Copyright © 1F AC Man-Machine S,'stems, Xi'an, PRC, 1989
HUMAN FUZZY CONTROL MODEL AND ITS APPLICATION TO FUZZY CONTROL SYSTEM DESIGN Long Shengzhao* and
*lmtitute of Space Medico-Engineering. p,a, Box 5f()-I. Brijillg. PRC **Department of Engineering Design . Tufts UniveI'sily . MedIaI'd , iHA 02155 . USA
Abstract. This paper proposes a Fuzzy Control Model (FCM) for a human operator in a man-machine-environment systems by means of fuzzy set theroy on the basis of human thinking activities (concepts, judgements, inferences and decisions). The FCM suggested in the paper can be used to simulate the control activity of driver, pilot or operator in aircraft, vehicle, vessel and many industrial processes. The establishment of the model can not only show a new way for the study of man-machineenvironment systems, but also provide a new approach for the design of fuzzy control systems. The emphasis of the paper is on modeling of the FCM and its application to fuzzy control system design. Man-machine-environment Keywords. activity; Fuzzy control.
and judge complicated phenomenon, and thus he has laid the foundation of fuzzy mathematics . Therefore, it is natural to describe human activity by means of fuzzy set theory.
In 1977, R.M. Tong noticed : "Modern control theory has had tremendous success in areas where the system is well defined, missile and space vehicle guidance for example, but it has failed to cope with the practicalities of many industrial processes despite the development of a huge body of mathematical knowledge. There are undoubtedly many reasons for this, but fundamentally it is the lack of detailed structural knowledge of the process which precludes the use of these ideas. Despite this, they are often satisfactorily controlled by a process operator, whose ability to interpret linguistic statements about the process and to reason in a qualitative fashion prompts the question: 'can we make comparable use of this information in automatic controllers?' " This paper will positively answer the question.
THE MODEL STRUCTURE Concept, judgement, inference and decision are the basic links in human thinking. A concept reflects the property of objective appearance. Many concepts in the human mind are generally fuzzy. A fuzzy set must be used to describe these concepts. A judgement is the combination of concept with each other. For example, "large error" is a definite judgement, it means that the error is large. These judgements must be described as the membership function of fuzzy set. This memberShip function is usually called a fuzzy variable. An inference reflects the combination of judgements with each other. It seems that the syllogism used in common inference is no longer effective in the case of concept and judgement being fuzzy, thus, only the method of likelihood inference could be used. It should be noted that the conclusion in likelihood inference can be expressed as a decision. Of course, this decision is also a fuzzy variable.
According to Man-Machine-Environment System Engineering (MMESE) theory [2,3], various artificial (or manual) control processes with human participation are typical man-machine-environment systems. Such a system can describe not only man's control over vehicles, ships, planes, even spaceships and space shuttle, but also man's control over common processes in industrial production (such as chemical industry, iron and steel making, etc.). The most notable feature of a manmachine-environment system is that man actively participates in it, and human action always takes thinking activity as the dominant factor. L. A. Zadeh, the founder of fuzzy sets theory, modified a mathematics absorbing the features that human thinking activity could distinguish
So far a cycle of human thinking activity has basically come to end. Still, in addition to the thinking course above, three other links must be considered, namely, sensation-perception, motion reaction and remnant for human control activity. In
Long Shengzhao and
control model of a human operator into the structural form shown in Figure 1. As will be readily see from this, operator first of all must sense the control error of the system and the changing rate of error and judge the information sensed , then make an inference according to the
inference behavior . Only factor 0( , we could have a on human inference rules.
by adjusting nimble change
It should be pointed out that every inference rule in Table 1 is a likelihood inference. On the basis of fuzzy set theory, the rule in the first column on the first line could be expressed as:
r-- ----- ----- ---- - - - - - -- - - -- - -- - - - - --- - ----- --,
Also the other rules such as C2 , C3, ... , C48 and C49 could be written with the same method. As the inference course is to select most possible one, so Table 1 could be expressed by fuzzy operation as follows : C=C1+C2+ ... +C49 =Eo(EnlxCpl)'Ro(RnlxCpl)+ EO(EnlxCpl)'Ro(RnmxCpl)+ . .. +Eo(EplxCnl)·Ro(RplxCnl)(3)
Fig. 1. Structure of Human Fuzzy Control Model. judgement above so as to decide what kind of control tactics should be taken (also decide the result of inference) , finally, the control quantity required is produced by putting the activity of nervous muscles into effect. Yet, a remnant white noise must be added in final output of control quantity because of the randomness of human activity. That is the complete course of human control activity.
R -3 -2 -1 E
THE MATHEMATICAL DESCRIPTION OF THE MODEL Human fuzzy control model can be derived under a condition of tracking a single degree of compensation on the basis of the above-mentioned analysis and the model structure in Figure 1. Dynamic characteristics of the display and control are assumed to be neglected in derivation. If they could be neglected, we may incorporate them in the controlled obje c t to consider, thus derivation does not lose its general characteristics. We assume that there are three universes of discourse to be studied: E--the error of the controlled object deviating from the target value as sensed by the human operator; R--the error changing rate sensed by human operator; C--the output of control quantity that the human operator produces on the controlled object. Based on the human physiological characteristics, human judgement and decision an object reasonably follows a normal distribution. Experimental results have confirmed this . So E, Rand Care all normal fuzzy variables. In order to describe the inference activity in human control behavior , we introduce an expression with weighting factor . C=-(c(E+(l-o/. )R
In the formula (1), 0( represents weighting factor, it may change between 0-1; sign (N) is a smallest integer which has the same sign as N, but its absolute value is INI+0.5; meanwhile, we suppose that pI, pm, ps, ze, ns, nm and nl in E, R and C universe of discourse can be separately expressed by 3, 2 , 1, 0, -1, -2, -3. Therefore, the 49 rules listed in Table 1 could roughly summarize human
Human Inference Rules (<< - 0.3)
1 2 3
3 3 2 2 1 1 1
2 2 2 1 1 0 0
2 1 1 1 0 0 -1
0 0 -1 -1 -2 -2 -2
-1 -1 -1 -2 -2 -3 -3
0 -1 -1
-1 -1 -1 -2
In the formula (2 ) and (3) , +, • , x and 0 express separately union, intersection, Cartesian product and combination operations. In fact, formula (3) has summarized the basic course of human thinking ( c oncepts, judgements, inferences and decisions) . These are the full view of fuzzy control model by human operator adding sensory delay e -~5 neuro-muscular lag 1 / (TnS+1) and remnat of human accidental activation r (n) (see Figure 1). Generally speaking, these are the seven basic variables of the model such as the three fuzzy variables (E(x), R(x) and C(x)) , inference rule, sensation-perception delay ~ neuro-muscular lag time constant Tn and accidental activation remnant r(n ) etc . This kind of fuzzy control model could portray the control behaviors of human operators. EXAMPLE FOR THE MODEL We give an example to observe the efficiency of the FCM. The example comes from some of the experimental data (the controlled obje c t is second-order integrator dynamic l/S~) [7,8] . The input (error) and output (control quantity) of the human operator were recorded on magnetic recorder in an experiment. The changing rate of error c ould be evaluated by first order derivate of error . What should be done now is to approach human output with the FCM. The FCM is realized in Personal Computer. The duration of experimental data sample is 100 seconds; the duration of sample is 0.1 second; the sampling rate is 10.
Human Fuzzy Control Model
We divide E, Rand C into 15 degrees in the range of 0-2 standard deviation. And we assume that the evaluating range of fuzzy variables E and R has 31 elements:
$ yscem Output
(E) = ( R) = ( -15, -14 , ... -1, 0,1 ... ,14,15) ; the evaluating range C has 41 elements: ,
(C)=(-20,-19, ... ,-1,0,1, ... ,19,20). The match between the model output and the human actual output indicated by one experimental data is shown in Figure 2. Out-put
(Sec o nd)
Fig. 3. Effect of Cs Value on System Perfonnance.
- - Human Outpu't
______ Model OutpU t
·1' System Output
Fig. 2. Comparison Between the Model Output and the Hunan Output. THE MODEL APPLICATION TO FUZZY CONTROL SYSTEM DESIGN Since the birth of the fuzzy control system in 1974 , people has been great ly interested in the design of fuzzy control systems, and have done considerable work (see [1,10,11,12,13]). Nevertheless, most of the works were done experimentally . Indeed, the designer's qualitative "feel" for system is directly used to construct the fuzzy controller. However, the final system design is usually obtained by the iterative process of trying the fuzzy controller, observing the result and the modifying the fuzzy controller accordingly. This is obviously not only time consuming, but also maybe not best system performance. The establishment of the FCM will provide a systematic design procedure for fuzzy control system design. It can be used not only flexibly to change parameters of fuzzy controller (including choose of fuzzy variables and adjustment of control rules), but also to adjust these parameters according to indices of system performances. Of course, applying the FCM to fuzzy control system design, we will neglect the human sensory delay, neuro-muscu1ar lag and remnant noise. In order to demonstrate the effectiveness of this application, we cite an example of a multi-order fuzzy control system with controlled object to be 1 / S 2 (0 .1S +1). This system is realized by Compiler Basic in IBM-PC-AT Personal Computer. Figure 3 and 4 give the closed-loop step response curves of the system. Figure 3 illustrates the effect of the fuzzy variable C (only Cs to be changing and
l Se co nd)
Fig. 4. Effect of 0( Value on System Perfonnance. Result at hand reveal shown that applying the FCM not only provide a new method for the fuzzy control system design, but also create advantagrous condition for building self-adapting fuzzy control systems. CONCLUSIONS This paper has established the human fuzzy control model for human operator by means of fuzzy set theory on the basis of some characteristics of human thinking. And the model effectiveness has been observed directly from human input/output data. The establishment of the model can not only show the broad prospects for researches of man-machine-environment systems, but also provide a systematic design procedure for the design of fuzzy control systems and lay the foundation for researches of fuzzy control theory.
Long Shengzhao and
Meantime, it would also help give insifht into the behaviour and basic structure of difficult control processes. REFERENCES Tong, R.M. (1977). A control engineering review of fuzzy systems. Automatica, Vol. 13. Chen Hsin and Long Shengzhao (1981). A summary introduction to man-machineenvironment system engineering. Collections of Theses, Institute of space Medico-Engineering, Vol. 3. Also see Nature Journal, Vol. 4. (In Chinese). Chen Hsin and Long Shengzhao (1984). Application of man-machine-environment system engineering theory to aerospace research. Abstracts of Papers, The 32nd International Congress of Aviation and Space Medicine. Zadeh, L.A. (1965). Fuzzy sets. Information and Control, Vol. 8. Long Shengzhao, He Kaiyuan, Zhao Xu and Zhou Yunlong (1981). The determination of human fuzzy concepts in man-machine systems. Fuzzy Mathematics, Vol. 1. (In Chinese). Long Shengzhao and Wang Peizhuang (1982). On self-regulation of fuzzy control rules. Fuzzy Mathematics, Vol. 2. No. 3. (In Chinese). Long Shengzhao, Giang Qiyuan, He Kaiyuan and Zhao Xu (1982). Human fuzzy control model in man-machine systems. Journal of Chinese Society of Astronautics, Vol. 2. (In Chinese).
Long Shengzhao and Chen Hsin (1985). Research on human fuzzy control model in man-machine-environment systems. Abstracts of Paper, The 33rd InternatiOn= 81 Congress of Aviation and Space Med cine . Mandani, E.H. (1974). Application of fuzzy algorithms for control of simple dynamic plant. Proc . lEE. Gaines, B.R. and Kohout, L.J. (1977). The fuzzy decade: a bibliography of fuzzy systems and closely related topics. Intrnational Journal of Man-Machine Studies, Vol. 9. Larsen, R.M. (1980). Industrical application to fuzzy logic control. International Journal of Man-Machine Studies, Vol. 2. Tong~.M. (1984). A retrospective view of fuzzy control systems . Fuzzy Sets and Systems, Vol. 14, No. 3, 1984. Maiers, J. and Sherif, Y.S. (1985). Application of fuzzy set theory . IEEE Trans. on Systems, Man and Cysernetics Vol. SMC-15.