RU2427870C1 - Adaptive control system for dynamic objects with periodic coefficients - Google Patents

Abstract

FIELD: electricity. ^ SUBSTANCE: series filter-compensator is introduced to the system; at that, input of series filter-compensator is connected to output of the first adder unit; output of filter-compensator is connected to the first and the second inputs of the first multiplier, as well as to the second input of the second multiplier; the first input of the second adder unit is connected to output of the first multiplier; the second input is connected to output of delay unit; output of the second adder unit is connected to the first input of the second multiplier and to input of delay unit; and output of the second multiplier is connected to input of control object. ^ EFFECT: providing asymptotic stability of control system with periodic modes of dynamic objects. ^ 2 dwg

Description

The invention relates to automatic control systems and can be used to control periodic modes of non-stationary dynamic objects.

The closest technical solution to the proposed one is an adaptive control system for dynamic objects with periodic coefficients (RF Patent No. 2265873, Official Bulletin “Inventions and Utility Models.” - 2005, No. 34, prototype), comprising a unit for setting coefficients, the first adder, the first a multiplier, a second adder, a delay unit, a second multiplier and a control object connected in series, the outputs of which are connected to the corresponding inputs of the coefficient setting unit, the inputs of the first adder are connected to the corresponding outputs of the coefficient setting unit, the first input of the second adder is connected to the output of the first multiplier, the second input is connected to the output of the delay unit, the output of the second adder is connected to the first input of the second multiplier and to the input of the delay unit, the output of the first adder is connected to the first and second inputs of the first multiplier and with the second input of the second multiplier, the output of the second multiplier is connected to the input of the regulatory object.

However, the disadvantage of this system is its inoperability for regulatory objects with a difference in the orders of the numerator and denominator of their transfer function in excess of one.

The technical problem to be solved by the claimed invention is directed is to provide asymptotic stability of the equilibrium position of the system under consideration for objects with a difference in the orders of the denominator and numerator of the transfer function greater than one.

The solution of this problem is achieved due to the fact that in the system containing the coefficient setting unit, the first summing unit, the first multiplier, the second summing unit, the delay unit, the second multiplier and the control object connected in series, the outputs of which are connected to the corresponding inputs of the coefficient setting unit, the inputs the first summing unit is connected to the corresponding outputs of the coefficient setting unit, according to the invention, a sequential filter compensator is additionally introduced, while input d serial filter-compensator is connected to the output of the first summing unit, the output of the filter-compensator is connected to the first and second inputs of the first multiplier, as well as to the second input of the second multiplier, the first input of the second summing unit is connected to the output of the first multiplier, the second input is connected to the output of the block delay, the output of the second summing unit is connected to the first input of the second multiplier and to the input of the delay unit, the output of the second multiplier is connected to the input of the control object.

Introduction to the system of a sequential filter-compensator, in the case of a difference in the orders of the denominator and numerator of the transfer function of the object, greater than one, allows you to get a workable control system.

The invention is illustrated by drawings, where figure 1 shows a block diagram of a system; figure 2 illustrates a block diagram of a serial filter compensator. The system contains a regulation object 1, a coefficient setting block 2, a first summing block 3, a serial filter-compensator 4, a first multiplier 5, a second summing block 6, a delay block 7, a second multiplier 8, ₁ , ..., _{m have} outputs of the regulating object , u is the scalar control action.

The object of regulation is described by the equation:

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

A (t + T), b (t + T) - respectively, non-stationary state matrix and control vector, whose elements are T-periodic functions of time;

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

* - transpose symbol;

L is the output matrix;

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

where χ _lane (t) is the adjustable periodic coefficient of the adaptation loop;

α ₀ - m-dimensional vector of coefficients of the unit for setting coefficients 2, selected from the condition:

α ₀ ^* α (λ) is the Hurwitz polynomial of degree n-1 with a positive leading coefficient, where α (λ) is the numerator of the transfer function of the control object (1).

Using the methodology of the hyperstability criterion of V.M.Popov, it can be shown that the implementation of the control algorithm in the form of:

where γ ₀ is some constant positive value;

will provide asymptotic stability of the regulatory system.

The system operates as follows.

The signals from the output of the regulatory object 1 are supplied to the inputs of the coefficient setting unit 2, inside which the signal is multiplied from the i-th input by a constant coefficient. The signals from the outputs of the unit for setting the coefficients 2 are supplied to the corresponding inputs of the first summing unit 3, where they add up. The signal from the output of the first summing unit 3 is fed to the input of the serial filter-compensator 4, the structural diagram of which is presented in figure 2. The input signal of the serial filter-compensator is supplied to the first input of the summing block 9 ₁ , the output signal of which goes to the input of the integrator 10 ₁ , as well as the first input of the summing block 9 ₂ . The second input of the summing unit 9 ₁ receives a signal from the output of the integrator 10 ₁ . The second and third inputs of the summing unit 9 ₂ receive signals from the output of the integrators 10 ₁ and 10 ₂ . Thus, each summation block 9 _j (j = 1,2, ..., k-1, where k is the difference of the orders of the numerator and denominator of the transfer function of the control object) performs the summation of the signals coming from the output of the summation block 9 _j-1 , and also outputs of the integrators 10 _j-1 and 10 _j . At the first input of the summing block 9 _k , which forms the output of the serial filter-compensator 4, a signal is output from the output of the summing block 9 _k-1 , the signal from the output of the integrator 10 _k-1 is supplied to the second input of the summing block 9 _k . The signal from the output of the summing block 9 _k (corresponding to the output of the serial filter of the compensator 4) goes to both inputs of the first multiplier 5 and to the second input of the second multiplier 8. The signal from the output of the first multiplier 5 is fed to the first input of the second summing block 6. The signal from the output of the second block summation 6 is supplied to the first input of the second multiplier 8 and to the input of the delay unit 7 by an amount equal to the period of change of the parameters of the control object. The signal from the output of the delay unit 7 goes to the second input of the second summing unit 6. The output signal of the second multiplier 8, corresponding to the scalar control action u, is fed to the input of the control object 1.

The technical result consists in ensuring the asymptotic stability of the control system of periodic modes of dynamic objects, the difference in the orders of the numerator and denominator of the transfer function of which exceeds unity.

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

Claims (1)

An adaptive control system for dynamic objects with periodic coefficients, comprising a coefficient setting block, a first summing block, a first multiplier, a second summing block, a delay block, a second multiplier and a control object connected in series, the outputs of which are connected to the corresponding inputs of the coefficient setting block, the inputs of the first block summation is connected to the corresponding outputs of the coefficient setting unit, characterized in that a sequential filter is added to mpensator, while the input of the serial filter-compensator is connected to the output of the first summing unit, the output of the filter-compensator is connected to the first and second inputs of the first multiplier, as well as to the second input of the second multiplier, the first input of the second summing unit is connected to the output of the first multiplier, the second input connected to the output of the delay unit, the output of the second summing unit is connected to the first input of the second multiplier and to the input of the delay unit, the output of the second multiplier is connected to the input of the control object.

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