SU1399700A1 - Adaptive control system - Google Patents

Abstract

The invention relates to automation and can be used in the management of non-stationary technological objects. The aim of the invention is to improve the accuracy and stability of the system under the conditions of interference of considerable intensity and changes in the parameters of the control object. The system contains adders 2,9,18,20, controllers 3,11,19, amplifier 4, control object 5, dividers 8.16, filters 7.15, prediction block 10, multiplier 17, limitation block 12, setpoint I input the signal, the shaper 13 of the signal levels of the limit, the shaper 14 of a single signal and the model 6 of the object. Self-tuning in the system is implemented. is by minimizing the predicted relative error of the gain of the control channel from the standard generated at the output of the prediction block 10. The system realizes the compensation of uncontrolled interference at the input of the object 5. 4 Il. O) with

Description

one

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with so

The invention relates to automation and can be used in the management of non-stationary objects under the conditions of uncontrolled disturbances in the chemical, petrochemical and metallurgical industries.

The aim of the invention is to improve the accuracy and stability of the system under the conditions of interference of considerable intensity and changes in the parameters of control objects.

Figure 1 shows the structural scheme of the proposed adaptive control system; Fig. 2 is a variable gain amplifier circuit; FIG. 3 is a diagram of the prediction block; figure 4 - scheme of filters.

The adaptive control system contains an input signal adjuster 1, the first adder 2, the first regulator 3, the amplifier 4, the control object 5, the object model 6, the first filter 7, the first divider 8, the second adder 9, the prediction block 10, the second regulator II , block 12 limiting, shaper 13 signals of limiting level, shaper 14 single signal, second filter 15, second divider 16, multiplier 17, third adder 18, third regulator 19 and fourth adder 20. Amplifier 4 (with variable gain) contains adder 2 and multiplier 22.

The prediction unit 10 includes series-connected differentiators 23 and 24, an amplifier 25, an adder 26, and an amplifier 27.

The first 7 and second 15 filters, which perform averaging of the signal over a sliding time interval T, include a delay unit 28, an adder 29, an integrator 30, and an amplifier 31.

The dividers 8 and 16 retain the performance at a divider signal value of zero, since they contain output limiting circuits.

The output of amplifier 4 (FIG. 2 is modified by the equation

Z (t) U (t) (l + uK (t)) U (t) -Kjt), where Z (t) is the output signal of amplifier 4; variable coefficient

gain;

output signal of block 12 limiting.

O

five

0 5 0 5

0

five

The signal at the output of the filters 7 and 15 is changed as follows:

x, j (t) | j (x, (9) -x, (e-T)) dO. -t

4 J, (6) 0,

t-t

where X, (9); X2 (t) is the input and output signal of the filter, which averages the signal in the interval T, respectively.

Adaptive control system works as follows.

A signal X is fed to the input of the first adder 2, one for the control system, to the other input of which a signal y (t) is supplied from the output of the control object 5. The output of the first adder 2 through the first controller 3 and the amplifier 4 with a variable gain factor is fed to the first input of the adder 20.

The output of the first controller 3 U (t) is also fed to the input of model 6 of the object, the output of which y (t) is fed to the input of the second filter 15 and the input of the second divider 16. The output signal y (t) of the object 5 of the control is also fed to the input the first filter 7 and the input of the second divider 16.

The output of the second divider 16, equal to the ratio of the signal y (t) of the output of the control object 5 to the signal y (t) of the output of the model 6 of the object, is fed to the input of the multiplier 17, to another input of which the signal comes from the output of the amplifier 4.

The signal from the output of multiplier 17 is fed to the input of adder 18, to another input of which a signal comes from the output of amplifier 4. To the input of the third regulator 19 comes from the signal from the output of adder 18. The output signal of the adder 20 is fed to the input of object 5 of the control, to the input of which there is an uncontrolled parametric disturbance fgCt) and a random interference f (t).

The first 7 and second 15 filters are designed to separate, the parametric perturbation fg (t), which is usually low-frequency, and the random high-frequency interference f (t), which is often an ergodic process with zero mean.

The output of the first divider, equal to the ratio of the smoothed signal y (t) to the smoothed signal y, (t) and being a measure of the change in the gain of the control object 5 at the current time, is fed to the input of the adder 9, to another input of which a signal is output a 1 A single signal generator equal in magnitude to such a signal at the output of the first 8 divider, which is formed when the signals y (t) and y (t) are equal at the inputs of the first divider 8.

The output signal of the adder 9, which is a relative error in the change of the gain of the control object 5, is fed to the input of prediction unit 10, which predicts a change in the relative gain of the gain for some time (p forward, which is determined taking into account the characteristics of the dynamic characteristics of the control object 5. the output of prediction block 10 is fed to the input of the second controller J1. The signal Ug (t) from the code of the second controller 11 is fed to the information input of the block 12 of limitation 12, to the first and second inputs Then, the limiting signal Ug and U are used to limit the output value of the block 12, respectively, the upper and lower bounds from the limiter level generator 13. The output signal of the limiting unit 12 & Kg (t) is fed to the control input of the first amplifier 4,

Consistently connected second divider 6, multiplier 17,. the sum of the torus 18, the third controller 19 and the adder 20 together with the connections connecting them provide compensation for the random noise f (t) acting at the input of the control object 5, thus making the control system invariant with respect to the noise f (t). We introduce the notation Wp (p), W (p). - transfer functions according to the object 5 pack

relations and model 6 of the object / Let Wo (p) K (p) / Re (p),

where K (p) is a variable coefficient

gain control object 5; ) nth order polynomial from P.

Wjp) VRo (p),

where K is the gain factor of the model 6 of the object — the reference value of the coefficient (}) of the gain of the gain of the object 5 of the control.

The expression for the image of the output signal of the control object 5 is written in the following form:

y (p) k (p) .K (p). and (p) + + K (p) -F (p) / R (p)

(one)

ten

0

0

with F (p) F (p) + U |. (p) - error compensation interference f (t),

where K (p); U (p); F (p); U (p) is the operator image in accordance with the variable gain of the amplifier 4, the output signal of the first regulator 3, the uncontrolled disturbance f (t), output of the third controller 19.

The expression for the output signal of object model 6 is

y (p) (p) / R, (p) (2).

For the signal at the output of the first filter 25, you can write the expression

y (p) K (p) and (p) W (p) W (p) + K (p) x

“F (p) W (p) / R (p)“ y, (p) + y2 (p), where W (p) is the transfer function of the first 7 and second 15 filter0

five

ditch

The expression Wo (p) K (p) / R (p) describes an inertial link of the nth order, which can be considered a filter. Therefore, at the output of the control object 5, we obtain the smoothed value of the interference f (t), then we can write

yJp) W (p) - F (P). (A) Consider the case when changes in the gain of the object 5 of the control are much lower -f frequency compared with the random noise f (t),

those. T |

to

Where

Tg and T are the times of the decline of the autocore. of random interference and parametric perturbation functions f (tj. Let the averaging interval of the first 7 second 15 filters be in the interval

Tj.: T Т T, (5) where T is the sliding interval of the averaging of the first 7 and second 15 filters.

0

55

Then for component y, (p) on the output of the first filter 7, you can write

1 f j y (t) - J f (0) de 0

(6)

i-t

since the integral of a random sporadic process with zero expectation on an interval satisfying condition (5), can be equated to zero.

Thus, for the signal at the output of the first filter 7, you can write the expression

y (p) y, (p)) U (p) W (p) W (p). (7)

The image of the output signal of the second filter 15 is

y (p) (p) W (p) / R (p). (eight)

 Then the image of the output signal of the first divider 8 is written in the form

Е | (Р) У (Р) / У „(Р) К, (р) К (р) / К„. (9)

For the signal at the output of the adder 9, write the expression D (p) l-E (p) l-K (p) K (p) / K. (ten)

Paragraph in the time domain, expressed in 10, can be written in this form:

; d (t) l-Kc (t) K (t) / K. (I) If conditions are fulfilled (5) the self-amplification of the gain coefficient K (t) of the amplifier 4 is necessary, it is necessary to fulfill the OE conditions for minimizing the functional n | of the parametric error (P). I | -,

: Therefore, the gain K (t) should be changed in such a way that the product K ,, (с) to “K (t) remains constant and equal to K, and Kt (t) –K (t) / K, to one At the output of prediction block 10, a signal is generated that equals the predicted value of the parametric error, which will be in the system in time (f, In case the predicted value of the parametric error is calculated, for example, by decomposing pf in the Taylor series, limited to three first terms, the expression for the output signal of the prediction block 10: looks like

d (t + 4) d (t) + d (t) cf + d (t) -t / V .. (12)

M | ing the prediction value of the parametric error (12) is carried out using the second controller II, which may be, for example, standard output of the HibiH pi controller, the output of which is calculated by the formula

and, (t) K, d (t + (f) + K, j d (9) d9, (13)

about

where K and K are the PI controller settings. The use of prediction block 10 will reduce the self-tuning error and thereby increase the accuracy of the adaptive control system. From the expression (11) it can be seen that with the equality of the values of K (t), the value of K (t) l. Deviations of the K (t) value from one will occur when K (t) itK. Then the algorithms for changing the coefficient Kj, (t) can be written as

K, (t) 1+ LCD1),

(54)

where & K. (t) is the self-tuning signal obtained by minimizing the functional (11).

Let us consider the compensation of the interference f (t) on the sliding time interval Tj satisfying the condition T T, (15). l signal at the output of the second divider 16 you can write the expression

0 (p) DDR) -K () / K. +

K (p) / VF (p) / U (p).

Then for the signal at the output of the jammers, 17 can be written in the time domain

n (t) Kc (t) U (t) K, (t) K (t) + K (t) K (t) / K „f (t). (16) subject to conditions (5) and (15), the gain of the object 5 of the control K (t) can be considered quasistationary over the time interval T. Then the quantity Kj, (t). K (t) is close to K on the interval Tj

K, (t) K (t) / K, 1. .. (17) In this case, for the signal at the output of the adder 18, you can write the expression

45

C (t) "K (t) -U (t), (t) U (t) + f (t)

- f (t).

(18)

On the output of the adder 18, we get a signal that is 1 the estimate of the compensation error f (t) with the opposite signs. AT

the first time, when U (t) 0, the signal at the output of the adder 18 is equal to the estimate of the random noise f (t). The signal from the code of the adder 18 to compensate for the random interference f (t) is given

through the third regulator 19 to the input of the adder 20, from the output of which the signal goes to the input of the object 5 of the control. This compensates for unmonitored interference.

f (t) and, thereby, increases the control accuracy in the proposed control system,

Consider the case when T T is comparable with T, and also assume that the random interference f (t) may change abruptly in the direction of decreasing or increasing. In this case, expression (6) will have a value, 1. independent of zero, depending on the magnitude of the disturbance f (t), and becomes- it is impossible to separate the response of the adaptive control system to random interference and parametric disturbance fgCt).

In this case, the control system will seek to compensate for the external disturbance along with the feedback loop, by changing the self-tuning coefficient). Then the output of the second regulator

11 U (t) in the case of a significant magnitude of the random disturbance f (t) can have such a value that the self-tuning signal & Kt «(t) will be uK (t) U (t) -I. In this case, the self-tuning coefficient Kg (t) may become zero or negative, and the control system may lose its stability and operability. Therefore, a restriction block 12 is inserted into the control system for these purposes.

Its purpose is to limit the output of regulator 1I to the values of the lower and upper permissible limits.

Limit 12 converts

Claims (1)

conditions under the conditions of the selected control quality criterion. Invention Formula g 0 Adaptive control system, which controls the input signal, the output of which is connected to the summing input of the first adder, connected by the output to the input of the first regulator, the control object, the output of which is connected to the reading input of the first adder, amplifier, object model, and the second controller , the first divider, the second, third and fourth adders, -o t - are characterized by the fact that, in order to increase the accuracy and stability of the system under conditions of action of considerable intensity and change the parameters of the object e audio, it entered the first and second filters, prediction unit, a limit, a level signal generator 5, the shaper of the single signal, the second divider, the multiplier, the third regulator, with the output of the control object connected to the input of the divisible second divider and 0 through the first filter - with the input of the divisible first divider, the input of the divider is connected to the output of the second filter, the input of which is connected to the input of the divider of the second divider and 5 output model of the object connected by the input to the output of the first controller and to the information input of the amplifier, the output of which is connected to the summing input of the third adder, with the first the output signal Ug (t) of the second regulator - 40 by the input of the multiplier and with the first input of torus 11 as follows:  u (t), npH04,) OB; uK (t); CC, with Uc (t). .and"; and, npHUjt) and „, where CC and Ug are respectively the values of the lower and upper bounds, and Pts 1. The introduction of restriction block 12 provides the adaptive control system with the necessary stability margin for self-tuning. The values of the settings K, and Kg of the second regulator 11, the values of the signals of the lower Uj, and the upper U bounds uKe (t), & the value of the prediction interval f must also be determined when examining and testing the Lree control system operating uncontrolled fourth-adder connected by the output to the input of the control object, and the second input to the output of the third . controller, the input of which is connected to 45 by the output of the third adder, the subtractive input of which is connected to the output of the multiplier connected by the second input to the output of the second divider, the output of the first divider is connected to the subtracted 50 input of the second adder connected to the output of the single signal conditioner by the input the prediction and the second regulator of the torus are connected to the information input of the limiting unit; the first and second inputs of the setting of the limiting level of which are connected respectively to the first and second outputs of the generator ate signavhodom multiplier and to the first input the fourth adder connected by the output to the input of the control object, and the second input to the output of the third controller, the input of which is connected to the output of the third adder, the subtracting input of which is connected to the output of the multiplier connected by the second input to the output of the second divider; - to the information input of the limiting unit, the first and second inputs of the setting of the limiting level of which are connected respectively to the first and second outputs of the imaging unit signal / {t) AKO / b) Thebes. 2 ditl  27 2i one  l dit