EXPMUL: an expert system for the design of multivariable control systems

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EXPMUL: an expert system for the design ofmultivariable control systemsAHMED A. BAHNASAWI a , SHAWKI Z. EID a & HESHAM A. HEFNY ba Department of Electronics and Communications , Faculty of Engineering, Cairo University ,Giza, Egyptb Arab Organization for Industrialization (AOI) , Cairo, EgyptPublished online: 16 May 2007.

To cite this article: AHMED A. BAHNASAWI , SHAWKI Z. EID & HESHAM A. HEFNY (1993) EXPMUL: an expert systemfor the design of multivariable control systems, International Journal of Systems Science, 24:12, 2345-2366, DOI:10.1080/00207729308949633

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INT. J. SYSTEMS SCI., 1993, VOL. 24, NO. 12,2345-2366

EXPMUL: an expert system for the design of multivariable controlsystems

AHMED A. BAHNASAWIt, SHAWKI Z. EIDt andHESHAM A. HEFNYj:

The development of an expert systemenvironment for the design of MIMO controlsystems using the frequency response approach is discussed. The aim is to provideassistance for non-experienced designersso that they can learn and gain experienceof a specific area of control systemtheory. As a preliminary,we discussthe differentconfigurations of expert systemsused in control systemdesign.The design heuristicis then declared, and followed by a comprehensive example.The implementation ofour expert system is then illustrated, and a detailed application is also given.

1. IntroductionAlthough many powerful control design packages have been developed in the last

decade, it is still difficult for the student, or the non-experienced designer, to exploitthem properly. This is due to the large number of instructions he needs to know, andthe several design approaches that have to be clear in his mind. Moreover, with thefact that there is no one package that can cover all analysis, and design techniques ofthe control system theory, then one has to know more than one package to solvedifferent design problems.

On the other hand, it is noted that the design process, in most cases, cannot becompleted successfully in an algorithmic way, but rather in a heuristic one. Thismeans that a clear cut design approach may not exist for many design problems.Therefore, an iterative feedback process based on a guided trial and error techniqueis the approach needed for many of such design cases. This heuristic way of thedesign process is based essentially on a practical experience, rather than on a theoretical literature (Astrom et al. 1986).

For the above reasons, it has been believed that a new design environment isneeded to be connected with the currently available conventional packages. Thisenvironment should contain a certain amount of experience so that it can guidethe user during the design process. It should also have the ability to provide theuser with different ad vices in different situations, while the user can make requestsfor explanations of them. Construction of such an environment enables the user tocomplete his design successfully, and use his conventional package efficiently.

Design environments having the above features are called knowledge-basedsystems (KBS), or generally expert systems (ES); see Taylor and Frederic (1984).The use of expert systems in control system design has seen a remarkable growth inrecent years. They have been proved to be the most efficient tools for what is called'transferring of experience'. These new design tools are also referred to as the 3rdgeneration of the computer-aided control engineer i.e. CACE-III, while the conven-

Received 16 March 1992.t Department of Electronicsand Communications, Faculty of Engineering, Cairo Univer

sity, Giza, Egypt.t Arab Organization for Industrialization (AOI), Cairo, Egypt.

0020.7721/93510.00 © 1993Taylor& Francis Ltd.

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2346 A. A. Bahnasawi et al.

tional packages are considered to be the 2nd one i.e. CACE-I1 (Taylor and Frederic1984).

In this paper we discuss the construction of a prototype expert system, which iscalled EXPMUL, that can aid the control engineer in the design of multivariablesystems. In section 2 we demonstrate the different configurations of expert systemsthat can be used in control system design with stress on those which are used todevelop such educational expert systems. A design heuristic of the MIMO systembased on the inverse Nyquist array (INA) method is described in section 3. In section4, an application of the design approach to an example is investigated in detail. Theimplementation of EXPMUL is presented in section 5 with illustrative configurationshowing its software structure. Section 6 presents a sample output of the interactionenvironment provided by EXPMUL during consultation for the same designexample. A number of conclusions, and directions of further research is outlinedin section 7.

2. Expert systems and control system designThe four essential components of KBS, as shown in Fig. I are: a knowledge base;

an inference engine; a knowledge acquisition module; and a user interface.The knowledge base contains the data, and knowledge of a particular domain

which are mapped from the knowledge of a human expert with some type of knowledge representations.

The inference engine interprets the knowledge stored in the knowledge base usingsome type of inference strategies.

The knowledge acquisition module deals with adding new knowledge to the

~I Knowledq, '"qulsllion

tKnowledllll be".

Irects

I

IInhrenc:. rulell I

:Inhrenc. engine

1 .....0.. 1

:UDer inte.-rece

IEXPllIl'WIllOnl

I 00••".0. I

:Us• .-

Figure I. Major components of an expert system.

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EXPMUL: expert system-multivariate control systems design 2347

Figure 2. General structure of on-line expert system.

knowledge base of the expert system, or changing or modifying its knowledge basethrough some sort of learning mechanisms. One of the ultimate goals of research inthe area of knowledge acquisition is to allow the domain expert to enhance thedomain knowledge of the program with only a little help from the knowledgeengineer.

The user interface contains explanation facilities which show the user how acertain fact is concluded. More comprehensive discussions about knowledge representations, and inference engine mechanisms can be found in Forsyth (1984), Brownston et al. (1985), Jackson (1987), Walters and Nielson (1988).

2.1. On-line and off-line expert systems

Having the structure shown in Fig. 1, then two types of expert systems used forcontrol engineering applications can be declared. The first is obtained if the previousstructure is connected to external dynamical process to provide a direct control overit. This type of expert system is generally called 'on-line', or 'real time'. As anexample of such systems, see Sripada et al. (1987) for an expert system whichcontrols a first order non-linear process based on bang-bang control. Anotherexample is given in Porter et al. (1987) in which a real-time expert tuner for PIcontroller is obtained. Figure 2 gives the general form of on-line expert controlsystems

On the other hand when the expert system (ES) is only required to give consultations for control system design, then it is called 'off-line'. Two different configurations of off-line ES are given in Fig. 3.

As an example of the first configuration in Fig. 3(a), see Fortuna et al. (1989) inwhich an ES for optimization of model reduction technique has been developed.About 200 production rules are included in its knowledge base so as to give consultations for best selection of approximation algorithms to be used for model orderreduction.

(0)

Figure 3. General configurations of off-line ES: (a) stand alone ES; (b) ES connected toexternal programs.

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(al (blUser

(c)

Figure 4. Different configuration of CACE-III system.

For examples of the second configuration in Fig. 3(b), see James et al. (1987),Lamont (1990). Both systems provide a CACE-IiI environment for the design oflead-lag compensator for SISO systems. Also see Pang and MacFarlane (1987) foran ES for the design of multivariable control systems using the frequency domainapproach.

2.2. Different configurations of CACE-Ill systems

There are two approaches for developing expert systems for a certain controldesign problem. The first approach makes the ES do all the design task without anycontribution of the user except entering data. The second one is to involve the userinto the designing loop. In this case each time the user consults the ES, a number ofprobable recommendations appears, and the user is free to select one of them toproceed in his designing process. The final design may, or may not be accepted by theES. The user has to continue through this designing process until obtaining asatisfactory result.

It is obvious that the second approach is much more useful for educationalpurposes. The guided trial and error mechanism provided by this approach, helpsthe user to gain experience of the considered design problem. In this case the ES actsas a design assistance.

There are three probable structures for this second approach. In Fig. 4(a) the ESgives the user the required advice which helps him to go through the used CACE-IIpackage. There is no direct connection between the ES, and the CACE-II package inthis structure. However, in Fig. 4(b) the ES can make an external calling to the usedpackage from its knowledge base which makes the design process much easier.Finally, in Fig. 4(c), it sometimes happens that some design methods are not directlyincluded in the instruction set of the available CACE-II package. This means thatsome external programs may be written as an external support to the used packagefor proper completion of the design method.

It should be noted that the selection of one of the above configurations fordeveloping a certain CACE-I1I system is based essentially on the available software, and the available hardware tools for the ES developer.

Figure 5. CACE-III system with its ES connected to multi CACE-II packages.

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User

Figure 6. CACE-1lI systems having the CACE-II package can be connected to many expertsystems.

2.3. Proposed configurationsfor CACE-III systems

The previous structures, shown in Fig. 4, represent the currently known configurations for CACE-III systems. However, the following three figures are proposedconfigurations for future enhancements of such systems.

According to the fact that there is no CACE- II package that includes, or caninclude, all analysis methods, or design techniques of the control system theory,some packages are found to be suitable for identification problems, while othersare preferable for time domain analysis. Another type of package may be neededfor frequency domain analysis ... etc. (Spang 1985).

This leads us to the suggestion of the configuration given in Fig. 5 in which thedeveloped KBS can make external calls to more than one CACE-II package. It isclear that CACE-III systems having such structure cannot be developed on microcomputers due to limitations on the packages available on such small machines, andalso due to the need of large memory size, and high processing power. Such systemsmay be well developed on workstations, or mainframes.

The next proposed CACE-III package depends basically on one CACE-II, andmore than one expert system-each developed for a certain design heuristicproblem-can be successfully connected to the CACE-II to give a different designproblem. In this case the user needs not to buy another CACE-II package when hisown package does not support a certain design method; he simply goes to his dealer,and selects an ES from the list of the ready made expert systems (which are speciallydeveloped for his own package) to support his designing problem. Figure 6 showshow this new package looks like.

The new configuration shown in Fig. 6 suggests the future form of the team workrequired to develop .control packages. Two groups of software developers arerequired: the first is the conventional programmer group, and the second is AIprogrammer group. The first group is responsible for developing conventionalCACE-II packages, and makes continuous improvements to existing ones. On the

User

Figure 7. The same configuration of Fig. 6 with additional external programs connected toeach ES.

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other hand, the second group is responsible for improving the entire interactiveenvironment by developing several knowledge based systems. In such a case, themarketing of a certain CACE-II package will be dependent on the number ofcurrently available expert systems which can be successfully connected to it.

As we have seen in Fig. 4(c), that some external programs may be needed to beconnected to both ES, and CACE-II package for some designing methods, this canbe added to Fig. 6 to obtain the new configuration shown in Fig. 7.

3. MIMO design heuristicThe design heuristic used for EXPMUL is based essentially on a direct appli

cation of INA method developed by Rosenbrock (1969, 1974). However, beforedeclaring such heuristic, we have to illustrate the motives behind the selection ofthe frequency response approach of the multivariable feedback systems to be put inan expert system form. This is due to the following features of using such generalizeddesign techniques (MacFarlane 1972, Pang and MacFarlane 1986).

(a) They are useful to work on limited amount of experimental data.

(b) They are insensitive to model inaccuracies.

(c) Such techniques are intuitively appealing, which is of great importance forpractising design engineers.

(d) Fairly simple controllers are sufficient for many purposes.

(e) They are well-suited for interactive computing.

These features meet our aim of developing an educational expert system.Figure 8 shows the general configuration of a multivariable feedback system.

Having this in mind, the following steps describe the iterative design procedure ofEXPMUL in detail.

Step I. Accept the plant transfer function matrix G(s). It may be entered directly, oras state space form, i.e. as A, B, C, D matrices, then convert them to G(s).

Step 2. Invert G(s). (Assuming that it is non-singular.)

Step 3. Test for diagonal dominance. Via the plot of qu(s). Gershgorin bands haveto exclude the origin. If diagonal dominance is achieved then go to Step 5.

Step 4. Select compensators to achieve diagonal dominance. Appropriate compensator forms can be selected (Rosenbrock 1974). Both pre and postcompensators can be used. Go to Step 3 for testing.

Step 5. Calculating the number of open loop poles in R.H.P.This is the number of transmission poles of Q(s) = L(s)G(s)K(s), or thetransmission zeroes of Q(s) = K(s)G(s)L(s). This can be obtained by putting Q(s), (or Q(s)) in its Smith-McMillan form. However, this may not beavailable on the used package. Therefore, we can take the number of R.H.P.

'~FlS)

Figure 8. The general multi variable closed loop system.

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poles of IQ(s) I (or zeroes of IQ(s) I) as a first trial. If the response of theclosed loop system, in Step 8, to a unit-step function is stable then the designis accepted. Otherwise, other choices of feedback gains, in Step 6, have to beselected. It should be noted that for most cases of design problems there aretwo regions allowed for the feedback gain/; in which to be located. The firstregion is the one encircled by qi;, and the second region is not. Therefore, forn-loop feedback system there are 2" probable combinations of regionlocations for the set of feedback gains {/;}. These combinations can betested until the stable response in Step 8 is obtained.

Step 6. Select the set of feedback gains.The set {/;} should satisfy the Rosenbrock stability criterion (Rosenbrock1974)

k = 1,2, ... ,n (1)

where Po is the number of R.H.P. poles of Q(s), J?~ is the number ofclockwise encirclements of qii about the origin, and Nq~f is the number ofclockwise encirclements of qii about the point (-/;,0). The set {/;} shouldalso result in small diameter for the Ostrowski band circles. Now we haveR=F+Q.

Step 7. Invert R.Now R must be dominant diagonal.

Step 8. Test of unit step response.This is obtained for elements of R(s). All responses should be stable. Onlythe diagonal elements should have unity response, while the off-diagonalelements have nearly zero response. A set of integral, or lead compensatorsmay be needed to eliminate the offsets in the unit-step response for thediagonal elements. If the behaviour is unacceptable then we should returnto Step 6 and choose another set of feedback gains.

The ability of the above heuristic to obtain suitable compensators is discussed inthe following section.

4. Example (Pang and MacFarlane 1987)

G s _ [2'15S2+16S+32'6

l'IS2+4S+9'4]

I (2)( ) - 1'05s2 + 4s + 6·2 s2 + 4s + 3 (s + 1)(s + 2)(s + 3)

It is clear that IG(s)I has no unstable poles. The INA plots of G(s) are shownin Figs 9 and 10. Testing of the row diagonal dominance (r.d.d.) using theGershgorin bands plots are shown in Fig. 11. It is obvious that only the secondrow is d.d. as it excludes the origin. This immediately suggests the following precompensator:

_ [5-433K, = G(O) =1·033

1'567]0·5

(3)

The resulting Gershgorin bands plots of the open loop t.f.m. QI = il; are shown

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n4 1uist plot of elenent 111 29 r-------""T"~"'-'-'''--'-'=~:...----____r::1~

a 16s

12 e-

9f----....--P'"---------------j

4~········-~.......~

------c, --·4 -

I I

5 6Real C(Jw)

4 5 6Real C(Jw)

I

4I

t 1 2

I , I

2

. tit

-1

I·1

·2

, I

·2

n41 lliS PIO 0 e e~en

l:£f-

I

,..

e-

e-

--1---....,..-".='-..

8 I , I , I I '-~ I I I I I

4

·3

12

9

·4

1 29Ma 16y

Figure 9. Inverse Nyquist plots of the first row of 6(s).

in Fig. 12. Now the first row is d.d., but the second is not. Testing of the r.d.d. usingbode style plots, take the log of the equation.

k

Igii(S) I - L Igij(s) I > 0j=1Hi

and plot the result on a log scale, which shows that the second row needs to bediagonalized over the frequency range extended w = 6, 10 w = 7; see Fig. 13. Usingthe technique of 'pseudo-diagonalization', see (Rosenbrock 1974), the followingprecompcnsator is found

. [I 0]K2 = 0.138 -0.99

(4)

The resulting Gershgorin bands are shown in Fig. 14. Now, a diagonal feedback

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4 5 6Real C(jw)

. tit f 1

·1

n~( uis Pia a e mnt 2 1l::.

-

-,-

-

~-- ----""'--I- --..._----~

~"I I I I I I I 1 .....1 I I. --8

3

-4

4

12

-4

5 6Real C(Jw)

-1-2

nUluist plot of eleMent 2,2l::.

I- -,<,

- '. ...-,........

- '<,,.' ...

I- ,...., ........

"....-

-I I I . I I I I I i I I , I

4

-8·3

12

I 20Ma 16g

Figure 10. Inverse Nyquist plots of the second row of O(s).

compensator needs to be selected in order to decrease interactions between loops inthe closed-loop system. However, the INA stability criteria needs to be satisfied, see(I). The allowed gain space of the feedback values can be directly deduced by eyefrom Fig. \4, as -II < 1·\ I, -/2 > -\·11 i.e.II > -\'1\, fz < \.\1. This means thatthe closed-loop system can be stable for a proper selection of +ve, or -ve feedbackvalues, However, to make most of the stable feedback values -ve, we have to makeih2 encircles most of the R.H.P. rather than the L.H.P. This can be easily obtainedby introducing the additional precompensator:

__ [\ 0]K3 - o -I

(5)

The effect of this compensator on the shape of q22 is shown in Fig. \5. Now theallowed feedbackvalues are II > -\'\\, and 12 > -\.1\,

After a number of trials it is found that the performance of the closed-loop

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Test of ~ow d.d. (G.B)

HI

r-Ir

kr'"

plot of u11(.iw)

<, ....-.:\>. """:.;/)j"------.....

10I I,-HI c..:_.1-,---'-_.1----'-...L.l.----I.._.l.-----L_

-HI

Test of ~ow d.d. (G,B)

10

,r-,j-

!Ir

HI

rI'r--ir

- HI :-1----JL.-...L..---l.._L...L...L-......L_L---L_-HI

Figure 11. Gershgorin bands plots for rows of G(s).

system is accepted for the selection of feedback compensator as

F=[0'60]° 0·6(6)

and a further forward lead compensator of the form

[

(1 + 0'05s)• 3(1 +0'5s)

K4 =

°(1 + :'05S)]3(1 +0'5s)

(7)

The effects of F on the interaction between loops are shown in Fig. 16, where theOstrowski bands are extremely small. The time responses of the outputs of the closedloop system are shown in Figs 17 and 18. Now, the final forward precompensator is

K(s) = K4K3KzK,Therefore, the required compensator is

K(s) = K,KzK3K4

(8)

(9)

It should be noted that the above solution is neither the only solution nor theoptimal one for this problem, but simply 'It is a solution!' The above heuristic helps

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Test of row d.d. <G.B>A

110

Test of row d.d.

HI

-HI-10

A

10

Figure 12. Gershgorin bands plots for rows ofQI(s) = KIG.

us to find but not to optimize a solution. As we noted in Fig. 11, that only the firstrow needed to be d.d. at low frequencies, therefore it was true to replace thecompensator given in (3) with the following compensator which takes only the firstrow of G(O)

, [5,433K= o (10)

If this compensator had been used initially, all the subsequent compensatorswould have been changed.

5. Implementation of EXPMULThe need for an expert system approach for the above design heuristic results

from our aim of providing a comprehensive design environment for education. Anexpert system can provide a user-computer interface that is more powerful, flexible,and helpful in the educational design process, as well as providing design experience(Lamont 1990).

The ability of the user to query the system to check the logical flow of the designheuristic is an essential requirements of the expert system. Thus, the focus is onenabling the user to understand what is happening as the heuristic is applied insteadof implementing the heuristic in the fewer number of lines of code (James et al. 1987).

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I d .t t r d'es 0 Iaqona OMlnance of row 1~

1'-••..,....

~<;

<;<,.....

I

-,............

<,'.

'."<,_---.-........

-------- I

, , , , ""~---~

10

dB 20

H 50a91 40tud 30e

100 101FreqllenC~ (radlm)

I d .es 0 Iaqona OMI nance 0 row 2LC!

--.............-<, j"<,

..........

~-- 0---...............1------

~........-.

<,

,,,,, , , "'" , , '"

20dB

H 60a9ni 40tIIde

109 JD1Frequenc.'l (l'acllsec)

Figure 13. Test of diagonal dominance for rows of QI using inverse bode style plots.

Therefore, the difference between implementing the above heuristic in a conventionalprogram, or in an expert system is the difference between explicit, and implicitrepresentation of knowledge (Faught 1986). Expert system has the advantage ofthe separating of knowledge from the execution of reasoning and inference. Generally, an expert system approach should be considered where (Martin and Law 1988):

(a) the domain contains complex interactions of knowledge that can be identified directly, or induced and therefore can be represented explicitly;

(b) the domain is sufficiently complex to lead to the expectation that there willbe several iterations and reorganizations of the knowledge during the development of the system.

5.1. System overview

The overall consultation process within EXPMUL can be listed as follows:

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Test of ~ow d.d. <G.B)A

10

Test of ~ow d.d. (G.B)A

10

pI °t of <122(.iw)

----'- -1

~~ , , , ,

HI

-HI-10

Figure 14. Gershgorin bands plots for rows of Q2(S) = K2Q\.

Test of ~ow d.d. <G.B)

10

A

___""p",I""O,t of <l22<.iw)

~r

tr

i-

-1.0-10

, , , ,10

Figure IS. Gershgorin bands plots for the second row of QJ = KJQ2'

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I'o .. d.d. <O.B>A

,,10 t of <tll (.;w>

Test of

HI

tI

-

--

\

I I I I I I

HI_ ,. ~'----...l.'_'-.L.-...L.JL.L----l..----l_.L.-...J

-HI

Test of I'OW d.d. <O.B>A

"Iot of <t22<-;w>HI L

~ Itf-

f0-

r-

r--f-

-HI I I I I I

-10 10

Figure 16. Ostrowski bands plots of the compensated plant usingI, = fi = 0-6.

(a) entering the system model;

(b) checking R.H.P. poles for Q(s) (or zeros for (2(s»;(e) selecting a suitable decoupling method of the given plant model, and advis

ing for suitable plots;

(d) selecting forward path compensators and testing the Gershgorin bandsthrough the calling of external routines;

(e) selecting a feedback compensator by checking the Ostrowski bands, and

(f) evaluating the closed-loop system by checking time response plots.

5.2. Expertise within EXPMUL

EXPMUL contains particular knowledge in the following areas:

(a) rules about what sort of decoupling method is needed;

(b) knowledge about suitable forms of compensators during different stages;

(e) rules for selecting the appropriate external routines or macros; and

(d) guidance of the user through the interaction in a user-friendly and intelligent manner.

5.3. Development of EXPMUL

Expert systems may be implemented using special programming languages such

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tiMe resuo11le of elenent 11

/~,80,. !

f.60

,20

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Figure 17. Closed-loop step response of the final design (step at input 1).

as Lisp, Prolog, Pascal, or C. However, such activity normally requires a great dealof effort (Fortuna et al. 1989). At present, there are several powerful software toolsavailable, generally called 'shells' which provide an inexpensive and efficient way todevelop an expert system. The reasons for selecting a micro-based expert system shellfor the development of EXPMUL are summarized as follows (EXSYS 1985, Fortunaet al. 1989).

(a) A shell requires no prior experience in knowledge system technology orspecial programming capabilities.

(11) A shell allows the knowledge engineer to concentrate on building the knowledge base, as both the inference engine and the user interface are readymade.

(c) A shell's support facilities allow editing, debugging, and built-in commands,necessary for 'rapid prototypic' capabilities.

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ti~e response of eleMent 2 1ou~ r-----~....!-'=~~~=l....!<.l-=-------7.71

1I

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,80 ~

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Figure 18. Closed-loop step response of the final design (step at input 2).

(d) A shell will generally provide enough reliability, and sophistication for thecomplexity of our task.

(e) The resulting system will be easy to maintain, and expand.

EXPMUL has been developed using three components:

(a) an expert system development tool, EXSYS 3.0 shell;

(b) CACE-II package, CC, release 3.2; and

(c) a group of external conventional routines which are written using theBorland Turbo BASIC package.

The general structure of EXPMUL is the same as that shown in Fig. 4(c). Thesecomponents are connected together to provide the highly interactive environment ofthe proposed CACE-IJI package. The external conventional routines have beenimplemented to support the used release of the CC package in the plotting of

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~B

Figure 19. Softwarearchitecture of EXPMUL.

Gershgorin bands, and Ostrowski ones. They are also used to generate many macrosthat are needed to be executed during the consultation of EXPMUL. The hardwaredevelopment tool of EXPMUL is the IBM PC-AT, or compatibles, with 640 KBmemory, one floppy disk drive and a hard disk drive.

5.4. Configuration of EXPMUL

The architecture of EXPMUL is shown in Fig. 19. The knowledge base containsmore than 60 production rules which can guide the user through the different steps ofthe above design heuristic. The EXSYS shell provides an inference engine whichutilizes a forward-, or backward-chaining reasoning process to each consultationof EXPMUL. At the start of the question-and-answer consultation, the user hasthe ability to activate, or not to activate, the external program-calling facility. If hechooses not to activate it, then the result of the consultation, according to hisanswers to different questions. will be a recommendation to execute a certainexternal routine, or a particular macro using the CC package. If he chooses toactivate the external calling facility, then he will be asked to give the name of therequired program, and the consultation will end with a successful calling process.The R.G. files are the report generator files which are printed outputs of the expertsystem consultations. The F.R. files are the frequency files generated from CC, andthe RAM-DISK files are the organized frequency files.

5.5. Knowledge base in EXPMUL

Knowledge in EXPMUL is built up using about 60 production rules. A rule isgenerally divided into five parts: an IF part, a THEN part, an optional ELSE part,an optional NOTE, and an optional REFERENCE. They are addressed as follows(EXSYS 1985):

IFconditions

THENand choices

ELSEconditionsand choices

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NOTE:---REFERENCE:-------

A condition is simply a statement of fact; the two main types are text and mathematical. A text condition, which we are interested in, is a sentence that may be trueor false. For example "THE DOMAIN OF THE SYSTEM MODEL IS FREQUENCY", or "THE ELEMENTS OF THE TRANSFER FUNCTIONMATRIX ARE RATIONAL". The condition is made up of two parts, a qualifierand one or more values. The qualifier is the part of the condition up to and includingthe verb (in the above examples THE DOMAIN OF THE SYSTEM MODEL IS,and THE ELEMENTS OF THE TRANSFER FUNCTION MATRIX ARE). Thevalues are the possible completion of the sentence started by the qualifier. Thefollowing set of rules are given to illustrate the above rule-structure of EXPMUL.RULE NUMBER: 13

IF:The external calling flag is not activated

and A system utility operation is not requiredand The system model is required to be enteredand The domain of the system model is frequencyand The elements of the T.F. matrix are rational

THEN:The external program to be called is CCj@Macl-Probability = 10/10

and stopRULE NUMBER: 14


and A system utility operation is not requiredand The system model is required to be enteredand The domain of the system model is frequencyand The elements of the T.F. matrix are irrational

THEN:The approximation method to be used is Pade approximation-Prob

ability = 6/10and The approximation method to be used is the classical engineer

approx.-Probability = 7/10and The approximation method to be used is the Taylor series expansion

approx.-Probability = 9/10and The external program to be called is CCj@Macl-Probability = 10/10and stop

NOTE:(1) exp (-st) = (I - st/2)10 + st/2) -> Pade approximation(2) exp(-st) = 1/(1 +st/n)'n, where {\rrn n} is a large number -> classical

control engineer approximation(3) exp (-st) = I - st + (st) '2/2! - (st) 3/3 + ... -> Taylor series expan

sion.RULE NUMBER: 15


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and A system utility operation is not requiredand The system model is required to be enteredand The domain of the system model is time

THEN:The external program to be called is CC/@Mac2-Probability = 10/10

and stopIt is worth noting that the fourth condition in rules 13 and 14 is then taken as the

first value of the following qualifier:Qualifier # 4

The domain of the system model isI. frequency2. time

On the other hand, the second value of the above qualifier is taken as the fourthcondition of rule 15. In the same way, the fifth condition in rules 13 and 14 is takenas the first, and second values of the following qualifier:

Qualifier # 5The elements of the T.F. matrix areI. rational2. irrational

Choices are the possible solutions to the problem among which the expert system willdecide. In the above rules these choices appear in the THEN part followed by aprobability number. This number can be interpreted as the degree of recommendation provided by EXPMUL to the user. There are three main systems available inEXSYS for assigning the probability value. Only one system can be used in a givenknowledge base. These systems are: the 0 to I system, the 0 to 10 system, and the-100 to 100 system. EXPMUL uses the 0 to 10 system. In this system a probabilityof 0/10 is equivalent to 'absolutely no' and locks the value at 0/10 regardless of anyother value the choice may have received in any other rule. A value of 0/10 eliminatesthe choice from further consideration. A value of 10/10 is equivalent to 'absolutelyyes' and also locks the value for the choice at 10/10. Values of I to 9 represent degreeof certainty, or recommendation ranging from 'very probably no' to 'very probablyyes'. The values from I to 9 do not lock the value, and are averaged, if they appear inother rules, to give the final value for a choice.

The following rule terminates a hypothetical consultation of EXPMUL withmany choices.RULE NUMBER: 57


and A system utility operation is not requiredand The decoupling design method is INAand The order of the T.F. matrix is squareand Test of system diagonal dominance is not requiredand The activated plot is Time response arrayand Diagonal dominance is not accepted

THEN:Design is not completely successfully-Probability = 10/10

and Repeating the design process and selecting more appropriate compensators is recommended-Probability = 10/10

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and Initializing all compensators is recommended-Probability = 10/10and Lead compensator in the forward path is recommended-Probability =

9/10and The external program to be called is CC/@Mac8-Probability = 9/10and Modification of the feedback gains is recommended-Probability =

8/10and The external program to be called is pg2-Probability = 8/10and Displaying all design information up to this point is recommended

Probability = 7/10and stop

The above consultation tells the user that his design is not accepted, and he is advisedto do one of the following:

(a) repeat the whole design process, and try to select more appropriate compensators-in this case he has to delete all previous compensators;

(b) add a lead compensator in the forward path (in fact more than one leadcompensator may be needed in the same design problem)-in this case, hehas to make an external calling to the CC package, and execute the macro""rnac8";

(e) modify the feedback gain, and the required external program to be called ispg2; or

(eI) display all design information up to this point - this can be done by makinga request for a system utility operation (see second condition in all the aboverules).

6. Interacting with EXPMULEXPM UL guides the user during the design process in an interactive

way. Therefore, each consultation of EXPMUL results in a group of multiplechoice questions that should be answered by the user. At any point through thisdialogue the user can query the system by entering "WHY". The system responds byshowing the user the rule(s) that need to be checked by the answer of the consideredquestion.

As we have mentioned earlier, EXSYS has the facility of generating reports thatcontain the results of different consultations, the following is a part of the generatedreport through the design of Example 1. It should be noted that the number ofconsultations is considerably reduced when the user becomes familiar with theEXPMUL environment, and the INA design technique. This is what we mean bylearning, and gain of experience.

Consultation # IRESULTS OF EXSYS RUNUSER INPUTS

The external calling flag is not activatedThe system model is required to be enteredThe domain of the system model is frequencyThe clements of the T.F. matrix are rationalA system utility operation is not required

CONSULTATION RESULTSThe external program to be called is CC/@Macl: Probability = 10/10

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Consultation # 2RESULTS OF EXSYS RUNUSER INPUTS

The external calling flag is activationThe external program to be called is CC

CONSULTATION RESULTSThe calling is succeeded: Probability = 10/I0


The external calling flag is not activatedA system utility operation is requiredThe required utility operation is displaying the current design information

CONSULTATION RESULTSThe external program to be called is CCj@Macf: Probability = 10/10


The external calling flag is activatedThe external program to be called is CC

CONSULTATION RESULTSThe calling is succeeded: Probability = 10/10

7. ConclusionsIn this paper we have discussed the design and the implementation of an expert

system environment that can assist non-experienced users throughout the design ofMIMO feedback control systems. Around this topic, many issues have been discussed, such as the different possible configurations of expert systems which canbe used in control system design and a design heuristic based on the frequencyresponse of MIMO systems which uses the INA method. Then a comprehensivedesign example has been solved using this design approach. A detailed presentationof the developed expert system has been given with stress on its software structureand knowledge base representation.

It is worth mentioning that some deficiencies have been found when using theabove expert system with high-order MIMO systems, due to the limitation in thecurrent release of the CACE-II package. However, we are trying to overcome thisdifficulty by introducing an external utility that can reduce the order of such largescale systems. We are also planning to support the system with an identification tool.The use of the INA approach in the above design heuristic encourages us to expandthe current rule base of EXPMUL to deal with feedback non-linearities via the circlecriteria method (Rosenbrock 1974).

REFERENCES

ASTROM, K. J., ANTON, J. J., and ARZEN, K. E., Automatica, 22, 277.BROWNSTON, L., FARRELL, R., KANT, E., and MARTIN, N., 1985, Programming Expert Systems

in OPS5 (Addison-Wesley).

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2366 EXPMUL: expert system-multivariate control systems design

EXSYS: Expert System Development Package, 1985 (EXSYS, Inc.).FAUGHT, W. S., 1986, Computer, 17 July.FORSYTH, R., 1984, Expert Systems: Principles and Case Studies (London, U.K. Chapman and

Hall).FORTUNA, L., GALLO, A., and NUNNARI, G., 1989, I.E.E.E. Control System Magazine, 9, 9.JACKSON, P., 1987, Proc. Instn elec. Engrs, Pt D, 134,224.JAMES, J. R., FREDERICK, D. K., and TAYLOR, J. H., 1987, Proc. Instn elec. Engrs, PtD, 134,

137.LAMONT, G. B., 1990, Int. J. appl. Engng. Ed., 6,177.MACFARLANE, A. G. J., 1972, Automatica, 8, 455.MARTIN, A., and LAW, R. K. H., 1988, In! Software Technol., 30, 579.PANG, G. K. H., and MACFARLANE, A. G. J" 1986, A systematic approach to control system

design using a reverse frame alignment design technique. IFAC Symposium on theSimulation ofControl Systems, Vienna, Austria, pp. 227-232; 1987, An Expert SystemApproach to Computer-aided Design of Multivariable Systems (Springer-Verlag).

PORTER, B., JONES, A. H., and McKEOWN, C. 8., 1987, Proc. lnstn elec. Engrs, Pt D, 134,260.ROSENBROCK, H. H., 1969, Proc. Instn elect. Engrs, 116,318; 1974, Computer Aided Control

System Design (Academic Press).SPANG, H. A., 1985, IEE.E. Control System Magazine.SRIPADA, N. R., FISHER, D. G., and MORRIS, A. J., 1987, Proc. Instn elec. Engrs, Pt D, 134,251.TAYLOR, J. H., and FREDERICK, D. K., 1984, Proc. Inst. elect. electron Engrs., 72, 1795.WALTERS, J., and NIELSON, N. R., 1988, Crafting Knowledge-based Systems (Wiley).

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EXPMUL: an expert system for the design of multivariable control systems