Real-time expert tuners for PI controllers

Prof. B. Porter, MA, PhD, DSc, CEngA.H. Jones, BSc, PhDC.B. McKeown, BSc

Indexing terms: Digital control, Digital computers and computation, Digital communication systems, Communication systems theory, Pattern recognition,Export systems

Abstract: The emergence of expert system tech-nology has made possible the capture of thecontrol engineer's knowledge of tuning problemsand the building of expert tuners for PI control-lers. In the paper, the architecturally relevantissues which arise in the development of experttuners for PI controllers are discussed, and thetechnical issues of representing the appropriateknowledge and using it effectively are addressed.

addressed. The expert tuner developed is fundamentallydifferent from existing expert tuners, in that both theplant outputs and the controller manipulated variables inresponse to set-point changes are used to adjust the con-troller gains, and also, in that the expert tuner providesfacilities for producing gain-scheduling look-up tables fornonlinear plants. Finally, the performance of the experttuner is demonstrated by the presentation of the resultsof laboratory trials of a pump and multiple-tankassembly.

1 Introduction

Even when the seminal results of Ziegler and Nichols [1]are used in the tuning of PI controllers for single-input/single-output plants, the final tuning of such controllers isleft to the control engineer. Indeed, almost all existing PIcontrollers are tuned manually using pattern-recognitiontechniques. Such pattern-recognition techniques involveintroducing set-point changes into the plant, while underclosed-loop control, and then adjusting the controllerparameters on the basis of a comparison of the actualclosed-loop response with the desired closed-loopresponse. The exact method for changing the controllerparameters is based on the experience and expertise ofthe control engineer.

This pattern-recognition technique for the manualtuning of PI controllers is a form of adaptive control.However, unlike all other forms of adaptive control [2],the pattern-recognition technique does not require amathematical model of the process. Instead, a skilledcontrol engineer deploys a number of tuning rules toadjust the controller gains. The emergence of expertsystem technology [3, 4] has, therefore, brought aboutthe possibility of capturing such an engineer's knowledgeand building an expert tuner [5]. Expert systems areproblem-solving programs that contain knowledge data-bases and intelligent reasoning mechanisms which closelymatch the knowledge and procedures used by humanexperts within well defined domains. Indeed, some con-troller manufacturers are beginning to market experttuners [6].

In this paper, the achitecturally relevant issues whicharise in the development of expert tuners for PI control-lers are discussed, and the technical issues of representingthe appropriate knowledge and using it effectively are

Paper 5410D(C4), first received 6th May and in revised form 9thOctober 1986Prof. Porter and Dr. Jones are, and Mr. McKeown was formerly, withthe Centre for Instrumentation & Automation, University of Salford,Salford M5 4VVT, United Kingdom

2 Control requirements of the expert tuner

In the evolution of adaptive control, the expert tunerconstitutes a new and significant milestone in the designof practical adaptive mechanisms. The two major down-falls of adaptive control, to date, have been the require-ment for an accurate model of the plant and the inabilityto set meaningful goals for the adaptive mechanism. Theexpert tuner does not suffer from such shortcomings, as itcircumvents the need for a mathematical model of theplant and provides meaningful time-domain-based goalsfor the adaptive design. These two, highly practical,requirements are achieved by deploying powerfulpattern-recognition techniques developed in the field ofartificial intelligence.

The objective of the expert tuner is to tune a PI con-troller such that the closed-loop step response lies withinlimits set by the commissioning engineer or plant oper-ator. The limits within which the expert tuner works aremaximum overshoot, maximum undershoot anddamping ratio. These limits are then used by the experttuner to compare the untuned closed-loop transient stepresponse with the desired response shape and to updatethe controller in accordance with this disparity.

3 Hardware architecture of the expert tuner

The performance of the expert tuner is governed by twomajor real-time constraints. These are, first, that of speedof processing to effect digital PI closed-loop control and,secondly, that of representing and using large bodies ofknowledge and dealing with recognition problems. Thesetwo broadly separate tasks are ideally suited to parallelprocessing, in which the communication between the twoprocessors is on a common bus. Because of the high-speed communication traffic, the use of a single bus cancause bottlenecks so that a hardware architecture withadditional local bus structures must be deployed tohandle input/output. This type of hardware configurationis readily available from most computer manufacturers.

260 IEE PROCEEDINGS, Vol. 134, Pt. D, No. 4, JULY 1987

4 Software architecture of the expert tuner

The expert tuner software architecture is built up from anumber of components which have been assembled so asto reflect the thinking process of a human expert. Theanatomy of the expert tuner is accordingly as shown inFig. 1. The software architecture of the expert tuner con-

current PIcontrol settingsand hypothesesof plantcharacteristicsand tuning strategy

inference engine

Fig. 1 Anatomy of real-time expert tuner

sists, therefore, of a hierarchy of tasks each of which isamenable to real-time control and to expert system tech-nology. The breakdown of the fundamental tasks in thishierarchy yields the following subsystems:

4.1 Expert signal conditionerThis is a real-time program for the expert conditioning ofengineering data. This is necessary because of the natureof the pattern-recognition technique for the tuning of PIcontrollers, where it is necessary to have well conditionedsignals.

4.2 Intelligent PI controllerThis is a real-time control system which providestwo-way communication between the solution black-board for changing the controller parameters. The soft-ware also includes a small rule base for dealing withactuator nonlinearities and saturation, together withanti-windup and bumpless transfer phenomena associ-ated with practical controller constraints.

4.3 Expert supervisorThis is a real-time front end to the expert tuner whichestablishes event priorities, ensures plant safety and alsoprovides a user-friendly interface to the system operator.

4.4 Expert tuner inference engineThis is a real-time intelligent mechanism for changing PIcontroller gains. The inference engine consists of the solu-tion blackboard, the consistency enforcer and the inter-preter.

4.5 Intelligent gain schedulerThis is a real-time mechanism which identifies open-loopstep-response plant characteristics from closed-loop data.

These characteristics are identified in real time, in termsof an autoregressive moving-average model using recur-sive least squares [7]. The gain scheduler stores tuned PIcontroller settings for various open-loop step-responsecharacteristics. The information can then be used tocreate look-up tables for nonlinear plants or can be usedto give initial controller settings when tuning new plants.

4.6 Expert tuner performance justifierThis is a real-time explanation facility which explains theactions of the system to the user. It indicates reasons forthe use of the current tuning strategy and provides infor-mation on plant characteristics.

5 Knowledge encoding within the expert tuner

The pattern-recognition technique developed within theexpert tuner uses meta-knowledge to enable the experttuner to deal with a variety of plants. The meta-knowledge enables previous experiences to be used tointerpret new situations. Each meta-rule contains infor-mation on both closed-loop transient-response character-istics and open-loop plant characteristics. Thecharacterisation of the closed-loop transient responseemploys the magnitude and time of both the first over-shoot and the first undershoot of both the plant outputand the manipulated variable in response to a stepchange in the set point, together with the integrals ofboth the plant output and the manipulated variableevaluated at strategic instants along the transient. Thesedata are used to establish the following nine categories ofclosed-loop transient-response characteristics:

(i) too low monotone(ii) too low oscillatory(iii) overshoot undershoot(iv) no overshoot undershoot(v) no overshoot no undershoot

(vi) overshoot no undershoot(vii) overshoot monotone(viii) overshoot oscillatory

(ix) over safety limit.

In these categories, the description of closed-looptransient-response characteristics as 'too low', 'overshoot'and 'undershoot' arises from the consideration of excur-sions outside the upper and lower closed-loop per-formance limits shown in Fig. 2. This information

2 -

12 15time, min

Fig. 2 Typical closed-loop transient-response characteristics

concerning closed-loop transient-response characteristicsis coupled with that concerning the following eight cate-gories of open-loop plant characteristics:

(i) no delay monotone(ii) no delay oscillatory(iii) short delay monotone

IEE PROCEEDINGS, Vol. 134, Pt. D, No. 4, JULY 1987 261

(iv) short delay oscillatory(v) medium delay monotone

(vi) medium delay oscillatory(vii) long delay monotone(viii) long delay oscillatory.

In these latter categories, the description of open-loopplants as 'short delay', 'medium delay' and 'long delay'arises from the consideration of the ratio of the pure timedelay in the plant to the dominant time constant.

The meta-knowledge, using this information, organisesthe transient responses into recognisable collections ofobjects, decides logically which tuning rule to apply andindicates the nature of the consequential improvement inthe transient response. The tuning rules which cause thecontroller gains to be modified are based on the com-bined experience of many control engineers and are con-structed in such a manner that a quantitative judgmentcan be made concerning the modification of controllergains. The rules are constructed in relation to a contextfor the application of the rule and a matching of thepresent closed-loop transient to previous experiences.The context for the application of the rule is establishedby the meta-rules, while the matching of the closed-looptransient response is effected by comparing the patternsof stored closed-loop transients (for which definite tuningrules are known) against the present closed-looptransient.

Such a rule can be illustrated by considering the casewhere the meta-knowledge has isolated the fact that theclosed-loop transient response is of the 'overshoot under-shoot' type and that the open-loop plant characteristicsare 'medium delay monotone'. Then, the following rulemight apply where the areas Au A2 and A3 are shown inFig. 2:

IF (the control variable continues to increase after thetransient first crosses the set-point)

THEN (reduce the integral gain by setting

The meta-rules in this application facilitate the control ofthe search space of the tuning-rule knowledge base andallow the system to differentiate between sets of closed-loop transient responses which are superficially similar,but which, in fact, are intrinsically different. Moreover,the approach can be implemented in a way that can bereadily accessed by the consistency enforcer and theexpert tuner performance justifier.

6 Knowledge deployment within the expert tuner

As the expert tuner is required to be capable of tuning abroad spectrum of plants, the application of certain rulesdepends on the open-loop characteristics of the plant.Because of this constraint, it becomes necessary to con-struct a hypothesis concerning the type of plant beingcontrolled. Therefore, to create a robust expert tunerwhich can explain and justify itself, both deep representa-tions and surface representations of knowledge are used.The deep representation rules (or meta-rules) are usedboth by the consistency enforcer to create intermediatehypotheses and by the inference engine to modify con-troller gains, whereas the surface representation rules (ortuning rules) are used only to change the controller gains.The consistency enforcer attempts to maintain a constantrepresentation of the emerging solution by using the

meta-rules to construct hypotheses concerning thecurrent plant characteristics and the current tuning strat-egy, and also possesses a facility to advance or retractthese hypotheses. The hypotheses created by the deeprepresentation rules in the consistency enforcer are con-tained in the solution blackboard. This contains informa-tion on the current hypothesis concerning plantcharacteristics, the current tuning strategy and thecurrent trend in changes in controller gains.

The operation of the expert tuner is that, initially, anopen-loop step-response test is performed and an initialhypothesis concerning the plant characteristics isadvanced. The interpreter then executes the agenda byapplying the appropriate meta-rules which trigger a rulein the surface representation knowledge base, after whichthe consistency enforcer examines the current contents ofthe blackboard and estimates the effect of applying therule. The consistency enforcer then implements appropri-ate changes in gains and, when the plant is in a steadystate, initiates a closed-loop step-response test. Then, byusing the closed-loop transient response, the consistencyenforcer either verifies or modifies the current hypothesis.Once this is complete, the interpreter is executed againand the whole process is repeated until the controller istuned to specification.

7 Performance of the expert tuner

The practical performance of the expert tuner was evalu-ated by tuning a digital PI controller on a laboratory testrig. This test rig is shown in Figs. 3 and 4, and consists of

BBC micro,system

discdrive

digi tal toanalogueconvertor

depth sensorsignalconditioner

copper tubing

supplypump

Perspex/tanks

outlet,valve

Fig. 3 Laboratory test rig

a pump and multiple-tank assembly, the manipulatedinput variable being pump flow rate and the controlledoutput variable being the level of the second tank. Thetest rig exhibited significant nonlinearities in both theactuator characteristics and plant dynamics. In this case,a sampling period of one second was chosen, together

262 IEE PROCEEDINGS, Vol. 134, Pt. D, No. 4, JULY 1987

with closed-loop performance limits of 5% maximumovershoot and 5% minimum undershoot. The initial PIcontroller settings were obtained from an open-loop stepresponse using the Ziegler-Nichols tuning rules.

8 Conclusion

The emergence of expert system technology has madepossible the capture of the control engineer's knowledge

plant

controller 1JDAC/jj amplifier -

supplypump - tanks -

depthsensor

signalcond. I ADC

..JFig. 4 Closed-loop system block diagram

u

max

1

\ ,

2 3time, min

>

8

Fig. 5system

Performance characteristics of initially tuned closed-loop

umax

2 3time min

Fig. 6 Performance characteristics of finally tuned closed-loop system

The performance of the initially and finally tunedclosed-loop system are shown in Figs. 5 and 6, respec-tively, and the trajectories of the proportional and inte-gral controller gains are shown in Fig. 7. These real-timetrials demonstrate the excellent performance of the experttuner in tuning a digital PI controller for a plant forwhich the standard Ziegler-Nichols tuning rules yieldpoor closed-loop performance.

101 U 6cycles

Fig. 7 Trajectories of proportional {K^ and integral {K2) controllergains

of the manual tuning of PI controllers and the building ofeffective expert tuners for PI controllers. In this paper,the architecturally relevant issues which arise in thedevelopment of expert tuners for PI controllers have beendiscussed and the technical issues of representing theappropriate knowledge and using it effectively have beenaddressed. Finally, the excellent performance of such anexpert tuner has been demonstrated in the context of theonline tuneup of a PI controller for a single-input/single-output laboratory test rig.

9 References

1 ZIEGLER, J.G., and NICHOLS, B.N.: 'Optimum settings for auto-matic controllers', Trans. ASME, 1942, 64, pp. 759-768

2 ASTROM, K.J. and WITTENMARK, B.: 'Computer-controlledsystems' (Prentice-Hall, 1984)

3 MICHIE, D.: 'Introductory readings in expert systems', (Gordon andBreach, 1984)

4 DAVIS, R.: 'Expert systems: where are we? and where do we go fromhere?', Artif. Intell. Spring 1982, pp. 3-22

5 JONES, A.H., and PORTER, B.: 'Expert tuners for PID controllers'.Proc. IASTED Int. Conf Comput. Aided Des. & Appi, Paris, June1985

6 KRAUS, T.W., and MYRON, T.J.: 'Self-tuning PI controllers usingpattern recognition approach', Control Eng., June 1984, pp. 106-111

7 JONES, A.H., and PORTER, B.: 'Design of adaptive digital set-pointtracking PID controllers incorporating recursive step-responsematrix identifiers for multivariable plants'. Proc. 24th IEEE Conf.Decis. & Control, Fort Lauderdale, December 1985

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