Every good regular of a system must be a model of that
system
Citation for published version (APA):
Eykhoff, P. (1994). Every good regular of a system must be a model of that system. Modeling, Identification and Control, 15(3), 135-139. https://doi.org/10.4173/mic.1994.3.2
DOI:
10.4173/mic.1994.3.2
Document status and date: Published: 01/01/1994
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134 The future of control MODELING, IDENTIFICATION AND CONTROL, 1994, VOL. 15, NO. 3, 135—139 should come under the heading of linear or nonlinear systems. It is permissible in
mathematics and physics, why not in control? In the same spirit it is probably also useful to exercise some care when promoting areas with a lot of hype.
6. Conclusions
Automatic control emerged as a discipline about 50 years ago and it has had a very dynamic development. It is one of the first systems disciplines to transcend the boundaries of traditional engineering fields. It has a wide range of applications which show up in all aspects of modern life and sometimes make it even more enjoyable. There are a large number of challenging problems ahead with the potential to attract the very best students. It is important that we accept the challenges and in particular that we are willing to deal with the full aspects including theory and applications.
References
CHESTNUT, H., Ed. (1982). Impact of Automatic Control Present and Future. (VDI VDE Gesellschaft, Düsseldorf).
LuoTo, U., Ed. (1978). 20 Years Old; 20 Years Young. An Anniversary Publication 1957 1977. Automatica, 14, 49 75.
GALLAGER, R. G. and MInER, S. K. (1990).From Servo Loops to Fibre Nets.(The Laboratory for Information and Decision Systems. Massachusetts Institute of Technology, Cambridge, M.A).
“Every good regulator of a system must be a model of that system”
1. Introduction
Dear reader, you are perfectly right: the title of the contribution is not original;.. .hence the use of quotation-marks. This title is identical to that of a paper by
Conant and Ashby (1970). Don’t you think it is a challenging statement? So do I. But, judging from the citation index, that paper received (far too) little attention; the control engineering community in particular responded sluggishly to this challenge.
While offering my apologies for the ‘borrowing’ just confessed, I also would like to express as my opinion that this title might be interpreted as strong support for the Editorial Board and the Editor of this journal. Fifteen years ago they chose the name ‘Modeling, Ident(fication and Control’. This choice can be seen as a statement of a professional conviction; it emphasizes their views on the crucial importance of the combination of these three aspects for control engineering and for its development. In this note we will study to what, degree this conviction was right.
2. The essence of feedback
“Every good regulator of a system must be a model of that system”? Probably no small number of control engineers, devoted to the successful PID-controllers as the real workhorses of automatic control in practice, might meet this statement with a howl of anguish.
What ‘fool’ would be prepared to defend the given proposition? Who recognizes in the (numerical values of the) P-, I- D-terms of a controller a fair, or even a roughly approximated model of the complex chemical physical electrical . . .process that is
being controlled by that controller?
Let us walk another trail; let us look at the essence of control principles in an old, simple and quite fundamental way (Smith, 1958). Figure 1, by means of block diagram substitutions through the sequence a, l~, c, d, gives a development of the control scheme for response improvement by feed back. In this scheme H~ viz. HM represent the process, viz, the model dynamics. The cx sign indicates an ‘operational amplifier’ with infinite gain. The essential aspect of this reasoning is the role that is played by the model
PIETER EYKHOFFt
Keywords: Modeling, ident
,~fi
cation, and controlA model for the process under control—do or don’t we really need it? Some elementary philosophical considerations confirming such a need, are well supported by examples of various ‘optimal’ control schemes. How does this affirmation influence the requirements to identification and the implementation of control using such a model?
Received 25 January 1994.
tDepartment of Electrical Engineering, Eindhoven University of Technology, NL-5600MB Eindhoven, The Netherlands.
136 P. Eykhoff Modeling, identification and control 137 a)
~
if HME H~:
d)~~H
ODH
H~
Figure 1. Development of a control scheme for response improvement.
HM. It is clear that for the case HM=HP the process acts as its own model, i.e. no separate model is needed!
Similar fundamental lines of thought hold for other control schemes like: disturbance compensation by feed forward,
disturbance compensation by feed back, and predictor control of a process with time delay.
For the purpose of this discourse there is no need to enter into a discussion on the limitations of this type of reasoning in practice. It is evident that in real life the ideal situation represented by such schemes can only be approximated because of the restrictions on feasibility and quality of the HM1approximation; the restrictions on the
components, e.g. their non-linear behaviour; the restrictions on amplitudes and speed of changes of the input due to the need for a ‘smooth’ operation of the process, etc. However, from such examples the potential role of models is clear, in spite of these practical limitations.
3. Various ‘optimal’ control schemes
As a next step in exploring the proposition given by the title of this paper, it would be of interest to analyse a substantial part of the numerous control schemes that have been proposed in literature. Do they or don’t they, explicitly or implicitly, use a ‘model’ of the process under control? And, if they do, what model-structure is required?
The size allowed for this contribution does not permit an extensive analysis. For the limited objective we have in mind, the following approach might be acceptable. Figures 2 and 3 give examples of very simple processes, as well as the associated controllers that result from particular ‘optimal’ control criteria:
Fig Control criteria Process
minimum variance pure time delay
2nd order dynamics+delay zero in right H.P. 2d dead beat 3a mm. integral with input constraints 3b time-optimal 3c 3d
Regulator, pure time delay Regulator; 2nd order process with time delay
Disturbances: Disturbances
optrn I tUn~z~R~ ~ ~, ~ Optwl ti ~tH0j
a)
~
TaRl b)~
R’Regulator; process with zero in RHP Dead beat control. 1st order process
Disturbances: Disturbances:
Optirnot controller ~ (s) ~x~i:ra t spectrum~ Optiwal controller ~we~.r~1P ~ step w(t)—c u(t)
i
t\%,Criterion.Process ,nin ,aria,nao ~~Criterion: dead beatProcessc)
~
d)Figure 2. Examples of controllers for various ‘optimal’ control criteria-I.
Mm. integral control with constraints Time_optimal control, 1st order process
Criterion: criterion:
Optiwal controtler~ Pontryagin~ ~1=f~x0dt mm. Optimal controller Euler— ~~.~fti(0. +ku°) dt mm.
I
~ n Lanranee\to:~::;
~
Time—optimal control, 2nd order process Optimal linear quadratic regulator
~ Euler— ~ Crmtor,on ~ ~. II Euler— ~criteron:
Oplirno controCr ~Lagrangn~.~ .ln0+kU~dt ‘in. p Lagrange ,_f.urRo)dt4!r(t)PO(t,l
~
~ ~ 2a 2b 2c 1st order dynamics 1st order dynamics 1st order dynamics 2nd order dynamics linear dynamicsFigure 3. Examples of controllers for various ‘optimal’ control criteria-Il.
138 P. Eykhoff Modeling, identification and control 139 These simple diagrams, which take into account invertibility restrictions on dynamics,
clearly indicate the similarity between the process dynamics and the corresponding controller. Apparently the proposition posed by the title holds very well indeed... 4. Relation between control theory and engineering
In the previous examples the process was assumed to be known completely and accurately, i.e. it was presumed that no information on parts be missing and that no errors do occur in the parameter values. These assumptions constitute the difference between practice and theory, between reality and model. This is expressed in Fig. 4, which suggests the control theory can be characterized by application of control principles (algorithms) to well-known, well-specified, well-behaving models, and control engineering by the application of such algorithms to reality, i.e. to partly and incompletely known processes. As the projection reality—>model is supported by identification, this technique is bound to play a role of increasing importance; more and more it will contribute to bridging the gap between ‘theory’ and ‘engineering’. This is schematically indicated in Fig. 4 by curve B.
Since the early stages in the development of identification (Eykhoff, 1974) much theory, many tools (computer software) and a wide variety of applications have been developed. The techniques have successfully been used in real industrial situations. Even under such challenging conditions the internal model control (IMC) scheme has demonstrated to be an effective expedient for improving disturbance reduction, for realizing decoupling between various input output relations, as well as for speeding up system dynamics, i.e. reducing change-over time for set point changes (Zhu and Backx, 1993).
Of course the last observation does not imply that all (classes of related) problems are solved and that we have all the answers; that is not the case, even not in principle. More insight is needed in at least the following aspects:
the best type of model and its (unavoidable) model uncertainty for particular control schemes, e.g. for robust Hco control;
the appropriate ways to introduce into the model the kind of a priori knowledge that is available on the process;
the relation between complexity of the model and the quality of control; the limitations on the speed of identification under specific (practical) circumstances, etc. control engineering ,/ / / /
For that reason we do not need a crystal ball in order to predict a continuing research along such paths. This holds the more as both theory and practice have a joint interest in such developments.
5. Conclusions
From the foregoing considerations the conclusion is clear: a compact and accurate process model is the key for the application (to industrial processes) of modern control theory. Hence in essence the statement “Every good regulator of a system must be a model of that system” reflects a correct and fruitful philosophy in control engineering; Fifteen years ago the Editorial Board and the Editor of this journal were perfectly right in choosing the name ‘Modeling, Ident(fication and Control (MIC)’ for their journal, witnessing the crucial role these three elements and their interaction play.
The result attained so far in this field, the challenges available these days, and the tempting promises for the future provide ample reasons to predict a healthy development and a useful role for MIC over a period of, at least, another fifteen years. Congratulations, best wishes to MIC, its Editor and its Editorial Board...
REFERENCES
CONANT,R. C., andA5HBY,W. R. (1970). Every good regulator of asystem must be amodel of that system.
mt.
J. Systems Sci., 1, 89 97.SMITH, 0. J. M. (1958). Feedback Control Systems(McGraw-Hill, New York).
EYKHOFF, P. (1974). System Ident(fication; Parameter and State Estimation(Wiley, Chichester). ZHU, Y., and BACKX, T. (1993). Idennfication of Multivariable Industrial Processes (for
Simulation, Diagnosis and Control)(Springer-Verlag, London).
control principle (algorithm) / / / / / / reality control theory model
