RU2474858C1 - Combined adaptive control system for nonstationary dynamic objects with observer - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: system, having a status observer, a coefficient unit, a first adder unit, a first multiplier, a second adder unit, a delay unit, series-connected second multiplier and adjustment unit, additionally includes an integrator and a third adder unit.

EFFECT: providing operating capacity and asymptotic stability when controlling a priori undefined unstable dynamic objects of periodic action.

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Description

The invention relates to technical cybernetics and can be used for automatic control of unsteady scalar a priori indefinite dynamic objects of cyclic action.

The closest technical solution to the proposed one is an adaptive control system for dynamic objects with periodic coefficients and an observer (RF Patent No. 2429516, Official Bulletin. Inventions. Utility Models. - 2011, No. 26, prototype), containing a state observer, 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 output of which is connected to the second input of the state observer, input The coefficient setting block is connected to the corresponding outputs of the state observer, the inputs of the first summing block are connected to the corresponding outputs of the coefficient setting block, the output of the first summing block is connected to the first and second inputs of the first multiplier and the second input of the second multiplier, the first input of the second summing block is connected to the output of the first multiplier, the second input is 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 the second multiplier is connected to the input of the regulatory object and to the first input of the state observer.

However, the disadvantage of this system is the loss of performance in the case of control of a priori indefinite unstable dynamic objects.

The technical problem, the solution of which the claimed invention is directed, is to expand the functionality of the system, i.e. ensuring operability and asymptotic stability when controlling a priori indefinite unstable dynamic objects of periodic action.

The solution of this problem is achieved due to the fact that in the system comprising a state observer, a coefficient setting unit, a first summing unit, a first multiplier, a second summing unit, a delay unit, a second multiplier and a control object connected in series, according to the invention, an integrator and a third a summing unit, wherein the output of the control object is connected to the second input of the state observer, the outputs of which are connected to the corresponding inputs of the coefficient setting unit, in The odes of the first summing block are connected to the corresponding outputs of the coefficient setting block, the output of the first summing block is connected to both inputs of the first multiplier, as well as the second input of the second multiplier, the first input of the second summing block is connected to the output of the first multiplier, the second input is connected to the output of the delay block, output the second summing unit is connected to the second input of the third summing unit and the input of the delay unit, the first input of the third summing unit is connected to the output of the integrator, the input of which with connected to the output of the first multiplier, the output of the third summing unit is connected to the first input of the second multiplier, the output of the second multiplier is connected to the input of the control object and to the first input of the state observer.

By introducing an integrator and a third summing unit, the system is asymptotically stable when controlling a priori indeterminate unstable objects in periodic modes.

- значения внутренних состояний объекта регулирования (производных скалярного выхода y).The invention is illustrated by drawings, where figure 1 shows a block diagram of a system; 2 illustrates a block diagram of a state observer. The system contains a regulation object 1, a state observer 2, a coefficient setting unit 3, a first summing unit 4, a first multiplier 5, a second summing unit 6, a delay unit 7, an integrator 8, a third summing unit 9, a second multiplier 10, y, u, respectively scalar output and control action of the regulatory object,

- the values of the internal states of the regulatory object (derivatives of the scalar output y).

The object of regulation is described by the equation

The equations of dynamics of a stationary NS have the form

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

- n-мерный вектор состояния наблюдателя, соответствующий оценкам недоступных переменных состояния x(t);

- n-dimensional state vector of the observer, corresponding to estimates of inaccessible state variables x (t);

A (t + T), b (t + T) - respectively non-stationary state matrix (unstable) and control vector, with T-periodically changing coefficients;

- матрица состояния наблюдателя;

- matrix of observer state;

And ₀ is the Hurwitz matrix;

N is the observation matrix;

y (t) is the scalar value of the output of the regulatory object;

* - transpose symbol;

, L^*=(1,0,…,0) - стационарные векторы;

, L ^* = (1,0, ..., 0) are stationary vectors;

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

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

χ _rob (t) is the robust part of the controller (3)

- некоторый n-мерный вектор блока задания коэффициентов 3, такой что полином

- Гурвицев;

is some n-dimensional vector of the block for setting coefficients 3, such that the polynomial

- Gurvitsov;

s is a complex variable.

Using the criterion of hyperastability of V.M.Popov, it can be shown that the asymptotic stability in the control system under consideration is ensured by the implementation of contour algorithms (3) in the form:

where γ ₀ , γ ₁ = const> 0.

The system operates as follows.

, поступают, во-первых, на соответствующие выходы наблюдателя состояния 2 и, во-вторых, на первые входы блоков суммирования 11_j (j=n-1, …, 1). На вторые входы блоков суммирования 11_j идут сигналы с выхода блока сравнения 13 с соответствующими коэффициентами. Сигналы с выходов наблюдателя состояния 2 поступают на соответствующие входы блока задания коэффициентов 3, внутри которого происходит умножение сигнала с i-го входа на постоянный коэффициент. Выходные сигналы блока задания коэффициентов 3 поступают на входы первого блока суммирования 4, где складываются. Сигнал с выхода первого блока суммирования 4 идет на оба входа первого умножителя 5 и на второй вход второго умножителя 10. На первый вход второго блока суммирования 6 с соответствующим коэффициентом поступает сигнал с выхода первого умножителя 5, на второй вход второго блока суммирования 6 идет сигнал с выхода блока задержки 7. Выходной сигнал второго блока суммирования 6 подается на второй вход третьего блока суммирования 9 и на вход блока задержки 7. На первый вход третьего блока суммирования 9 с соответствующим коэффициентом поступает сигнал с выхода интегратора 8, на вход которого подается сигнал с выхода первого умножителя 5. Выходной сигнал третьего блока суммирования 9 идет на первый вход второго умножителя 10. Сигнал с выхода второго умножителя 10, соответствующий сигналу скалярного управляющего воздействия u поступает на вход объекта регулирования 1, а также на первый вход наблюдателя состояния 2.The signal y from the output of the control object 1 is fed to the second input of the state observer 2 (the block diagram is shown in figure 2), the first input of which receives the control signal u. The signal from the second input of the state observer 2 goes to the second input of the comparison unit 13, to the first input of which the output signal of the integrator 12 ₁ is supplied. Inside the comparison unit 13, the difference of the signals supplied to it is calculated. The signal u from the first input of the state observer 2 is fed to the first input of the summation block 11 _n (n is the dimension of the state vector of the control object 1), the output signal of the comparison block 13 with the corresponding coefficient is received at the second input of the summation block 11n. The remaining n inputs of the summing block 11 _n are the signals from the outputs of the integrators 12 _i (i = n, n-1, ..., 1) with the corresponding coefficients. The output signals of integrators 12 _i corresponding to estimates of inaccessible state variables

, arrive, firstly, at the corresponding outputs of the observer of state 2 and, secondly, at the first inputs of the summation blocks 11 _j (j = n-1, ..., 1). The second inputs of the summing blocks 11 _j send signals from the output of the comparison block 13 with the corresponding coefficients. The signals from the outputs of the state 2 observer are supplied to the corresponding inputs of the coefficient assignment unit 3, inside which the signal is multiplied from the ith input by a constant coefficient. The output signals of the unit for setting the coefficients 3 are supplied to the inputs of the first summing unit 4, where they are added. The signal from the output of the first summing unit 4 goes to both inputs of the first multiplier 5 and to the second input of the second multiplier 10. The signal from the output of the first multiplier 5 comes to the first input of the second summing unit 6, the signal from the second input of the second summing unit 6 the output of the delay unit 7. The output signal of the second summing unit 6 is fed to the second input of the third summing unit 9 and to the input of the delay unit 7. A signal is received at the first input of the third summing unit 9 with the corresponding coefficient l from the output of the integrator 8, the input of which is the signal from the output of the first multiplier 5. The output signal of the third summing unit 9 goes to the first input of the second multiplier 10. The signal from the output of the second multiplier 10, corresponding to the signal of the scalar control action u, is fed to the input of the control object 1 , as well as the first input of the state observer 2.

The technical result consists in expanding the functionality of the system, namely, ensuring its operability and asymptotic stability when controlling periodic modes of a priori indefinite unstable dynamic objects.

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

Claims (1)

A combined adaptive control system for non-stationary dynamic objects with an observer, comprising a state observer, coefficient setting unit, first and second summing units, first and second multipliers, delay unit, control object, the output of which is connected to the second input of the state observer, the outputs of which are connected to the corresponding the inputs of the coefficient setting block, the inputs of the first summing block are connected to the corresponding outputs of the coefficient setting block, the output of the first summing block connected to both inputs of the first multiplier, as well as the second input of the second multiplier, characterized in that an integrator and a third summing unit are additionally introduced, while 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 delay unit, the output of the second the summing unit is connected to the second input of the third summing unit and the input of the delay unit, the first input of the third summing unit is connected to the output of the integrator, the input of which is connected to the output of the first multiply The output of the third summing unit is connected to the first input of the second multiplier, the output of the second multiplier is connected to the input of the control object and to the first input of the state observer.

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