RU2265873C1 - Adaptive control system for dynamic objects with periodical coefficients - Google Patents

Abstract

FIELD: engineering cybernetics.

SUBSTANCE: system can be used for controlling objects with parameters to be time-dependent values with constant period of change. System has object to be controlled, coefficient setting unit, two adders and two multipliers, delay unit.

EFFECT: stabilization of adaptive system.

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Description

The invention relates to technical cybernetics and can be used in systems for controlling objects whose parameters are periodically changing values.

The closest technical solution to the proposed one is the adaptive stabilization system / USSR Copyright Certificate No. 1019400, class. G 05 B 13/02, 1983 (prototype) /, containing the regulation object, coefficient setting unit, adder, first multiplier, integrator, second multiplier. The signals from the outputs of the regulatory object are supplied to the corresponding inputs of the coefficient setting block, which is a block of multipliers. In the unit for setting the coefficients, the signal is multiplied from each output of the regulatory object by a constant coefficient. The signals from the outputs of the coefficient setting block are supplied to the corresponding inputs of the summing block, where they are added. The signal from the output of the summing unit comes to the first input of the second multiplier and to both inputs of the first multiplier. In the first multiplier, the signal is multiplied from the output of the summing unit by the same signal. The signal from the output of the first multiplier is fed to the input of the integrator. The signal from the output of the integrator goes to the second input of the second multiplier. In the second multiplier, the signal is multiplied from the output of the summing unit by the signal from the output of the integrator. The signal from the output of the second multiplier is fed to the input of the regulatory object.

The disadvantage of this system in the presence of periodically changing parameters in the object is the instability of the equilibrium position.

The objective of the invention is to provide asymptotic stability of the equilibrium position of the system in the presence of periodically changing parameters in the object.

The solution of this problem is achieved by the fact that in a system containing a coefficient setting unit, a first adder, a first multiplier, an integrator, 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 task unit coefficients, instead of an integrator, a second adder and a delay unit are introduced, while the first input of the second adder is connected to the output of the first multiplier, the second input d - to the output of the delay unit, the output of the second adder is connected to the input of the second multiplier and to the input of the delay unit.

The technical result consists in the possibility of stabilization of the adaptive system in the presence of objects with parameters whose elements are periodic functions.

The drawing shows a block diagram of a system. The system comprises a regulation object 1, a coefficient setting unit 2, a first adder 3, a first multiplier 4, a second adder 5, a delay unit 6, a second multiplier 7.

The object of regulation is described by the equation

where x∈R ⁿ is the state vector of the regulatory object, A (t + T), b (t + T) are the non-stationary matrix and the vector with periodic coefficients, T is the period of change of the coefficients, L is the output matrix, the symbol * means transposition, y = (y ₁ , ... y _m ) is the output of the control object, u is the scalar control action satisfying the equation

where χ is a tunable coefficient, α ₀ is the m-dimensional vector of coefficients of block 2 for setting the coefficients, chosen from

- гурвицевый квазиполином степени n-1 с положительным старшим коэффициентом (α(λ) - числитель передаточной функции объекта регулирования);

- Hurwitz quasi-polynomial of degree n-1 with a positive highest coefficient (α (λ) is the numerator of the transfer function of the control object);

y is the m-dimensional vector of the output coordinates of the object. Using the Popov hypersensitivity criterion, it can be shown that the implemented tuning algorithm

where β> 0 is a number, provides the asymptotic stability of the system.

The system operates as follows.

The signals from the outputs of the regulatory object 1 are supplied to the corresponding inputs of the coefficient setting block 2. In the coefficient setting block 2, the signal from each output of the regulatory object 1 is multiplied 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. The signal from the output of the summing unit 3 comes to the second input of the second multiplier 7 and to both inputs of the first multiplier 4, the signal from the output of the first multiplier 4 goes to the first input of the second adder 5 The signal from the output of the second adder 5 goes to the first input of the second multiplier 7 and to the input of the delay unit 6, the signal from the output of the delay unit 6 goes to the second input of the second adder 5. The signal from the output of the second multiplier 7 goes to the input of the 1.

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 adder, a first multiplier, 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 adder are connected to the corresponding outputs of the coefficient setting block, characterized in that a second adder and a delay unit are introduced into it, while the first input of the second adder is connected to the output of of the second 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 to the second input of the second multiplier.