- Email: [email protected]
The Value of Computer Aided Design
THE VALUE OF COMPUTER AIDED DESIGN D. P. Atherton Electrical Engineering Department, University of New Brunswick, Fredericton, N.B., Canada Present address: Control Engineering Department, University of Sheffield, Mappin Street, Sheffield, England
Abstract . The paper first considers the various ways in which a computer may assist the student in control engineering or the designer of control systems . It then dis cusses the requirements for a computer-ai ded design system and the benefits it can provide for education , research and industry . A major advantage is claimed ~o be the opportunity it provides for examining control system designs using several d~fferent approaches in a relatively short time. Some examples are given to illustrate the relevance of this approach for nonlinear systems. Keywords. Computer-aided design, computer graphics, control theory, education, nonlinear control systems . INTRODUCTION The aim of this paper is to provide an overview of the field of computer - aided design of control systems and to endeavour to evaluate its advantages for use in education , research and industry . Taken in its broad context and to use a definition similar to that which has been used for computer aided learning, computer - aided design of control systems can be defined as any use of a computer which assists in the design of a control system. Engineers have, of course, been using computers, especially if we include the analog machine, in this context for many years and certainly before the phrase computer- aided design was first used. Early use of digital computers by engineers was for solving specific numerical problems in a batch mode. Only rarely were programs written which allowed the solution of a variety of problems by, say, the inclusion of branching instructions dependent on the card or tape data input, and where graphical resultswere needed laborious plotting of numerical outputs was usually necessary . The best plot outputs available with digital simulation languages were from a printer plotter so that features such as a phase plane trajectory, because of the requirement to reorganise the output data, were relatively uncommon .
possibilities that we will primarily be concerned . In the next section , however , an overview of the broader uses of the computer in a control systems environment where real time data can also be used will be briefly discussed. Justification a priori of the use of computers in any project is never easy even whe re the benefits can be defined more clea rl y, for example in terms of a return of the investment within three years for an industrial process control, than is the case in education and possibly industrial design . The value of work in an educa ti onal and research environment cannot be judged solely on a cost basis and therefore claims regarding the benefits of computer-aided design (CAD) will in some cases be subjective . On the other hand there have been projects on computer-aided instruction (CA!) which it is maintained are viable in cost benefit terms. THE CAD SPECTRUM Fig . 1 shows the components and possible uses of a dedicated computer system for use in engineering design. On the left of the centre line are the system components which are interfaced via the digital computer to blocks which show the various tasks which might be performed from a terminal to the system . To the authors knowledge there is no single system set up to perform all these tasks although all the concepts, some much more than others, are made use of in universities and industry. It is not necessarily the intention to advocate such a system but it is introduced to show the various ways in which an engineer uses a computer and what in principle he could do from a single terminal. Our major concern is with the digital computer and the lower right hand
The major change in recent years and the features which most would regard as an integra l part of computer- aided design are the availabili ty of graphics termina~ and the interaction with the programs that is avai lable from these terminals . A good review of program packages using these features and the facilities involved was given at the IFAC Symposium in Barcelona by Lemmens and Van den Boom (1977), a paper which has recently been published in Automatica. It is with the requirements of this type of system and its 447
448
D. P. Atherton
Hardware
-
Real time tasks
Real time expe riments systems
Di gital computer
Simulation
Analo g comput e r
Fig . 1.
Data bases ward proc .
---
can be mo ni tored in t he simulation and in many cases rea l time system hardware may be tested whilst interfaced to the simulation. All these possibilities exist with the general configur a t ion of Fig. 1. In CAl, however, t he word simulation is also used with a broader meaning to describe programs which use t he graphics capability of the terminal to po r t r ay the system behaviour . The components of a process may be displayed and the effect of a disturbance in the input flow on levels within the process will be seen, or in the case of medicine the effect of prescribing a drug to a ' patient', whose symptoms have hopefully been identified at the terminal, will be observed.
CAt CAI
Analysis Design
Computers have been used in instruction and learning for several years mainly in areas such as high school mathematics and first year science , computer science and engineering courses at technical schools. Special languages have been developed for the unique requirements of these applications which are indicated in Fig. 2.
Computer Usage in Engineering
block£ but first it is ap propriate to comment on the tasks mention ed i ,) t:1e blocks and the additional capabilities provided by this complete system.
Ar)rLlC~-~
r--CENEI:Al MlEI\S Of OF THE COiV\PUHI1IN H'-JSTRUCTION
! I
Real Time Tasks The real time tasks feature 'illS oeen incorporated with CAD facilities in several control systems laboratories where a dedi cated mini computer is available (van der B,'sch 1975 , Isermann and Dymchiz 1976). Thp ~ain use is in identification as real time 2ata can be fed to the computer either from il process or an analog simulation. The accuracy of the computed model can be seen by cOl'" " aring the process and model responses to t' ' ! same input and the effects of reducing the order of a model may also be observed. ppal time experments can be controlled ,"rom the terminal and the data obtained submitted to a variety of computational algorithms . Data Bases Many data bases exist, usually on large frame computers, perhaps the most well known of which to the engineer and scientist are those containing published literature. These can normally be search using keywords, as for example CAD, logic combinations of keywords or by author. Other data bases of interest to the designer, such as one on components, exist and there are many possibilities for further additions in both universities and industry. Simulation To most control engineers simulation means the solution of the system equations either on an analog, hybrid or digital computer. Usually all the system variables of interest
Fig . 2 .
Application of the computer in instruction.
Considerable time is required to write programs which include a high level of instruction management and it is doubtful if this sophistication is required for computer instruction in control theory at the University level . Hopefully with a minimum of guidance students will be able to make suitable decisions on using CAD programs for learnin g . Many advantages are claimed for CA[ pe r haps the most important of which are that the student can go at his own pace, have gui dance without a teacher and can return to the terminal for revision exercises whenever he wishes . Wiegele (1978) describes a computer assisted learning project in control engineering which incorporates both CAI and CAD. The CAI material is written in the PLAKIT language and a structure of the concept is shown in Fig. 3. The features of the re maining block for analysis and design are considered in the next section .
The Value of Computer Aided Des i gn ----+- dirrct acc~$S - - + nciilTCt accr.ss
htnKIuclion
I
lat t er but too many choices for a student may prove cumber some and time consuming . Because of t he r elatively low cost of memory the possibility of incorporat ing more than one routine which can perform similar tasks should the r efore no t be ruled out . Characteristics, mainly conce r ning the graphics capability, which are desirable for all users are: The user should be able to use the programs without a knowledge of the programming language . 2. Manuals describing the programs should be available either typed or callable at the terminal and guidance regarding the avai l able options should preferably be included in the program package . A response to a terminal ' help ' request ' is desirable. 3. The response time must be sufficiently fast. This may be a problem on a main frame computer with a large number of terminals. 4 . The format for entering data should be clear it should be easily accomplished and e;ror messages given. For entering polynomials in transfer functions sev~ral formats may be desirable. Where poss~ble, default options should be provided and the values printed. 5. Output should be easily routable to other devices so that to obtain hard copy an X- Y plotter may be used as an alternative to the use of a video copier connected to the graphics terminal. 6. The graphics routines should be separate. from the control software . Both automat~c or manual scaling of plots sh ould be possible . 7 . The values of some points on frequency response and root locus plots should be marked . Values at other points should be obtainable using a cursor, or light pen, as input . 8. It should be possible to obtain several graphs , with different line types if so desired, on one dis p lay . This enables uncompensated and compensated system frequency responses, for example, to be obtained on the same plot. 9 . Additional data which may be added to a graph, i.e . M circles, should be optional. It may also be advantageous to have plots scaled to fit available graph paper, say for Bode diagrams, to avould the drawing of a detailed grid at the terminal. 10 . Algorithms which correctly sort the roots and draw the correct lines for a root locus plot can require a significant programming effort. Just marking ~he roots, provided enough are found, ~s often adequate and should probably always be available as an option. 11. Several methods have been reported for selecting the points on a root locus or frequency response plot at which the values are obtained . Difficulties often occur in certain cases, for example in obtaining the polar frequency locus of a system with a pair of very lightly damped poles. One possibility is to have the capability to add more points between specific frequencies on the plot.
1.
~S l$tanc.
l~vcl
Fig . 3 .
Structure of a CAL package
CAD SYSTEMS The bas i c elements of a CAD system are the digital computer, the graphic~ terminal.and the program library of analys~s and des~gn r outines. Other components of the non real time blocks such as an instruction package of various possible levels of complexity and a digital simulation language may be included . The program package may be run on a dedicated micro or minicomputer, a minicomputer with multi - user facilities or a large main frame computer with mUltiple, possibly remote, t e r minals . Programs currently available cover all areas of control systems analysis, design and synthesis such as frequency response and root locus methods for single and multivariable sys t ems, absolute stability and describin~ function me t hods for nonlinear systems , t~me domain calculations and/or simulations , state space transformations, system representation t ran sformations, pole placement, observer and optimal control design algorithms, discre~e system methods and so on. For some techn~ques those which will be our main concern, the int eraction available from the terminal and the availability of a graphics display are essential whilst for others the terminal is just a po r t for feeding input to and obtaining output from the computer . Several languages have been used to write CAD packages but Fortran appears to be the most common. To permit changes and extensions and to enable several people to be involved in program deve l opment a modular structure is desirable , whilst to allow portability of the software the dependence on the machine and its peri pherals should be as limited as possible . Desirable Features for the User The type of features a user requires will be dependent to some extent on whether he is an undergraduate student, a research worker or an industrial designer . An undergraduate student and in many cases an industrial designer will normally require to implement fairly standard procedures whereas a research worker may require to interact more and assemble differently the available routines, especially if he desires to check new concepts. Fl exibility is therefore desirable for the
449
D. P. Atherton
450
12. Root locus plots should be possible for a negative as well as a positive gain . THE BENEFITS OF CAD There are obvious advantages to CAD in such areas as the use of frequency response techniques and root locus methods for multivariable systems and some frequency response methods for nonlinear systems in that without the graphics facility analysis would be more difficult and the design procedure probably impossible. Engineers often require a large amount of information about a system or process and normally its presentation in graphi cal form is the most efficient and helpful . Other benefits can be more specific to the user and these are discussed from an educational and industrial viewpoint below .
Industry Most of the advantages cited above are also relevant for the industrial designer but the true measure is the cost of completing a given amount of work. This cost when a CAD package is used will depend upon the system available, the experience of the user etc. and must be less than the cost of the time saved. Obviously the following factors will be important considerations. 1. 2. 3.
Education
4.
Even without the inclusion of a CAI component there is no doubt that the student can learn from using many programs in a CAD package. The experience can be improved by adding simple extensions to the programs for example providing assymptotic approximations with Bode plots, allowing the display of intermediate results in state transformations etc. so the student can check his own calculations . Questions can be asked and answered at the students convenience. Some other advantages are:-
5.
1.
2.
3.
4.
5.
A student can accomplish more in a given time and can be spared the tedium of routine calculations and the plotting of graphs . A greater appreciation can be obtained of some laboratory experiments since theoretical graphs can be obtained quicker and more measurements taken. He can examine different analytical techniques to see if they yield additional information and more graphs may be generated than might be used without CAD . It may be important to do this especially for nonlinear systems. He can compare designs using different methods and give more thought to the significance of the various approaches in the time previously spent doing calculations. He can consider real problems since complicated transfer functions, A matrices with non integer terms etc . are in principle no more difficult to handle.
A possible disadvantage in educational appli cations is that a student may not learn satisfactorily and become a 'cookbook engineer' not able to check or recognise the signifi cance of answers he obtains. Obtaining a correct motivation and setting suitable tests can hopefully take care of this pitfall. The growth of control theory in the last two decades means that any method which offers the possibility of covering more material in a given time should be welcome.
The ability to use various design techniques and look at designs from different viewpoints. The elimination of inefficient calculation methods, graph plotting and other procedures which can be replaced by CAD. The direct generation of graphical output suitable for incorporation in reports. Design data which can be saved and used for training new personnel. The possibility of including instructional packages to train or keep up to date a design team. ADVANTAGE S OF ALTERNATIVE METHODS
A claim that has been made in the previous section for CAD is that it allows the designer to analyse a system using different approaches with only a small increase in time taken. The ability to compare designs done by two different methods is always valuable and a better understanding of the system behaviour may be obtained by having information from different approaches. This is particularly true of nonlinear systems where if approximate techniques, such as the describing function method are used, results given by other analytical approaches or simulations may reveal the possibility of unusual behaviour. To illustrate this point consider the situation of investigating the possibility of limit cycles in a nonlinear system using the describing function method. Conventionally this is done using only a Nyquist diagram of G(jw) but interesting aspects of the system behaviour may be more easily seen if, in additio~ a root locus plot of G(s) is obtained. Where multiple limit cycle solutions exist a root locus plot clearly shows why the Loeb criterion is a necessary but not sufficient condition for a stable limit cycle frequency. (Choudhury and Atherton 1974). There are also several statements in the literature regarding the properties of G(jw) which might lead to a breakdown of the Aizerman conjecture. An interesting point, however, is that a pole transformation does not alter the stability of an autonomous system yet can change completely the frequency response of the linear transfer function. Noting this fact and also that if the root locus of G(s) is plotted for both positive and negative gains it does not change under a pole transformation, it was decided to examine (Shanker 1976) thp root locus plots of counterexamples to this conjecture . An interesting common property was observed, namely that the root
The Value of Computer Aided Design loci had branches cutting the imaginary axis and then curving over to intersect the positive real axis. The root locus for the Dewey and Jury counterexample which has G(s) (52 - 0.5)/ {(s+1)(s2 + l)} is shown in Fig. 4. III
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,,----- ....... ,
,,
,
RL,1O
451
insignificant but if the system is structured with portability in mind exchanges of material can reduce the total cost. On the other hand is it possible with todays technology to justify an engineer plotting graphs point by point especially when the results may be part of a trial and error process and not further required? ACKNOWLEDGEMENTS
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-2
-1
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Fig. 4. Root iocus for an Aizerman counterexample CONCLUSIONS This paper has given an overview of computeraided design and commented on the possible and desirable features of CAD packages for use in universities and industry. It is argued that the availability of a CAD package for student use can increase the amount of material which can be learnt in a given time and if used correctly can improve understanding of the subjec~ Most benefit is obtained with a graphics capability and it is probably the lack of such terminals for undergraduate student use that is the current limit on usage at this level. Many would contend, particularly in industry, that without a detailed cost benefit study the value of CAD cannot be convincingly justified. Costs for writing the software, documentation and maintaining it are by no means
The author wishes to acknowledge the facilities provided by the Control Engineering Department of the University of Sheffield during his sabbatical leave. REFERENCES Choudhury, S.K. and Atherton, D.P. (1974) Limit cycles on high order nonlinear systems. Proc. lEE, 121, pp. 717-724. Isermann, R. and Dymchiz, E. (1976). A software package for process computer-aided control system design. Proc. IFAC/IFIP Symposium, Talinn. Lemmens, W.J.M. and Van den Boom, A.J.W. (1971) Interactive computer programs for education and research, a survey. Proc. Symposium, Barcelona. Shankar, S. (1976) Stability analysis of nonlinear control systems. M.Sc.E. Thesis, Univ. of New Brunswick. Van den Bosch, P.P.J. (1975) TRIP, transformation and identification package for interactive computer-aidea control system design. Journal A, 16. Wiege1e, B. (1978) Computer assisted learning of methods and problem solving in control engineering. Proc. lMACS SYmposium, Vienna, pp. 117-119.
Abstract . The paper first considers the various ways in which a computer may assist the student in control engineering or the designer of control systems . It then dis cusses the requirements for a computer-ai ded design system and the benefits it can provide for education , research and industry . A major advantage is claimed ~o be the opportunity it provides for examining control system designs using several d~fferent approaches in a relatively short time. Some examples are given to illustrate the relevance of this approach for nonlinear systems. Keywords. Computer-aided design, computer graphics, control theory, education, nonlinear control systems . INTRODUCTION The aim of this paper is to provide an overview of the field of computer - aided design of control systems and to endeavour to evaluate its advantages for use in education , research and industry . Taken in its broad context and to use a definition similar to that which has been used for computer aided learning, computer - aided design of control systems can be defined as any use of a computer which assists in the design of a control system. Engineers have, of course, been using computers, especially if we include the analog machine, in this context for many years and certainly before the phrase computer- aided design was first used. Early use of digital computers by engineers was for solving specific numerical problems in a batch mode. Only rarely were programs written which allowed the solution of a variety of problems by, say, the inclusion of branching instructions dependent on the card or tape data input, and where graphical resultswere needed laborious plotting of numerical outputs was usually necessary . The best plot outputs available with digital simulation languages were from a printer plotter so that features such as a phase plane trajectory, because of the requirement to reorganise the output data, were relatively uncommon .
possibilities that we will primarily be concerned . In the next section , however , an overview of the broader uses of the computer in a control systems environment where real time data can also be used will be briefly discussed. Justification a priori of the use of computers in any project is never easy even whe re the benefits can be defined more clea rl y, for example in terms of a return of the investment within three years for an industrial process control, than is the case in education and possibly industrial design . The value of work in an educa ti onal and research environment cannot be judged solely on a cost basis and therefore claims regarding the benefits of computer-aided design (CAD) will in some cases be subjective . On the other hand there have been projects on computer-aided instruction (CA!) which it is maintained are viable in cost benefit terms. THE CAD SPECTRUM Fig . 1 shows the components and possible uses of a dedicated computer system for use in engineering design. On the left of the centre line are the system components which are interfaced via the digital computer to blocks which show the various tasks which might be performed from a terminal to the system . To the authors knowledge there is no single system set up to perform all these tasks although all the concepts, some much more than others, are made use of in universities and industry. It is not necessarily the intention to advocate such a system but it is introduced to show the various ways in which an engineer uses a computer and what in principle he could do from a single terminal. Our major concern is with the digital computer and the lower right hand
The major change in recent years and the features which most would regard as an integra l part of computer- aided design are the availabili ty of graphics termina~ and the interaction with the programs that is avai lable from these terminals . A good review of program packages using these features and the facilities involved was given at the IFAC Symposium in Barcelona by Lemmens and Van den Boom (1977), a paper which has recently been published in Automatica. It is with the requirements of this type of system and its 447
448
D. P. Atherton
Hardware
-
Real time tasks
Real time expe riments systems
Di gital computer
Simulation
Analo g comput e r
Fig . 1.
Data bases ward proc .
---
can be mo ni tored in t he simulation and in many cases rea l time system hardware may be tested whilst interfaced to the simulation. All these possibilities exist with the general configur a t ion of Fig. 1. In CAl, however, t he word simulation is also used with a broader meaning to describe programs which use t he graphics capability of the terminal to po r t r ay the system behaviour . The components of a process may be displayed and the effect of a disturbance in the input flow on levels within the process will be seen, or in the case of medicine the effect of prescribing a drug to a ' patient', whose symptoms have hopefully been identified at the terminal, will be observed.
CAt CAI
Analysis Design
Computers have been used in instruction and learning for several years mainly in areas such as high school mathematics and first year science , computer science and engineering courses at technical schools. Special languages have been developed for the unique requirements of these applications which are indicated in Fig. 2.
Computer Usage in Engineering
block£ but first it is ap propriate to comment on the tasks mention ed i ,) t:1e blocks and the additional capabilities provided by this complete system.
Ar)rLlC~-~
r--CENEI:Al MlEI\S Of OF THE COiV\PUHI1IN H'-JSTRUCTION
! I
Real Time Tasks The real time tasks feature 'illS oeen incorporated with CAD facilities in several control systems laboratories where a dedi cated mini computer is available (van der B,'sch 1975 , Isermann and Dymchiz 1976). Thp ~ain use is in identification as real time 2ata can be fed to the computer either from il process or an analog simulation. The accuracy of the computed model can be seen by cOl'" " aring the process and model responses to t' ' ! same input and the effects of reducing the order of a model may also be observed. ppal time experments can be controlled ,"rom the terminal and the data obtained submitted to a variety of computational algorithms . Data Bases Many data bases exist, usually on large frame computers, perhaps the most well known of which to the engineer and scientist are those containing published literature. These can normally be search using keywords, as for example CAD, logic combinations of keywords or by author. Other data bases of interest to the designer, such as one on components, exist and there are many possibilities for further additions in both universities and industry. Simulation To most control engineers simulation means the solution of the system equations either on an analog, hybrid or digital computer. Usually all the system variables of interest
Fig . 2 .
Application of the computer in instruction.
Considerable time is required to write programs which include a high level of instruction management and it is doubtful if this sophistication is required for computer instruction in control theory at the University level . Hopefully with a minimum of guidance students will be able to make suitable decisions on using CAD programs for learnin g . Many advantages are claimed for CA[ pe r haps the most important of which are that the student can go at his own pace, have gui dance without a teacher and can return to the terminal for revision exercises whenever he wishes . Wiegele (1978) describes a computer assisted learning project in control engineering which incorporates both CAI and CAD. The CAI material is written in the PLAKIT language and a structure of the concept is shown in Fig. 3. The features of the re maining block for analysis and design are considered in the next section .
The Value of Computer Aided Des i gn ----+- dirrct acc~$S - - + nciilTCt accr.ss
htnKIuclion
I
lat t er but too many choices for a student may prove cumber some and time consuming . Because of t he r elatively low cost of memory the possibility of incorporat ing more than one routine which can perform similar tasks should the r efore no t be ruled out . Characteristics, mainly conce r ning the graphics capability, which are desirable for all users are: The user should be able to use the programs without a knowledge of the programming language . 2. Manuals describing the programs should be available either typed or callable at the terminal and guidance regarding the avai l able options should preferably be included in the program package . A response to a terminal ' help ' request ' is desirable. 3. The response time must be sufficiently fast. This may be a problem on a main frame computer with a large number of terminals. 4 . The format for entering data should be clear it should be easily accomplished and e;ror messages given. For entering polynomials in transfer functions sev~ral formats may be desirable. Where poss~ble, default options should be provided and the values printed. 5. Output should be easily routable to other devices so that to obtain hard copy an X- Y plotter may be used as an alternative to the use of a video copier connected to the graphics terminal. 6. The graphics routines should be separate. from the control software . Both automat~c or manual scaling of plots sh ould be possible . 7 . The values of some points on frequency response and root locus plots should be marked . Values at other points should be obtainable using a cursor, or light pen, as input . 8. It should be possible to obtain several graphs , with different line types if so desired, on one dis p lay . This enables uncompensated and compensated system frequency responses, for example, to be obtained on the same plot. 9 . Additional data which may be added to a graph, i.e . M circles, should be optional. It may also be advantageous to have plots scaled to fit available graph paper, say for Bode diagrams, to avould the drawing of a detailed grid at the terminal. 10 . Algorithms which correctly sort the roots and draw the correct lines for a root locus plot can require a significant programming effort. Just marking ~he roots, provided enough are found, ~s often adequate and should probably always be available as an option. 11. Several methods have been reported for selecting the points on a root locus or frequency response plot at which the values are obtained . Difficulties often occur in certain cases, for example in obtaining the polar frequency locus of a system with a pair of very lightly damped poles. One possibility is to have the capability to add more points between specific frequencies on the plot.
1.
~S l$tanc.
l~vcl
Fig . 3 .
Structure of a CAL package
CAD SYSTEMS The bas i c elements of a CAD system are the digital computer, the graphic~ terminal.and the program library of analys~s and des~gn r outines. Other components of the non real time blocks such as an instruction package of various possible levels of complexity and a digital simulation language may be included . The program package may be run on a dedicated micro or minicomputer, a minicomputer with multi - user facilities or a large main frame computer with mUltiple, possibly remote, t e r minals . Programs currently available cover all areas of control systems analysis, design and synthesis such as frequency response and root locus methods for single and multivariable sys t ems, absolute stability and describin~ function me t hods for nonlinear systems , t~me domain calculations and/or simulations , state space transformations, system representation t ran sformations, pole placement, observer and optimal control design algorithms, discre~e system methods and so on. For some techn~ques those which will be our main concern, the int eraction available from the terminal and the availability of a graphics display are essential whilst for others the terminal is just a po r t for feeding input to and obtaining output from the computer . Several languages have been used to write CAD packages but Fortran appears to be the most common. To permit changes and extensions and to enable several people to be involved in program deve l opment a modular structure is desirable , whilst to allow portability of the software the dependence on the machine and its peri pherals should be as limited as possible . Desirable Features for the User The type of features a user requires will be dependent to some extent on whether he is an undergraduate student, a research worker or an industrial designer . An undergraduate student and in many cases an industrial designer will normally require to implement fairly standard procedures whereas a research worker may require to interact more and assemble differently the available routines, especially if he desires to check new concepts. Fl exibility is therefore desirable for the
449
D. P. Atherton
450
12. Root locus plots should be possible for a negative as well as a positive gain . THE BENEFITS OF CAD There are obvious advantages to CAD in such areas as the use of frequency response techniques and root locus methods for multivariable systems and some frequency response methods for nonlinear systems in that without the graphics facility analysis would be more difficult and the design procedure probably impossible. Engineers often require a large amount of information about a system or process and normally its presentation in graphi cal form is the most efficient and helpful . Other benefits can be more specific to the user and these are discussed from an educational and industrial viewpoint below .
Industry Most of the advantages cited above are also relevant for the industrial designer but the true measure is the cost of completing a given amount of work. This cost when a CAD package is used will depend upon the system available, the experience of the user etc. and must be less than the cost of the time saved. Obviously the following factors will be important considerations. 1. 2. 3.
Education
4.
Even without the inclusion of a CAI component there is no doubt that the student can learn from using many programs in a CAD package. The experience can be improved by adding simple extensions to the programs for example providing assymptotic approximations with Bode plots, allowing the display of intermediate results in state transformations etc. so the student can check his own calculations . Questions can be asked and answered at the students convenience. Some other advantages are:-
5.
1.
2.
3.
4.
5.
A student can accomplish more in a given time and can be spared the tedium of routine calculations and the plotting of graphs . A greater appreciation can be obtained of some laboratory experiments since theoretical graphs can be obtained quicker and more measurements taken. He can examine different analytical techniques to see if they yield additional information and more graphs may be generated than might be used without CAD . It may be important to do this especially for nonlinear systems. He can compare designs using different methods and give more thought to the significance of the various approaches in the time previously spent doing calculations. He can consider real problems since complicated transfer functions, A matrices with non integer terms etc . are in principle no more difficult to handle.
A possible disadvantage in educational appli cations is that a student may not learn satisfactorily and become a 'cookbook engineer' not able to check or recognise the signifi cance of answers he obtains. Obtaining a correct motivation and setting suitable tests can hopefully take care of this pitfall. The growth of control theory in the last two decades means that any method which offers the possibility of covering more material in a given time should be welcome.
The ability to use various design techniques and look at designs from different viewpoints. The elimination of inefficient calculation methods, graph plotting and other procedures which can be replaced by CAD. The direct generation of graphical output suitable for incorporation in reports. Design data which can be saved and used for training new personnel. The possibility of including instructional packages to train or keep up to date a design team. ADVANTAGE S OF ALTERNATIVE METHODS
A claim that has been made in the previous section for CAD is that it allows the designer to analyse a system using different approaches with only a small increase in time taken. The ability to compare designs done by two different methods is always valuable and a better understanding of the system behaviour may be obtained by having information from different approaches. This is particularly true of nonlinear systems where if approximate techniques, such as the describing function method are used, results given by other analytical approaches or simulations may reveal the possibility of unusual behaviour. To illustrate this point consider the situation of investigating the possibility of limit cycles in a nonlinear system using the describing function method. Conventionally this is done using only a Nyquist diagram of G(jw) but interesting aspects of the system behaviour may be more easily seen if, in additio~ a root locus plot of G(s) is obtained. Where multiple limit cycle solutions exist a root locus plot clearly shows why the Loeb criterion is a necessary but not sufficient condition for a stable limit cycle frequency. (Choudhury and Atherton 1974). There are also several statements in the literature regarding the properties of G(jw) which might lead to a breakdown of the Aizerman conjecture. An interesting point, however, is that a pole transformation does not alter the stability of an autonomous system yet can change completely the frequency response of the linear transfer function. Noting this fact and also that if the root locus of G(s) is plotted for both positive and negative gains it does not change under a pole transformation, it was decided to examine (Shanker 1976) thp root locus plots of counterexamples to this conjecture . An interesting common property was observed, namely that the root
The Value of Computer Aided Design loci had branches cutting the imaginary axis and then curving over to intersect the positive real axis. The root locus for the Dewey and Jury counterexample which has G(s) (52 - 0.5)/ {(s+1)(s2 + l)} is shown in Fig. 4. III
RLo
,,----- ....... ,
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insignificant but if the system is structured with portability in mind exchanges of material can reduce the total cost. On the other hand is it possible with todays technology to justify an engineer plotting graphs point by point especially when the results may be part of a trial and error process and not further required? ACKNOWLEDGEMENTS
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Fig. 4. Root iocus for an Aizerman counterexample CONCLUSIONS This paper has given an overview of computeraided design and commented on the possible and desirable features of CAD packages for use in universities and industry. It is argued that the availability of a CAD package for student use can increase the amount of material which can be learnt in a given time and if used correctly can improve understanding of the subjec~ Most benefit is obtained with a graphics capability and it is probably the lack of such terminals for undergraduate student use that is the current limit on usage at this level. Many would contend, particularly in industry, that without a detailed cost benefit study the value of CAD cannot be convincingly justified. Costs for writing the software, documentation and maintaining it are by no means
The author wishes to acknowledge the facilities provided by the Control Engineering Department of the University of Sheffield during his sabbatical leave. REFERENCES Choudhury, S.K. and Atherton, D.P. (1974) Limit cycles on high order nonlinear systems. Proc. lEE, 121, pp. 717-724. Isermann, R. and Dymchiz, E. (1976). A software package for process computer-aided control system design. Proc. IFAC/IFIP Symposium, Talinn. Lemmens, W.J.M. and Van den Boom, A.J.W. (1971) Interactive computer programs for education and research, a survey. Proc. Symposium, Barcelona. Shankar, S. (1976) Stability analysis of nonlinear control systems. M.Sc.E. Thesis, Univ. of New Brunswick. Van den Bosch, P.P.J. (1975) TRIP, transformation and identification package for interactive computer-aidea control system design. Journal A, 16. Wiege1e, B. (1978) Computer assisted learning of methods and problem solving in control engineering. Proc. lMACS SYmposium, Vienna, pp. 117-119.