RU2287847C1 - Combined adaptive control system for dynamic objects with periodic coefficients - Google Patents

Abstract

FIELD: technical cybernetics.

SUBSTANCE: into known system additionally introduced are second and third adding blocks, and block for delaying for value equal to period of alternation of adjustment object parameters, while first input of second adding block is connected to output of first multiplexer, second input of second adding block is connected to output of delay block, output of second adding block is connected to input of third adding block and to input of delay block, second input of third adding block is connected to output of integrator, output of third adding block is connected to input of second multiplexer. System contains: adjustment object, block for setting coefficients, three adding blocks, integrator, two multiplexers, delay block.

EFFECT: possible stabilization of adaptive system if parameters are present on object, which represent periodical time functions.

1 dwg

Description

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

The closest technical solution to the proposed one is an adaptive stabilization system [1, AS No. 1019400], comprising a coefficient assignment unit, a summation unit connected in series, a first multiplier, an integrator, a second multiplier, a control object whose outputs are connected to the corresponding inputs of the coefficient assignment unit, inputs the summing unit is connected to the corresponding outputs of the coefficient setting unit, the output of the summing unit is connected to the second inputs of the first and second multipliers. 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, where it is integrated. 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 essence of the invention lies in the fact that in a system containing a coefficient setting unit, a summing unit connected in series, a first multiplier, an integrator, a second multiplier, a control object whose outputs are connected to the corresponding inputs of the coefficient setting unit, the inputs of the summing unit are connected to the corresponding outputs of the task unit coefficients, the output of the summing block is connected to the second inputs of the first and second multipliers, the second and third summing blocks and the delay block are additionally introduced by an amount equal to the period of changing the parameters of the control object, while the first input of the second summing unit is connected to the output of the first multiplier, the second input of the second summing unit is connected to the output of the delay unit, the output of the second summing unit is connected to the input of the third summing unit and to the input of the delay unit, the second input of the third summing unit is connected to the output of the integrator, the output of the third summing unit is connected to the input of the second multiplier.

Figure 1 presents a block diagram of a system. The system contains a regulation object 1, a coefficient setting block 2, a first summing block 3, a first multiplier 4, an integrator 5, a second summing block 6, a delay block 7, a third summing block 8, a second multiplier 9, y ₁ , ..., y _m - outputs of the regulatory object.

The object of regulation is described by the equation

where x is the n-dimensional state vector of the control object, A (t + T) and b (t + T) is the state matrix and control vector, respectively, whose elements are periodic functions with period T, y is the m-dimensional vector of the object’s output coordinates , L is the output matrix, u is the scalar control action satisfying the equation

where χ is a custom coefficient of adaptation loop;

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

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

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

Using the Popov hypersensitivity criterion, it can be shown that the tuning algorithm implemented in a combined way in the form of:

χ = χ ₁ + χ ₂

χ ₂ = χ ₂ (tT) -h ₂ (α ₀ ^* y) ² ,

where χ ₁ and χ ₂ ^{are the} integral and periodic components of the adaptation algorithm, h ₁ , h ₂ > 0 are numbers, respectively, provides the asymptotic stability of the system.

The system operates as follows.

The signals from the outputs of the control object 1 are supplied to the corresponding inputs of the unit for setting the coefficients 2. In the block for setting the coefficients 2, the signal is multiplied from the i-th output of the object of regulation 1 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 first summing unit 3 comes to the second input of the second multiplier 9 and to both inputs of the first multiplier 4, the signal from the output of the first multiplier 4 goes to the input of the integrator 5 and to the first input of the second summing unit 6. The signal from the output of the second summing unit 6 goes to the first input of the third summing unit 8 and to the input of the delay unit 7, the signal from the output of the delaying unit 7 goes to the second input of the second summing unit I 6. The signal from the output of the integrator 5 goes to the second input of the third summing unit 8, the output of the third summing unit 8 is connected to the second input of the second multiplier 9. The output of the second multiplier 9 goes to the input of the regulation object 1.

The technical result consists in the possibility of stabilization of the adaptive system if the object has parameters that are periodic functions of time.

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

THE SOURCE OF INFORMATION

1. USSR Copyright Certificate No. 1019400, cl. G 05 B 13/02, 1983 (prototype).

Claims (1)

A combined adaptive control system for dynamic objects with periodic coefficients, comprising a coefficient assignment unit, a summing unit connected in series, a first multiplier, an integrator, and a second multiplier, a control object in series, the outputs of which are connected to the corresponding inputs of the coefficient setting unit, the inputs of the summing unit are connected to the respective outputs of the coefficient setting unit, the output of the summing unit is connected to the second inputs of the first and the second multiplier, characterized in that the second and third summing blocks and a delay block are added to the system by an amount equal to the period of change of the parameters of the control object, the first input of the second summing block connected to the output of the first multiplier, the second input of the second summing block with the output delay unit, the output of the second summing unit is connected to the input of the third summing unit and to the input of the delay unit, the second input of the third summing unit is connected to the output of the integrator, the output is third its summation block coupled to the input of the second multiplier.