RU2541848C1 - Adaptive control system - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: system comprises five setting devices, six adders, two controllers, a control object, two dime delay units with fixed and adjustable delay, a prediction unit with an adjustable prediction interval, a correcting filter with an adjustable prediction interval, two limiting level signal formers, three averaging units on a sliding time interval, three multiplier units and a divider unit.

EFFECT: high accuracy and stability of the system.

2 cl, 9 dwg

Description

The invention relates to automatic control systems. The system is designed to control non-stationary objects with delay, operating in conditions of a high level of uncontrolled disturbances. The system can find application in the chemical, petrochemical, metallurgical and other industries.

A number of adaptive systems are known that solve the problem of high-quality regulation of non-stationary objects operating under conditions of a high level of uncontrolled disturbances, for example, systems using reference models [1] - Solodovnikov VV, Shramko LS Calculation and design of self-tuning systems with reference models. M: Engineering, 1972, p. 35-37 and [2] - Gromyko V.D., Sankovsky E.A. Self-tuning systems with a model. M .: ENERGY, 1974, p.17-22, as well as systems with an inverse reference model [3] - USSR Author's Certificate No. 591821, class. G05B 17/02, 1977, [4] - USSR Copyright Certificate No. 824142, cl. G05B 17/02, 1979 and [5] - USSR Copyright Certificate No. 1113781, cl. G05B 17/02, 1982.

The systems described in [1] have higher accuracy and adaptability to changes in the parameters of an object compared to conventional single-loop control systems, and have a fairly simple structure. However, these advantages are manifested when the transmission coefficient of the signal self-tuning loop is large, and its increase is limited by the stability condition, and this restriction is especially pronounced for objects with delay. Systems similar to those described in [2] were synthesized on the basis of the second Lyapunov method according to the stability condition, when a definite positive, usually quite simple, quadratic function of phase coordinates is taken, and such conditions are imposed on the self-tuning loop that the derivative of the Lyapunov function is negative sign-constant. As a result, the stability of the self-tuning circuits is ensured, but the quality of the self-tuning can be low, since the choice of the Lyapunov function is usually based on the intuition of the designer, and this function represents an arbitrary quadratic form. Therefore, a system based on the selected Lyapunov function is not necessarily the best. A system with an inverse reference model [3] has double invariance up to ε, has a much higher accuracy compared to conventional control systems, but loses stability if the model does not coincide in structure with the object. Systems [4 and 5] are devoid of this drawback, their stability due to the inclusion of a corrective filter in the signal self-tuning circuit and the selection of its structure in accordance with certain conditions can be ensured even if the structure of the model and the object are different.

As is known, the expression for the Laplace image of the output signal of the system object [5], through the parameters of the systems and input actions, has the form:

where Y (p) is the Laplace image of the output signal of the object Y (t);

X (p) - Laplace image of the input action (reference signal) X (t);

G (p) - Laplace image of an uncontrolled disturbance g (t);

W _o (p) is the transfer function of the object, the regulator;

W _p (p) is the transfer function of the regulator;

W _F (p) is the transfer function of the correction filter,

W _m ^-1 (p) is the transfer function of the ideal inverse (inverse) model of the object;

e ^-pΔ is the transfer function of the delay unit.

If the model of the control object is described by the transfer function W _m (p) equal to

then the transfer function of the ideal inverse model of the object has the form

However, such a transfer function is not physically feasible. As was shown in [5], the transfer function of a real physically realizable inverse model can be represented in the following form:

Where W _mr ^-1 (p) is the transfer function of a real physically realizable inverse model of an object;

W _m ^-1 (p) is the transfer function of the ideal inverse model of the object;

e ^-pΔ is the transfer function of the time delay block;

Δ is a sufficiently small delay determined by the conditions of physical realizability of the inverse model of the object.

For the convenience of analyzing the limiting properties of the system, we assume that the model is adequate to the object W _m (p) = W _o (p), then W _o (p) W _m ^-1 (p) = 1, in addition, in this case we can put for simplicity W _F (p) = 1. Since as Δ → 0, e ^-pΔ → 1 and (1-e ^-pΔ ) → 0, choosing the value of the delay interval Δ is sufficiently small, we can ensure that the condition

Then, taking into account the accepted conditions, after multiplying the numerator and denominator by W _m (p) and reducing it by W _o (p), expression (1) takes the form:

As can be seen from expression (6), the transfer function of the system along the control channel is close to the reference one, and with a limited external disturbance G (p), one can choose a value Δ such that the condition is satisfied:

При этом минимальное значение запаздывания будет ограничено величиной t_O, которая определяется только свойством объекта. Очевидно, в этом случае цепи сигнальной самонастройки будут иметь эффективность, если выполняется условие:where ε is any small, predetermined number. Those. the system has invariance up to ε to external perturbations. However, for objects with a transport delay, the time delay block will include the value of the transport delay of the object -τ _O , and its transfer function will have the form $$e^{-p(\Delta +{\tau }_o)}.$$

In this case, the minimum delay value will be limited by the value of t _O , which is determined only by the property of the object. Obviously, in this case, the signal self-tuning circuits will be effective if the condition is satisfied:

As a result of substitution p = jω and transformation, expression (8) takes the form:

It follows from (9) that

The restriction on the delay time, under which the compensation circuits of uncontrolled disturbances (signal self-tuning circuits) are effective, will take the form for frequencies in the object passband

where ω _с is the cutoff frequency of the object.

Thus, the accuracy of systems [4, 5] in the presence of transport lag in the control object is obviously significantly reduced.

Closest to the proposed system, selected as a prototype, is a system for automatic control of objects with delay [6] - USSR Author's Certificate No. 591821, cl. G05B 17/02, 13/04, 1986, comprising a first adder, a regulator, a second adder, a control object, an inverse model of the control object, a third adder, a prediction unit with a tunable forecast interval and a correction block, the output of the correction block is inverted to the second the input of the second adder, the first input of the first adder is connected to the output of the input signal generator unit, its second input is inverted to the output of the control object, the second input of the third adder is inverted with a time delay unit with tunable delay, the input of which is connected to the output of the second adder, the output of the third adder is connected to the first and second input of the first multiplication unit, the output of which is connected to the input of the integration unit on a moving time interval, the output of the first adder is connected to the first and second input the second unit of multiplication, the output of which is connected to the input of the second integration unit on a moving time interval, the output of the second integration unit on a moving time interval is connected with the first input of the division unit, and the output of the first integration unit on a moving time interval is connected to the second input of the division unit, the output of the division unit is connected to the input of the self-adjustment unit, and the output of the self-adjustment unit is connected to the control input of the prediction unit and the control input of the time delay unit with tunable delay . An uncontrolled disturbance acts on the control object; the transfer function of the channel of this action is generally unknown. A signal is received at the input of the self-tuning unit, numerically equal to the ratio of the integral-quadratic estimate of the mismatch signal between the reference (input signal) and the output signal of the object and the integral-quadratic estimate of the uncontrolled disturbance. The self-tuning unit forms the value of the forecast interval, which minimizes its input signal. Thus, by organizing a forecast for evaluating an uncontrolled disturbance in a system, optimizing a forecast interval for a forecasting unit, a higher compensation efficiency for uncontrolled disturbances and a higher accuracy of stabilization of the output signal of an object of regulation are achieved.

However, the known system has several disadvantages.

1. The integrally quadratic estimate of the mismatch signal between the object output signal and the task depends on the task signal, which is changed by operating personnel in industrial facilities control systems, or in tracking systems - by an external signal to this system. Therefore, the proposed system will function normally with a constant value of the reference signal, i.e. in stabilization mode, fixed in time values of the output signal of the object. When the reference signal changes, the input signal of the self-tuning unit will be determined by the nature of the changing of the reference signal and to a lesser extent by external disturbances, the self-tuning unit under these conditions will generate false values of the forecast interval, as a result, the system may lose stability.

2. The delay interval correction implemented in the system in the time delay block by the value of the forecast interval will disrupt the synchronization of the output signal of the delay block and the inverse model. Indeed, the time delay block is designed to exclude the control action from the output signal of the inverse model, which represents an estimate of the sum of two signals: the control action generated at the output of the second adder, and the evaluation of uncontrolled disturbance brought to the input of the control channel. In order to exclude the influence of the control action on the estimation of an uncontrolled disturbance, to synchronize it with the output signal of the inverse model of the object, the time interval of the delay block of the delay unit is chosen equal to the sum of the time delay of the control object and the delay in the inverse model due to its physical feasibility. In other words, the time delay interval does not depend on the forecast interval. Therefore, adjusting the delay interval in proportion to the forecast interval leads to a violation of the synchronization of the control signals and the output signal of the inverse model, which can lead to a deterioration in the accuracy of regulation and with an increase in the forecast interval to a violation of the system stability.

3. The forecasting algorithm used in the system is described by a simple expression close to the linearized Taylor formula, which limits the accuracy of the forecast and the effectiveness of using the forecast block.

The technical result from the use of the invention is to increase the accuracy of regulation and stability of the system.

This result is achieved by the fact that in an adaptive control system containing a first input signal generator, the output of which is connected to the summing input of the first adder connected to the input of the first controller, the output of the first controller is connected to the summing input of the second adder, the control object, the input of which is connected to the output of the second adder, and the output of the control object is connected to the input of a physically feasible inverse model of the object and to the subtracting input of the first adder, the first block Arms connected to the output of the second adder, and the output of the first time delay unit connected to the subtracting input of the third adder, the summing input of which is connected to the output of a physically feasible inverse model of the object, a prediction unit with a tunable forecast interval, the input of which is connected to the output of the third adder, is introduced correction filter with a tunable time constant, the first and second restriction blocks and the first and second signal generator of the restriction levels, the first, second and third th averaging blocks on a moving time interval, the first, second and third multiplication blocks, the fourth, fifth and sixth adders, the second time delay block with tunable delay, the division block, the second, third, fourth and fifth signal adjusters, the second controller, the first input the correction filter is connected to the output of the predictive block, the output of the correction filter is connected to the input of the first limiting block, the output of which is connected to the subtracting input of the second adder, the second and third inputs of the first block are the boundaries are connected to the outputs of the first driver of the signals of the restriction levels, the input of the first averaging unit on a moving time interval is connected to the output of the third adder, and the output of the first averaging unit on a moving time interval is connected to the subtracting input of the fourth adder, the summing input of which is connected to the output of the third adder, input the second block of time delay with tunable delay is connected to the output of the fourth adder, the first and second inputs of the first block of multiplication are connected the output of the fourth adder, the first input of the second multiplication unit is connected to the output of the fourth adder, and the second input of the second multiplication unit is connected to the output of the second time delay unit with tunable delay, the output of the first multiplication unit is connected to the input of the second averaging unit on a moving time interval, the output of which is connected to the first input of the division unit as a divider, the output of the second multiplication unit is connected to the input of the third averaging unit on a moving time interval, the output of which is sub is connected to the second input of the division unit as a dividend, the output of the division unit is connected to the summing input of the fifth adder, the subtracting input of the fifth adder is connected to the output of the second master, the output of the fifth adder is connected to the first information input of the second controller, the second parametric input of the second controller is connected to the third master , the output of the second regulator is connected to the first input of the second limiting block, the second and third inputs of the second limiting block are connected to the outputs of the second signal shaper in the levels of limitation, the output of the second limiting block is connected to the first input of the third block of multiplication, to the second parametric input of the second block of time delay with tunable delay and to the second parametric input of the forecast block, the second input of the third block of multiplication is connected to the output of the fourth setter, the output of the third block of multiplication connected to the first input of the sixth adder, the second input of which is connected to the output of the fifth setter, the output of the sixth adder is connected to the second parametric input to corrective filter.

In an adaptive control system, a prediction unit with a tunable forecast interval contains a series-connected smoothing filter, a first and second differentiator, a first amplifier, a fourth multiplication unit, a seventh adder, and a second amplifier, the input of which is connected to the output of the first differentiator, and a fifth multiplication unit, the first the input of which is connected to the output of the second amplifier, and the output to the second input of the seventh adder, the output of the smoothing filter is connected to the third input of the seventh adder, the input from lazhivayuschego filter connected to the output of the third adder and the second inputs of the fourth and fifth multiplication units connected to the output of the second regulator.

The invention is illustrated by the following drawings:

figure 1 presents the structural diagram of the proposed adaptive control system.

figure 2 is a structural diagram of a forecasting unit with a tunable forecast interval.

figure 3 is a structural diagram of averaging blocks on a moving time interval.

figure 4 is a structural diagram of an implementation of a block of time delay with tunable delay.

figure 5 is a structural diagram of the implementation of a correction filter with a tunable time constant.

6 is a diagram of the implementation of the inverse model of the control object.

Fig.7 is an illustration of the quality of transients of the optimal PID controller.

on Fig - illustration of the dependence of the accuracy of regulation of the proposed adaptive system on the ratio of the time constant of the correction filter and the forecast interval.

figure 9 is an illustration of the dependence of the accuracy of regulation of the proposed adaptive system from the value of the transport delay of the object.

The adaptive system (Fig. 1) contains an input signal adjuster - 1, a first adder - 2, a first regulator - 3, a second adder - 4, a control object with a delay - 5, a physically implemented inverse dynamic model of the object - 6, a time delay block - 7 , the third adder is 8, the forecasting unit with a tunable forecast interval is 9, the correction filter with a tunable time constant is 10, the first limiting block is 11, the first signal generator of the limiting levels is 12, the first averaging block on a moving time interval is 13, the fourth adder is 14, the first multiplication block is 15, the second averaging block on a moving time interval is 16, the second time delay block with a tunable delay interval is 17, the second multiplication block is 18, the third averaging block on a sliding time interval is 19, the division block - 20, the fifth adder - 21, the value adjuster of the autocorrelation function for evaluating the uncontrolled disturbance - 22, the second regulator - 24, the initial value integrator of the integral part of the second regulator - 23, the second limiting block - 26, the second signal conditioning the limits are 25, the third multiplication block is 28, the proportionality coefficient adjuster between the correction filter time constant T _F and the forecast interval Tpro is 27, the sixth adder is 29, and the minimum permissible correction filter time constant value generator is 30.

In figure 1, the following notation:

X is the reference signal;

Y is the output signal of the object;

g is an uncontrolled disturbance;

ε is the error signal between job X and the output signal of object Y;

U _p is the output signal of the first controller 3;

U is the total control action;

- оценка полного управляющего воздействия; $$\widehat{U}$$

- assessment of the full control effect;

- сигнал оценки неконтролируемого возмущения; $$\widehat{g}$$

- signal evaluation of uncontrolled disturbance;

- оценка центрированного сигнала $$\widehat{g}$$

; $${\widehat{g}}_c$$

- centered signal estimation $$\widehat{g}$$

;

T _F - time constant of the correction filter;

ΔU is the final value of the self-tuning signal;

ΔU _H - signal limiting the maximum value of the output signal of the block 11 - signal self-tuning;

ΔU _L is the signal for limiting the minimum value of the output signal of block 11 - the self-tuning signal;

, при временном сдвиге между значениями сигнала $$\widehat{g}$$

, равном τ;R (τ) is a moving estimate of the autocorrelation function of the signal $$\widehat{g}$$

, with a time shift between signal values $$\widehat{g}$$

equal to τ;

при τ=0;R (0) - moving estimate of the autocorrelation function of the signal $$\widehat{g}$$

at τ = 0;

Z _R - set value of the signal ratio R (τ) / R (0);

U _T is the output signal of the controller 24;

U _TH - signal limiting the maximum value of the signal U _T ;

U _TL - signal limiting the minimum value of the signal U _T ;

на входе блока 18, соответствующая заданному отношению сигналов R(τ)/R(0);τ is the value of the time shift between the signal values $$\widehat{g}$$

at the input of block 18, corresponding to a given signal ratio R (τ) / R (0);

Tpro is the forecast interval in the self-tuning signal generation circuit corresponding to a given value of the ratio R (τ) / R (0).

The prediction block 9 (Figure 2) includes a series-connected smoothing filter 31, differentiators 32 and 33, an amplifier 34, a multiplication unit 37, an adder 38, and an amplifier 35, the input of which is connected to the output of the differentiator 32, and a multiplication unit 36, the input of which connected to the output of the amplifier 35, and the output to the second input of the adder 38, the output of the smoothing filter 31 is connected to the third input of the adder 38. The algorithm of the prediction block 9 is described by an expression similar to the Taylor formula limited by the first three members:

where Y (t + Tpro) is the output signal of the prediction block;

- отфильтрованный от высокочастотных шумов (сглаженный) входной сигнал; $$\tilde{Y}(t)$$

- filtered (from smooth) high-frequency noise input signal;

K ₁ ≤1 and K ₂ ≤0.25 - amplification factors of amplifiers 35 and 34 respectively, in the general case, are chosen experimentally;

Tpro - forecast interval.

The averaging blocks on a moving time interval 13, 16 and 19 (Figure 3) include serially connected time delay block 39, an adder 40, an integrator 41 and a division unit 42. The output signal of the averaging block on a moving time interval (Figure 3) is described by the expression:

where Y (t) is the output signal of the averaging block on a moving time interval;

X (t) is the input signal of the averaging block on a moving time interval;

T is the value of the moving time interval.

The time delay unit 17 with tunable delay (Figure 4) contains an analog-to-digital converter (ADC) 43, amplifiers 44-1, ... 44-n, inverters 45-1, ... 45-n, controlled keys 46-1, ... 46 -n, delay blocks 47-1, ... 47-n, managed keys 48-1, ... 48-n. The circuit block delay with tunable delay works as follows.

A signal is received at the ADC input numerically equal to the value of the delay interval T, this signal is converted by the ADC 43 into a digital parallel binary code. The signals from each of the n bits through the matching amplifiers 44-1, ... 44-n are supplied to the controlled keys 48-1, ... 48-n and through the inverters 45-1, ... 45-n to the keys 46-1, ... 46-n . If the i-th bit of the ADC is equal to a logical unit, then it opens the 48-i-th key and closes the 46-i-th key, passing the input signal of the delay unit X (t) through the corresponding delay unit having a delay value equal to τ · 2 ⁱ , where τ = U _HT / (2 ⁿ -1), and U _HT is the maximum allowable value for the forecast interval (see Figure 1). If the i-th bit of the ADC is logical zero, then it closes the 48th i-key and opens the 46th i-key, as a result, the input signal is passed through the 46th i-key bypassing the corresponding delay block. Thus, having in the composition of the delay block with tunable delay n delay blocks with fixed delay intervals τ, τ · 2 ¹ , ..., τ · 2 ⁱ , ..., τ · 2 ⁿ , the circuit shown in figure 2 allows you to vary the value delay interval in the range from τ to τ · (2 ^{n + 1} -1).

Corrective filter with tunable time constant 10 can be made in the form of an inertial link, a diagram of which is presented in Fig.5. The following notation is used in the diagram:

R, R1, R2 - electrical resistance;

C is the capacitance of the varicond, which varies depending on the control voltage Uc applied to it;

U1 is the voltage at the input of the filter;

U2 is the voltage across the varicond;

U3 is the voltage at the output of the filter;

i1 is the electric current flowing through the resistance R and the varicond C;

i2 is the electric current flowing through the resistance R1 and R2.

The transfer function of the correction filter has the form:

и

Where

and

является суммой оценок сигнала управления $$\widehat{U}$$

и внешнего возмущения $$\widehat{g}$$

.The inverse model of the control object 6, the direct model of which is described by expression (2), can be implemented in the form of a circuit depicted in Fig.6. Where the input signal of the circuit Y is the output signal of the control object under the influence of the sum of the control signal U and the external disturbance g, and the output signal of the circuit $$\widehat{S}$$

is the sum of the estimates of the control signal $$\widehat{U}$$

and external disturbance $$\widehat{g}$$

.

. $$\widehat{S}=\widehat{U}+\widehat{g}$$

.

The transfer function of the circuit shown in Fig.6 will be:

. Как известно, наличие большого числа малых постоянных времени в схеме можно учесть в виде постоянного транспортного запаздывания, равного сумме этих постоянных времени Δ=nτ.The transfer function (15) differs from the transfer function of the ideal inverse model (3) by the presence of a factor $$\frac{\mathrm{one}}{{(\mathrm{one}+p\tau )}^n}$$

. As is known, the presence of a large number of small time constants in the circuit can be taken into account in the form of a constant transport delay equal to the sum of these time constants Δ = nτ.

Then the expression for the physically realizable inverse model (15) is transformed to the form represented by formula (3): W _mr ^-1 (p) = W _m ^-1 (p) · e ^-pΔ .

The proposed adaptive control system is designed to control technological parameters in chemistry, petrochemistry, metallurgy and other industries characterized by a continuous nature of production. The control systems of such processes operate mainly in the mode of stabilization of the technological parameters of the regulated objects in the vicinity of the set values close to optimal. Therefore, we can assume that the random disturbances acting on the control objects are close to stationary and obey the ergodicity hypothesis, when the average value of a random signal in the set is equal to the corresponding time average.

Adaptive system (Figure 1) works as follows.

и оценки неконтролируемого возмущения $$\widehat{g}$$

, сдвинутых по времени на величину Δ1=τ_O+Δ относительно истинных значений U и g. Запаздывание суммарного входного воздействия объекта обусловлено наличием запаздывания τ_O в объекте 5 и Δ в физически реализуемой инверсной модели 6. В сумматоре 8 из оценки суммарного входного воздействия объекта вычитается полное управляющее воздействие U, синхронизированное по времени с $$\widehat{U}$$

с помощью блока задержки 7. В результате на выходе сумматора 8 получается оценка неконтролируемого возмущения $$\widehat{g}(t-\Delta 1)$$

, сдвинутая по времени относительно истинного возмущения g(t) на величину Δ1. Чтобы уменьшить величину запаздывания в цепи оценки неконтролируемого возмущения, сигнал $$\widehat{g}(t-\Delta 1)$$

с выхода сумматора 8 подается на вход прогнозирующего блока 9. Величина интервала прогноза формируется следующим образом. Сигнал $$\widehat{g}(t-\Delta 1)$$

вначале поступает на вход первого блока усреднения на скользящем интервале 13 и на первый вход сумматора 14, выходной сигнал блока 13 поступает на вычитающий второй вход сумматора 14, в результате на выходе сумматора 14 получается центрированный сигнал оценки неконтролируемого возмущения $$\widehat{g}(t-\Delta 1)$$

. С выхода сумматора 14 центрированный сигнал $$\widehat{g}(t-\Delta 1)$$

подается на первый и второй входы блока умножения 15, на вход блока временной задержки с перестраиваемым запаздыванием 17 и на первый вход блока умножения 18, на второй вход которого поступает выходной сигнал блока 17 временной задержки с перестраиваемым запаздыванием. Выходной сигнал блока умножения 15 поступает на вход второго блока усреднения на скользящем интервале времени 16. На выходе блока 16 получается оценка автокорреляционной функции центрированного сигнала $$\widehat{g}(t-\Delta 1)$$

при нулевом временном сдвиге между перемножаемыми значениями центрированного сигнала $$\widehat{g}(t-\Delta 1)$$

. Иными словами, на выходе блока 16 получается значение дисперсии сигнала $$\widehat{g}(t-\Delta 1)$$

. Выходной сигнал блока умножения 18 поступает на вход третьего блока усреднения на скользящем интервале времени 19. На выходе блока 19 получается сигнал, равный оценке автокорреляционной функции центрированного сигнала $$\widehat{g}(t-\Delta 1)$$

, при временном сдвиге между перемножаемыми значениями центрированного сигнала $$\widehat{g}(t-\Delta 1)$$

, равном τ. Сигнал с выхода третьего блока усреднения на скользящем интервале времени 19 поступает на первый вход блока деления 20 в качестве делимого, а сигнал с выхода второго блока усреднения на скользящем интервале времени 16 поступает на второй вход блока деления 20 в качестве делителя. В результате на выходе блока деления 20 получается сигнал, равный отношению величин оценок автокорреляционных функций R(τ)/R(0) на скользящем интервале времени, гдеFrom the setpoint 1, the reference signal - X (t) is supplied to the first input of adder 2, the second input of which inverts the output signal of the control object 5 - Y (t), the output of the first adder produces a mismatch signal ε between the reference X and the output signal of the object Y The mismatch signal ε is converted by controller 2 into a control action U _P , which is fed to the first input of adder 4, to the subtracting input of which a self-tuning signal ΔU is received, which is the final estimate of the uncontrolled disturbance g. At the output of adder 4, a complete control action U is obtained, which is supplied to object 5. An uncontrolled disturbance g also arrives at the object. The final estimate of the uncontrolled disturbance ΔU is obtained in the system as follows. At the output of a physically implemented inverse (reverse) model 6, the input of which receives the output signal of the object Y, an estimate of the total input effect of the object, reduced to the input of the control channel, is obtained. The output signal of the inverse model is equal in magnitude to the sum of the estimate of the total control action $$\widehat{U}$$

and estimates of uncontrolled disturbance $$\widehat{g}$$

shifted in time by Δ1 = τ _O + Δ relative to the true values of U and g. The delay of the total input effect of the object is due to the delay τ _O in object 5 and Δ in the physically realizable inverse model 6. In adder 8, the total control action U, time synchronized with $$\widehat{U}$$

using delay unit 7. As a result, at the output of adder 8, an estimate of the uncontrolled disturbance is obtained $$\widehat{g}(t-\Delta \mathrm{one})$$

shifted in time relative to the true perturbation g (t) by Δ1. To reduce the amount of delay in the uncontrolled disturbance estimation circuit, the signal $$\widehat{g}(t-\Delta \mathrm{one})$$

from the output of the adder 8 is fed to the input of the predictive block 9. The value of the forecast interval is formed as follows. Signal $$\widehat{g}(t-\Delta \mathrm{one})$$

first it enters the input of the first averaging block on a sliding interval 13 and the first input of the adder 14, the output signal of the block 13 goes to the subtracting second input of the adder 14, as a result of the output of the adder 14, a centered signal for evaluating the uncontrolled disturbance $$\widehat{g}(t-\Delta \mathrm{one})$$

. From the output of the adder 14 centered signal $$\widehat{g}(t-\Delta \mathrm{one})$$

fed to the first and second inputs of the multiplication block 15, to the input of the time delay block with tunable delay 17 and to the first input of the multiplication block 18, to the second input of which the output signal of the time delay block 17 with tunable delay arrives. The output signal of the multiplication block 15 is fed to the input of the second averaging block on a moving time interval 16. At the output of block 16, an estimate of the autocorrelation function of the centered signal is obtained $$\widehat{g}(t-\Delta \mathrm{one})$$

at zero time shift between the multiplied values of the centered signal $$\widehat{g}(t-\Delta \mathrm{one})$$

. In other words, at the output of block 16, the signal dispersion value is obtained $$\widehat{g}(t-\Delta \mathrm{one})$$

. The output signal of the multiplication unit 18 is fed to the input of the third averaging unit on a moving time interval 19. At the output of block 19, a signal is obtained that is equal to the estimate of the autocorrelation function of the centered signal $$\widehat{g}(t-\Delta \mathrm{one})$$

, with a time shift between the multiplied values of the centered signal $$\widehat{g}(t-\Delta \mathrm{one})$$

equal to τ. The signal from the output of the third averaging block at the moving time interval 19 is supplied to the first input of the division unit 20 as a dividend, and the signal from the output of the second averaging block at the moving time interval 16 is fed to the second input of the division unit 20 as a divider. As a result, at the output of the division unit 20, a signal is obtained that is equal to the ratio of the values of the estimates of the autocorrelation functions R (τ) / R (0) on the moving time interval, where

As is known, the autocorrelation function determines the dependence of a random variable at a subsequent time x (t1) from a previous value x (t) at a time t. This is a measure of the connection between them. Obviously, when the moments of time t1 = t coincide, the autocorrelation function takes the maximum value. The value of the ratio R (τ) / R (0) is actually an estimate of the normalized communication measure, with a maximum value equal to one.

, интервал прогноза Tpro с точки зрения минимизации запаздывания оценки $$\widehat{g}(t-\Delta 1)$$

относительно истинного значения неконтролируемого возмущения g(t) должен стремиться к величине Δ1. Однако при возрастании интервала прогноза из-за случайного характера g(t) растут ошибки в оценке прогноза $$\widehat{g}(t)$$

, поскольку с ростом Tpro уменьшается корреляция между последующими и предыдущими значениями прогнозируемого сигнала. Для стабилизации точности прогноза в системе организована стабилизация отношения R(τ)/R(0) на заданном достаточно высоком уровне, например, на уровне 0.85-0.95, путем коррекции интервала запаздывания τ, в блоке временной задержки 17 с перестраиваемым запаздыванием. А поскольку в системе (Фиг 1) τ=Tpro, это автоматически обеспечивает стабильно высокую корреляцию между текущими $$\widehat{g}(t-\Delta 1)$$

и прогнозируемыми $$\widehat{g}(t-\Delta 1+Tpro)$$

значениями оценок неконтролируемых возмущений и стабильную точность прогноза. Система автоматического регулирования интервала задержки в блоке временной задержки с перестраиваемым запаздыванием 17 из условия стабилизации отношения R(τ)/R(0) на заданном уровне реализована блоками 20-26. Выходной сигнал блока деления 20 поступает на первый вход сумматора 21, на второй вычитающий вход которого поступает сигнал с задатчика 22, задающего величину отношения R(τ)/R(0), т.е. фактически на степень корреляции между текущим и прогнозируемым сигналом оценки неконтролируемого возмущения. Сигнал рассогласования между текущим и заданным значением отношения R(τ)/R(0) поступает на вход второго регулятора 24, на второй вход которого подается сигнал I_O с задатчика 23 начального значения интегральной части регулятора 24. Выходной сигнал регулятора 24 поступает на вход второго блока ограничения 26, на параметрические входы которого подаются сигналы верхнего и нижнего уровней ограничения с формирователя сигналов уровней ограничения 25. Блок ограничения 26 предназначен для повышения устойчивости системы, в случаях, когда на входе объекта могут возникать скачкообразные возмущения и пусть временные, но значительные приращения отношения R(τ)/R(0). С выхода блока ограничения 26 сигнал параметрической самонастройки τ подается на параметрический вход блока временной задержки 17 с перестраиваемым запаздыванием и одновременно на параметрический вход блока прогнозирования 10 в качестве интервала прогноза Tpro. Чтобы обеспечить повышенную устойчивость системы, выходной сигнал блока прогнозирования 9 подается на вход корректирующего фильтра 10.When predicting a random signal, which is an estimate of an uncontrolled disturbance $$\widehat{g}(t-\Delta \mathrm{one})$$

, the forecast interval Tpro from the point of view of minimizing the lag estimates $$\widehat{g}(t-\Delta \mathrm{one})$$

relative to the true value of the uncontrolled disturbance g (t) should tend to the value Δ1. However, as the forecast interval increases due to the random nature of g (t), errors in the forecast estimate increase $$\widehat{g}(t)$$

, since the correlation between subsequent and previous values of the predicted signal decreases with increasing Tpro. To stabilize the accuracy of the forecast, the system organizes stabilization of the ratio R (τ) / R (0) at a predetermined sufficiently high level, for example, at the level of 0.85-0.95, by correcting the delay interval τ, in the time delay block 17 with a tunable delay. And since in the system (Fig 1) τ = Tpro, this automatically ensures a consistently high correlation between the current $$\widehat{g}(t-\Delta \mathrm{one})$$

and predictable $$\widehat{g}(t-\Delta \mathrm{one}+Tpro)$$

values of estimates of uncontrolled disturbances and stable forecast accuracy. The system for automatically adjusting the delay interval in the time delay unit with a tunable delay 17 from the condition of stabilization of the ratio R (τ) / R (0) at a given level is implemented by blocks 20-26. The output signal of the division unit 20 is supplied to the first input of the adder 21, the second subtracting input of which receives a signal from the setter 22, which sets the value of the ratio R (τ) / R (0), i.e. in fact, the degree of correlation between the current and the predicted signal for evaluating the uncontrolled disturbance. The mismatch signal between the current and the set value of the ratio R (τ) / R (0) is supplied to the input of the second controller 24, the second input of which is supplied with the signal I _O from the set point 23 of the initial value of the integral part of the controller 24. The output signal of the controller 24 is fed to the input of the second restriction block 26, to the parametric inputs of which signals of the upper and lower restriction levels are supplied from the signal generator of restriction levels 25. Limitation block 26 is designed to increase the stability of the system, in cases where at the input of the object spasmodic perturbations can occur and even temporary, but significant increments of the ratio R (τ) / R (0). From the output of the restriction block 26, the parametric self-tuning signal τ is supplied to the parametric input of the time delay block 17 with a tunable delay and simultaneously to the parametric input of the prediction block 10 as the forecast interval Tpro. To ensure increased stability of the system, the output signal of the prediction unit 9 is fed to the input of the correction filter 10.

Since when the forecast interval increases, high-frequency errors in the estimation of the predicted uncontrolled disturbance increase, the system provides for the organization of automatic generation of the filter time constant 10 - T _F using blocks 27-30. To this end, the output signal of block 26 is supplied to the first input of the third multiplication block 28, the second input of which receives a signal from the setter 27, equal to the specified proportionality coefficient between the time constant of the correction filter T _F and the forecast interval Tpro. The output signal of the multiplication unit 28 is supplied to the first input of the sixth adder 29, to the second input of which a signal is supplied from the setter 30, which is equal to the minimum allowable value of the time constant of the correction filter 10. As a result, the output of the sixth adder 29 produces a signal numerically equal to the time constant of the correction filter 10 which is fed to input parametric filter 10. Thus, the automatic change of the time constant T _F correcting filter 10 changes proportionally Tpro prediction interval pos olyaet with increasing Tpro automatically flatten the high frequency components for prognosis uncontrolled perturbations, reduce oscillatory transients in the system and improve system stability. As a result, the proposed system eliminates the previously noted drawbacks of the system [6]: the self-tuning circuit does not depend on changing the task along the main control loop, automatically adapts to changes in the statistical properties of random uncontrolled disturbances, the output signals of time delay unit 7 and inverse model 6 are synchronized in time, and the operation of the prediction unit 10 does not violate the synchronization, finally, it becomes possible to use a more complex and efficient algorithm for predicting estimates controlled disturbances (see (18)) and increase the forecast interval, while maintaining an acceptable forecast accuracy, since with a change in the forecast interval in the system, the correction filter time constant is automatically adjusted, thereby ensuring higher accuracy and stability of the system.

Thus, by introducing into the compensation circuit an uncontrolled disturbance of new loops for automatically adjusting the prediction interval of the prediction unit 9 and the time constant of the correction filter 10 and using a more complex structure of the prediction unit 10, the aim of the invention is achieved - higher compensation efficiency for uncontrolled disturbances, therefore, higher accuracy and provides higher system stability.

To illustrate the achieved goal, below are the results of digital modeling of the proposed system in comparison with the analogue [5] and prototype [6]. An integrally quadratic system control criterion based on the optimal PID controller was used as a reference. We considered the control object described by the second-order inertial link with transport delay, the transfer function of which has the form:

Where K _o = 1, T ₁₀ = 35, T _2o = 75, τ _O = 10

, и оптимальные значения параметров регулятора равнялись: k_p=4.906, k_i=0.0171, k_d=65.889. При моделировании такт дискретности был принят равным 1 (Takt=1).PID controller transfer function $$W_p(p)=k_p+k_i\cdot \frac{\mathrm{one}}{p}+k_d\cdot p$$

, and the optimal values of the controller parameters were: k _p = 4.906, k _i = 0.0171, k _d = 65.889. In modeling, the discrete time step was taken equal to 1 (Takt = 1).

Figure 7, which shows the response of the optimal PID controller to a step change in the task, illustrates the quality of tuning the parameters of the PID controller. In figure 7, the following notation:

Z (t) - task to the regulator;

Upid - control action (output signal of the PID controller);

y (t) - object output signal (adjustable parameter).

On Fig presents the results of comparing the accuracy of regulation of the proposed adaptive control system and the closest analogue [5] (the prototype system [6] under these conditions loses stability) for an object under the influence of a random not measured exponentially correlated disturbance with the frequency spectrum in the passband object and at the same time under the influence of step perturbation. The parameters of the model were taken equal to the parameters of the object, the specified value of the signal ratio R (τ) / R (0) was taken equal to Z _R = 0.95, as a result, the forecast interval stabilized in the vicinity of Tpro≈10 ± 2, the time constant of the correction filter Tf was maintained proportional to the forecast interval Tf = A · Tpro + 1, the gain of the correction filter was taken equal to Kf = 1. In Fig. 8, Qpid is the integral-quadratic criterion for regulating the system based on the optimal PID controller, Qas is the integral-quadratic criterion for regulating the proposed adaptive control system.

Curve 1 illustrates the dependence of the Qpid / Qas ratio on parameter A (in fact, on the filter time constant) with a fully functioning system structure, with the implementation of the forecast in the signal self-tuning circuit, and curve 2, when the forecast block is fed to the parametric input, instead of the one generated at the output of the second controller forecast interval, zero signal, i.e. virtually no forecast. As follows from the results presented in Fig. 8, the effectiveness of the proposed system compared to the efficiency of the system [5] is obvious.

Figure 9 presents the results of comparing the accuracy of regulation of the proposed adaptive control system and the closest analogue [5] for an object located in the same conditions as in Fig. 8, depending on the magnitude of the transport delay of the control object τ _O. The prototype system with increasing τ _O forecast interval loses stability. Curve 1 illustrates the dependence of the Qpid / Qas ratio on τ _{O of the} proposed system, with the implementation of the forecast of the self-tuning signal, and curve 2 - systems without forecast. As follows from Fig. 9, the effectiveness of the proposed system with an increase in the transport delay of the object decreases, but remains significantly higher than the efficiency and adaptive system without a forecast block and, moreover, an optimal PID controller.

We studied the effectiveness of the proposed system in suppressing a random uncontrolled exponentially correlated disturbance acting on an object under conditions when the task of the main (first) controller changes abruptly with inaccurate knowledge of the object's dynamics. The case was considered when the time constants of the object had the values T ₁₀ = 55, T ₂₀ = 95, and the time constants of the reference model did not change and remained equal to T _1m = 35, T2 _m = 75. Under these conditions, the accuracy of working out a jump-changed task in the proposed system is approximately 50% higher than that of a system based on a PID controller, and the efficiency of suppressing random uncontrolled disturbances is approximately 4 times higher than that of a PID controller, and 2 times higher than adaptive system without forecast block. The prototype system, in conditions when the task of the regulator changes, loses stability.

Thus, the proposed adaptive system makes it possible to increase the accuracy of regulation and the stability of the system by introducing into the signal self-tuning circuit a new circuit for automatically adjusting the forecast interval of the forecasting unit and the loop for setting the time constant of the correction filter. The forecast interval in the proposed system automatically adjusts to the changing statistical properties of an uncontrolled disturbance. Automatic adjustment of the time constant of the correction filter in proportion to the forecast interval allows you to further complicate the structure and increase the efficiency of the prediction block.

The proposed adaptive system can most easily be implemented on the basis of industrial microprocessor controllers.

LITERATURE

1. Solodovnikov V.V., Shramko L.S. Calculation and design of self-tuning systems with reference models. M.: Mechanical Engineering, 1972, p. 35-37.

2. Gromyko V.D., Sankovsky E.A. Self-tuning systems with a model. M .: ENERGY, 1974, p.17-22.

3. Copyright certificate of the USSR No. 591821, cl. G05B 17/02, 1977.

4. Copyright certificate of the USSR No. 824142, cl. G05B 17/02, 1979.

5. Copyright certificate of the USSR No. 1113781, cl. G05B 17/02, 1982.

6. Copyright certificate of the USSR No. 591821, cl. G05B 17/02, 13/04, 1986.

Claims (2)

1. Adaptive control system containing a first input signal generator, the output of which is connected to the summing input of the first adder, connected by the output to the input of the first controller, the output of the first controller is connected to the summing input of the second adder, the control object, the input of which is connected to the output of the second adder, and the output of the control object is connected to the input of a physically feasible inverse model of the object and to the subtracting input of the first adder, the first block of time delay connected by the input to the output of the second th adder, and the output of the first time delay block is connected to the subtracting input of the third adder, the summing input of which is connected to the output of a physically feasible inverse model of the object, the forecast block with a tunable forecast interval, the input of which is connected to the output of the third adder, characterized in that in order to increase system accuracy in terms of delay in the control object:
a correction filter with a tunable time constant, the first and second restriction blocks and the first and second signal conditioners of the restriction levels, the first, second and third averaging blocks on a moving time interval, the first, second and third multiplication blocks, the fourth, fifth and sixth adders are introduced , a second block of time delay with tunable delay, a division block, a second, third, fourth and fifth signal setter, a second regulator, and the first input of the correction filter is connected to the output of of the nosing block, the output of the correction filter is connected to the input of the first block of limitation, the output of which is connected to the subtracting input of the second adder, the second and third inputs of the first block of limitation are connected to the outputs of the first driver of signals of the restriction levels, the input of the first averaging block is connected to the output of the third the adder, and the output of the first averaging unit on a moving time interval is connected to the subtracting input of the fourth adder, the summing input of which is connected to the output of the third adder, the input of the second delay delay block with tunable delay is connected to the output of the fourth adder, the first and second inputs of the first multiplication unit are connected to the output of the fourth adder, the first input of the second multiplication unit is connected to the output of the fourth adder, and the second input of the second multiplication unit is connected to the output of the second block of the time delay with tunable delay, the output of the first block of multiplication is connected to the input of the second block of averaging over a moving time interval, the output is connected to the first input of the division unit as a divider, the output of the second multiplication unit is connected to the input of the third averaging unit on a sliding time interval, the output of which is connected to the second input of the division unit as a dividend, the output of the division unit is connected to the summing input of the fifth adder, subtracting the input the fifth adder is connected to the output of the second master, the output of the fifth adder is connected to the first information input of the second controller, the second parametric input of the second controller is connected to To the setter, the output of the second controller is connected to the first input of the second restriction block, the second and third inputs of the second restriction block are connected to the outputs of the second signal generator of the restriction levels, the output of the second restriction block is connected to the first input of the third multiplication block, to the second parametric input of the second time delay block with tunable delay and to the second parametric input of the prediction block, the second input of the third multiplication block is connected to the output of the fourth setter, the output is tr This multiplication unit is connected to the first input of the sixth adder, the second input of which is connected to the output of the fifth setter, the output of the sixth adder is connected to the second parametric input of the correction filter. 2. The control system according to claim 1, characterized in that the prediction unit with a tunable forecast interval comprises a smoothing filter in series, first and second differentiators, a first amplifier, a fourth multiplication unit, a seventh adder, and a second amplifier, the input of which is connected to the output the first differentiator, and the fifth multiplication unit, the first input of which is connected to the output of the second amplifier, and the output to the second input of the seventh adder, the smoothing output is connected to the third input of the seventh adder about the filter, the input of the smoothing filter is connected to the output of the third adder, and the second inputs of the fourth and fifth blocks of multiplication are connected to the output of the second controller.

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