A SPECIAL CASE OF A SELF-TUNING AUTOMATIC CONTROL SYSTEM USING THE PRINCIPLE OF PATTERN RECOGNITION

V. M. Razin

(Presented by the scientific seminar of the Department of Mathematical and Computing Instruments and Devices)

In a number of works [1, 2, 3] it has been shown that in none of the presently known search-type extremal systems is it possible to obtain a control law which, under continuous variation—according to arbitrary laws—of disturbing functions causing displacement of the extremal characteristic in the horizontal and vertical directions, would provide control of the system solely as a function of its error. In addition to the system error, under these conditions the control law inevitably contains additional, predominantly nonlinear terms that depend on the form of the disturbing function causing displacement of the extremal characteristic in the vertical direction. This leads to the fact that, for a certain relation among the parameters of the system, the disturbances, and the initial conditions, the search-type extremal system loses the ability to track the extremum and becomes inoperative. The statement set forth above, quoted almost verbatim from the work of V. I. Vasil’ev [2], testifies to the need for further development of new principles for constructing extremal systems for betatrons, since in these installations the disturbances mentioned are strongly expressed.

In the report of A. G. Ivakhnenko [4] at the Second Symposium on extremal problems, three principal possibilities are considered for carrying out extremal control that does not require the use of special trial steps in changing the control actions:

1) differential systems;
2) “passive experiment” systems based on the application of correlation or regression analysis;
3) learning recognition systems.

Differential systems developed by V. I. Vasil’ev [2, 3] are extremely difficult to apply to betatron installations.

In ordinary noncombined systems, multiple-correlation (regression) analysis requires large expenditures of time for averaging and processing data by solving regression equations on digital computers, which is possible only with very slow control of the extremal object. The requirements on speed are reduced if the regression controller is used in a combined system only as a corrector for a fast-acting open-loop control system. This latter circumstance once again confirms the advisability of using

in betatron installations of various combined control and regulation systems. The response speed of the corrector can be increased if regression analysis or other methods are used only for training the recognition system, which afterward can itself serve as the corrector. The system distinguishes situations by simple features, the computation of which takes considerably less time [5, 6, 8].

These ideas, set forth in the report by A. G. Ivakhnenko, can undoubtedly also find application in betatron installations. We shall illustrate this proposition by the example of a specialized control computing device in the system for regulating the radiation-dose power of a betatron.

Under real conditions, the dependence of the optimal injection phases \(t(x)\) on the disturbing action is determined by the equation

\[ t(x)=a\sqrt{\,b+\frac{1}{x}\,}. \tag{1} \]

When the method of magnetizing a permalloy zero magnetic-field sensor by two components [7] is used, and when the injection voltage is not stabilized, the real dependence of the injection phases on the disturbing action has the form

\[ t_0(x)=\frac{c}{x}+d. \tag{2} \]

Depending on the values of the parameters \(c\) and \(d\) in equation (2), set by the corresponding adjustment of the control system by changing the ratio between the constant and alternating components of magnetization of the zero-field sensor, various situations may arise, some of which are shown in Fig. 1.

Let us assume that the betatron installation together with the automatic-control system is under the influence of a disturbing action \(x\) in the form of a randomly varying mains voltage. The action \(x\) varies randomly about some value \(x_0\), which is the mathematical expectation of the random function \(x(t)\), sometimes also going beyond the limits \(x < x_{\min}\) and \(x > x_{\max}\). For a combined betatron control and regulation system having the indicated circuit for double magnetization of the zero-field sensor, the most favorable situation is evidently the mutual arrangement of the characteristics shown in Fig. 1,a. It is natural to expect that, in the presence of such a situation, the mathematical expectation of the betatron radiation output will be maximal. As is seen from Fig. 1,a, a sufficiently informative and at the same time simple feature of the most favorable situation in the sense of setting the corresponding parameters \(c\) and \(d\) is the presence of two maxima in the dependence \(I(x)\) at \(x=x_{\min}\) and \(x=x_{\max}\), i.e., at quite definite values of the magnitude of the disturbing action \(x\). The presence of other possible situations also makes it possible to determine how the parameters \(c\) and \(d\) should be changed in order for the system to arrive at the most optimal situation.

A hypothetical scheme of a combined optimal searchless-type system is presented in Fig. 2. In this scheme the disturbing action \(x\) is fed to an amplitude discriminator \(AD\), the outputs of which control the switching elements \(K_1, K_2 \ldots K_5\). The quality function in the form of the radiation-dose power \(I\), through the switching elements \(K_1 \div K_5\), is fed to the memory devices \(ZU_1 \div ZU_5\), which carry out a stepwise approximation of the curve \(I(x)\). Approximate

Fig. 1. Possible variants of beta-radiation characteristics as a function of the line voltage.

the values of the parameters $c$ and $d$ are computed by the computing device $VU$ and are fed to the recognizing logic device $LU$, which plays the role of a corrector.

The recognizing logic device recognizes situations and, on this basis, generates corrected values of the control parameters $c'$ and $d'$, which act on the controlled object—the betatron. The control circuit can be supplemented by the computing device $VU_2$, using multiple-correlation (regression) analysis, which makes it possible to carry out an even more precise correction, approaching the maximum of the radiation. Obviously, the control system considered can operate only in the presence of random changes in the disturbance $x$.

Fig. 2. Block diagram of the combined extremal control system for betatron radiation

Bearing in mind that the computing device $VU_2$ may turn out to be complex and bulky, it should be recommended that it be replaced by initial training of the recognizing system with the aid of an operator, or by some other method. Initial adjustment of the recognizing system by an operator can, apparently, create the prerequisites also for eliminating from the system the computing device $VU_1$, which is also rather complex in structure.

Let us note that the considerations set forth are of a tentative nature, since the control and regulation system for the betatron under consideration is still only in the development stage and has not been implemented in hardware.

REFERENCES

1. V. M. Kundevich. Investigation of pulsed extremal systems under drift of the extremum. “Avtomatika i telemekhanika,” Vol. XXIII, No. 7, 1962.

2. V. I. Vasil’ev. Searchless differential systems of extremal control. In: “Self-Tuning Automatic Systems.” Proceedings of the 1st All-Union Conference on the Theory and Practice of Self-Tuning Systems (December 10–14, 1963), Nauka, Moscow, 1965.

3. V. I. Vasil’ev. Differential systems of extremal regulation. Publishing House of the Academy of Sciences of the Ukrainian SSR, 1963.

4. A. G. Ivakhnenko. The problem of searchless extremal regulation. Abstracts of papers of the II Symposium on Extremal Problems (Riga, May 25–28, 1965).

5. V. I. Grubov, A. G. Ivakhnenko, B. Yu. Mandrovskii-Sokolov. Industrial Cybernetics. Naukova Dumka Publishing House, Kiev, 1966.

6. A. G. Ivakhnenko. Self-learning systems with positive couplings. Publishing House of the Academy of Sciences of the Ukrainian SSR, 1963.

7. V. M. Razin. Izvestiya TPI, Vol. 87, 1957, 206–215.

8. A. G. Ivakhnenko. The problem of searchless extremal regulation. “Avtomatika i vychislitel’naya tekhnika,” No. 13, Zinatne Publishing House, Riga, 1966.