low-cost microcomputing system. The timetaken to run typical frequency domain programs (i.e.about 40 seconds) is about 50% slower than similar onesrun on a PDP8 computer. This is due to the fact that theBasic software is interpretative rather than compiled; acompiled version of Basic will shortly become available andit is then expected that the programs will actually run fasterthan those designed for the PDP8. In most time-sharedsystems run on large main-frame machines, the total programrun time is usually very slow indeed. However, for designpurposes, thinking time greatly exceeds computation timein the design process so that the overall efficiency is notgreatly improved by faster computation.

The current television graphics display provided by themanufacturers of the 380Z microcomputer is very coarse,but a fine resolution graphics system has been promised fordelivery in the near future at little extra cost. It must beemphasised, however, that the efficiency of the design pro-cess is not impaired by the use of a coarse graphics displaybecause the information provided for the designer in thisway merely indicates trends; the detailed design infor-mation such as rise time and maximum value appear asalphanumerics. Also the complete accurate informationcan always be called up by means of the TYPE command.

Cycloid has an advantage over many programs in that ithas a command structure so that the user can demand aresponse from the computer. This is in contrast to the'option' oriented type of program in which the user has tofollow a path dictated by the computer to obtain a particu-lar response.

The use of c.a.d. with interactive graphics is especiallyapplicable to the area of control systems design, but thereare many other subject areas to which it has been applied togreat advantage. Its universal application in higher edu-cation and small industry has been hindered largely by therelatively high cost of minicomputers with graphics andadequate random access and backing memory. The readyavailability of low-cost microprocessing systems should nowovercome this problem. The development of the Cycloidsoftware and its use in teaching laboratories has shown thatreasonably extensive software can be developed quitequickly to operate on these new systems. Although thesoftware developed for Cycloid has been specifically codedfor operation with the Research Machines 380Z microcom-puting system, it should be noted that conversion for oper-ation on other machines will not involve major restructuringof the software. However most microcomputing facilities

117

have non-standard features in their interpretive Basic,especially in the control of the graphical display, so thatmicrocomputer software can never be directly transportable.

Experience of the use of Cycloid in the teaching environ-ment indicates that students like to use the system and thatthey are able to solve a large number of graded design prob-lems. The design example given in this paper indicates thesatisfactory level the students can attain at the end of theirformal instruction on Cycloid.

6 References

1 ROSENBROCK, H.H.: 'Computer-aided control system design'(Academic Press Inc. (London) Ltd., 1974)

2 BELLETRUTTI, J.J.: 'Computer-aided design and the character-istic locus method', IEE Conf. Publ. 96, 1973, pp. 79-86

3 SHEARER, B.R., DALY, K.C., GOODWIN, G.C. and WAITE,P.: 'A suite of programs for classical control systems design',ibid., pp. 113-118

4 SHANKAR, S., ATHERTON, D.P. and MACNEIL, D.G.:'Computer aided design of control systems using a.p.l.', Pro-

ceedings of the IFAC symposium on trends in automatic controleducation, Barcelona, 1977, pp. 170-189

5 FALLSIDE, F., PATEL, R.V. and SERAJI, H.: 'Interactivesingle-input system design using a graphics terminal', IEE Conf.Publ. 86, pp. 86-91

6 MUNRO, N.: 'Conversational mode c.a.d. of control systemsusing display terminals', ibid., pp. 418-431

7 ATKINSON, P.: 'Computer-aided design of closed-loop controlsystems'. Comput. AidedDes., 1972,4,120-128

8 ATKINSON, P.: 'Feedback control theory for engineers'(Heineman Educational Books, London, 1972, 2nd edn.) pp.268-271

9 ATKINSON, P.: 'Feedback control theory for engineers', ibid.,pp. 432-435

10 TRUXALL, J.G.: 'Automatic feedback control system synthesis'(McGraw Hill, New York, 1945) pp. 318-342

11 ASHWORTH, M.J. and TOWILL, D.R.: 'Computer-aided designof tracking systems', Radio and Electron. Eng., 1978, 48, pp.479-492

12 WEST, J.C. and SOMERVILLE, M.J.: 'Integral control withtorque limitation', Proc. IEE, 1956,103 C, 4, pp. 407-419

13 ALLEN, A.J. and ATKINSON, P.: 'Interactive design of sampled-data control systems'. IEE Conf. Publ. 96,1973, pp. 141-148

ErrataCALVERLEY, H.B.: 'Developments for medium-capacityurban public transport', Proc. IEE, 1979, 126, 11R, pp.1097-1125

The following errors occur in the printed text:

Section 2.2, paragraph 3, line 5, 'pushing' should read'push button'

In Table 2, the following entries are all dependent onelectricity: 'Trolley/battery', 'Trolley/I/C engine', 'Battery','Flywheel', 'I/C engine/battery' and 'I/C engine'

In Table 3, column 5, row 5, '2-52' should read '1-52'

Three lines from the bottom of Section 2.4, 'requirements'should read 'features'

On p. 1102, four lines from the top of the right-handcolumn, 'Section 3.2.2. (ft)' should read 'Section 3.2.2.00(0'In Table 8, the following errors occur:

(i) column 2, row 2, 'copper' should read 'cobber'(ii) column 2, row 3, '1-signal copper' should read

'one line earthed'(iii) column 9, row 3, '7 kW should read 9-4 kW

On p. 1113, the following errors occur in the left-handcolumn:

(i) 12 lines down, 'one sixth of atmospheric pressure'is a pressure difference

(ii) 12 lines down, 'energy' should read 'power'(iii) 13 lines down, '0-5 kJ' should read '0-5 kW/t'(iv) 23 lines down, 'controlled' should read 'main-

tained'(v) 32 lines down, 'of should be deleted

The words 'assumed parameter' should be deleted from theheading of column 1 on Table 12

Section 5.1, paragraph 7, line 7, 'and also tried in practisefor' should read 'for electric traction with'

In Table 13, the following errors occur:

(i) column 1, row 5, 'DOT' should be referenced toReference 22

(ii) column 1, row 6, '22' should read '11'(iii) column 1, rows 16,17 and 18, ' 1 ' , '2' and '3 ' should

read 'a', V and 'c', respectively(iv) the term '£m' should be at the top of columns 2

and 4

118 IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980