RU2530277C1 - Adaptive control system for priori unclassified objects of periodic action with time lagging - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: system includes two coefficient setting units, a time-lag unit, six adding units, four multipliers, two delay units, a control object and an integrator.

EFFECT: providing stability of a system at control of unstable dynamic objects containing periodic coefficients and known time lagging as to state.

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Description

The invention relates to technical cybernetics and can be used in control systems of a priori-indefinite non-stationary dynamic objects with a delay as in periodic modes.

The closest technical solution to the proposed one is an adaptive control system for dynamic objects with periodic coefficients and delay (RF Patent No. 2450301, official bulletin “Inventions and Utility Models.” - 2012, No. 13, prototype), containing the first and second blocks for setting the coefficients , delay unit, first, second, third, fourth and fifth summing blocks, first, second, third and fourth multipliers, first and second delay blocks, control object, the outputs of which are simultaneously connected to the corresponding the inputs of the first coefficient setting block and the delay block inputs, the outputs of the first coefficient setting block are connected to the inputs of the first summing block, the output of which is connected to both inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the first input of the second summing block, the output of which connected to the first input of the second multiplier and the input of the first delay unit, the output of the first delay unit is connected to the second input of the second summing unit, the output of the second The amplifier is connected to the first input of the third summing unit, the outputs of the delay unit are connected to the corresponding inputs of the second coefficient setting unit, the outputs of which are connected to the corresponding inputs of the fourth summing unit, the output of which is connected to both inputs of the third multiplier and to the second input of the fourth multiplier, the output of the third multiplier is connected with the first input of the fifth summing block, the output of which is connected to the first input of the fourth multiplier and the input of the second delay block, the output of the second block Since the delay is connected to the second input of the fifth summing unit, the output of the fourth multiplier is connected to the second input of the third summing unit, the output of which is connected to the input of the control object.

The disadvantage of this system is the loss of performance in case of instability of a priori-indefinite control object.

The objective of the invention is the expansion of the functionality of the system, i.e. ensuring stability when controlling unstable dynamic objects with periodic coefficients and delayed state.

The essence of the invention lies in the fact that in an adaptive control system for a priori indefinite objects of periodic action with delay, which includes the first and second blocks for setting coefficients, a delay block, the first, second, third, fourth and fifth blocks of summation, the first, second, third and the fourth multipliers, the first and second delay units, an object of regulation, the outputs of which are simultaneously connected to the corresponding inputs of the first unit for setting the coefficients and inputs of the delay unit, the outputs of the first block The coefficients are connected to the inputs of the first summing block, the output of which is connected to both inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the first input of the second summing block, the output of which is connected to the input of the first delay block, the output of the first delay block is connected to the second input of the second summing unit, the output of the second multiplier is connected to the first input of the third summing unit, the outputs of the delay unit are connected to the corresponding inputs of the second coefficient setting lock, the outputs of which are connected to the corresponding inputs of the fourth summing block, the output of which is connected to both inputs of the third multiplier and to the second input of the fourth multiplier, the output of the third multiplier is connected to the first input of the fifth summing block, the output of which is connected to the first input of the fourth multiplier and the input the second delay unit, the output of the second delay unit is connected to the second input of the fifth summing unit, the output of the fourth multiplier is connected to the second input of the third unit with the mating unit, the output of which is connected to the input of the regulating object, the sixth summing unit and integrator are additionally introduced, while the integrator input is connected to the output of the first multiplier, and the integrator output is connected to the first input of the sixth summing unit, the second input of the sixth summing unit to the output of the second summing unit , the output of the sixth summing unit is connected to the first input of the second multiplier.

The drawing shows a block diagram of a system. The system comprises: regulation object 1, first coefficient setting unit 2, first summing unit 3, first multiplier 4, second summing unit 5, first delay unit 6, second multiplier 7, third summing unit 8, delay unit 9, second coefficient setting unit 10 , the fourth summing block 11, the third multiplier 12, the fifth summing block 13, the second delay block 14, the fourth multiplier 15, the integrator 16, the sixth summing block 17, y ₁ , ... y _m are the outputs of the control object, u is the scalar control action.

The object of regulation is described by the equations

$$\frac{dx(t)}{dt}=A(t+T)x(t)+D(t+T)x(t-\tau )+b(t+T)u(t),(\mathrm{one})$$

^{y (t) = L * x} (t),

where x (t) is the n-dimensional vector of state variables of the regulatory object;

A (t + T) is an unstable state matrix;

D (t + T) is a non-stationary matrix with a delayed argument;

b (t + T) - non-stationary control vector;

T is the period of changing the parameters of the matrices and the vector of the object;

y (t) is the m-dimensional vector of the output coordinates of the object;

* - transpose symbol;

L is the output matrix;

τ is the known time delay;

u (t) is a scalar control action satisfying the relation:

$$u(t)=-{\chi }_{\mathrm{one}}(t)({\alpha }_0^{*}y(t))-{\chi }_2(t)({\beta }_0^{*}y(t-\tau )),(2)$$

₁ where χ (t), χ ₂ (t) - adjustable coefficients adaptation circuit;

, $${\beta }_0^{*}\alpha (\lambda )$$

- гурвицевы полиномы степени (n-1) с положительными коэффициентами; α(λ) - числитель передаточной функции объекта регулирования (1).α _0, β ₀ - m-dimensional vectors of coefficients of the first 2 and second 12 reference coefficients respectively selected from the blocks conditions: $${\alpha }_0^{*}\alpha (\lambda )$$

, $${\beta }_0^{*}\alpha (\lambda )$$

- Hurwitz polynomials of degree (n-1) with positive coefficients; α (λ) is the numerator of the transfer function of the regulatory object (1).

Using the methodology of the criterion of hyperstability V.M. Popov, it can be shown that due to the synthesis of the regulator parameter settings in the form

χ ₁ (t) = χ _1per (t) + χ _1int (t),

$${\chi }_{\mathrm{one}PeR}(t)={\chi }_{\mathrm{one}PeR}(t-T)-{\gamma }_0{({\alpha }_0^{*}y(t))}^2,(3)$$

, $${\chi }_2(t)={\chi }_2(t-T)-{\gamma }_2{({\beta }_0^{*}y(t-\tau ))}^2$$

, $$\frac{{\chi }_{\mathrm{one}\mathrm{and}nt}(t)}{dt}=-{\gamma }_{\mathrm{one}}({\alpha }_0^{*}y{(t)}^2$$

, $${\chi }_2(t)={\chi }_2(t-T)-{\gamma }_2{({\beta }_0^{*}y(t-\tau ))}^2$$

,

where γ ₀ , γ ₁ , γ ₂ are some positive constant values;

will provide asymptotic stability of the control system.

The system operates as follows.

The signals from the outputs of the control object 1 simultaneously arrive at the corresponding inputs of the first block for setting the coefficients 2 and the inputs of the delay unit 9. Inside the first block for setting the coefficients 2, the signals supplied to it are multiplied by constant coefficients α _0i , i = 1, ..., m. The output signals of the first block for setting the coefficients 2 are supplied to the corresponding inputs of the first block of summation 3, inside which are added. The signal from the output of the first summing unit 3 goes to both inputs of the first multiplier 4 and to the second input of the second multiplier 7. The output signal of the first multiplier 4 is simultaneously supplied with the corresponding coefficients to the first input of the second summing unit 5 and to the input of the integrator 16. The signal from the output of the integrator 16 arrives at the first input of the sixth summing block 17. The signal from the output of the second summing block 5 goes to the second input of the sixth summing block 17 and the input of the first delay block 6. The output signal of the first delay block 6 is fed to and the second input of the second summing unit 5. The signal from the output of the sixth summing unit 17 is fed to the first input of the second multiplier 7, the output signal of which goes to the first input of the third summing unit 8. The output signals of the delay unit 9 are supplied to the corresponding inputs of the second unit for setting the coefficients 10, inside of which the ix signals are multiplied by constant coefficients β _0i . The signals from the outputs of the second block for setting coefficients 10 go to the corresponding inputs of the fourth block of summation 11, inside which are added. The output signal of the fourth summing block 11 is simultaneously supplied to the first and second inputs of the third multiplier 12, as well as to the second input of the fourth multiplier 15. The signal from the output of the third multiplier 12 with the corresponding coefficient is fed to the first input of the fifth summing block 13, the output signal of which goes to the input the second delay unit 14 and the first input of the fourth multiplier 15. The signal from the output of the second delay unit 14 is fed to the second input of the fifth summing unit 13. The output signal of the fourth multiplier 15 goes to the second th input of the third summing block 8, the signal from the output of which is input to the controlled object.

The technical result consists in ensuring the stability of the system when controlling unstable dynamic objects containing periodic coefficients and a known time delay by state.

This device can be implemented industrially based on a standard elemental base.

Claims (1)

Adaptive control system for a priori-indefinite objects of periodic action with delay, including the first and second blocks for setting coefficients, a delay block, the first, second, third, fourth and fifth blocks of summation, the first, second, third and fourth multipliers, the first and second delay blocks , an object of regulation, the outputs of which are simultaneously connected to the corresponding inputs of the first block for setting the coefficients and the inputs of the delay unit, the outputs of the first block for setting the coefficients are connected to the inputs the first summing unit, the output of which is connected to both inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the first input of the second summing unit, the output of which is connected to the input of the first delay unit, the output of the first delay unit is connected to the second input of the second summing unit, the output of the second multiplier is connected to the first input of the third summing unit, the outputs of the delay unit are connected to the corresponding inputs of the second unit for setting the coefficients, the outputs of which are connected to the corresponding inputs of the fourth summing block, the output of which is connected to both inputs of the third multiplier and the second input of the fourth multiplier, the output of the third multiplier is connected to the first input of the fifth summing block, the output of which is connected to the first input of the fourth multiplier and the input of the second delay block, the output of the second the delay unit is connected to the second input of the fifth summing unit, the output of the fourth multiplier is connected to the second input of the third summing unit, the output of which is connected to the input control object, characterized in that the sixth summing unit and integrator are additionally introduced into the system, while the integrator input is connected to the output of the first multiplier, and the integrator output is connected to the first input of the sixth summing unit, the second input of the sixth summing unit to the output of the second summing unit, the output of the sixth summing unit is connected to the first input of the second multiplier.