RU2427869C1 - Self-adjusting control system for objects with control delay - Google Patents

Abstract

FIELD: electricity. ^ SUBSTANCE: adaptive system includes the following: delay unit by value ä, the second adder, the second integrator, the third adder; at that, the first input of the second adder is connected to output of the second multiplier; the second input of the second adder is connected to output of the second integrator; the third input of the second adder is connected to output of delay unit; output of the second adder is connected to input of the second integrator the output of which is connected to the first input of the third adder and to the second input of the second adder; the second input of the third adder is connected to output of the first adder; the third input of the third adder is connected to output of the second multiplier; output of the third adder is connected to the second input of the first multiplier, and input of delay unit is connected to output of the second multiplier. ^ EFFECT: possible stabilisation of adaptive system in case of objects with control delay. ^ 1 dwg

Description

The invention relates to technical cybernetics and can be used in systems for controlling objects whose parameters are unknown constant or slowly varying in time.

The closest technical solution to the proposed one is an adaptive stabilization system (ed. St. USSR No. 1019400, class G05B 13/02, 1983, prototype), which contains an object of regulation, a block for setting coefficients, an adder, a first multiplier, an integrator, and a 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.

However, the disadvantage of this system in the case of the presence of a control delay in the object is the instability of the equilibrium position.

The technical problem to which the claimed invention is directed is to provide asymptotic stability of the equilibrium position of the system in the presence of a control delay in the object.

The solution of this problem is achieved by the fact that in a system containing a coefficient setting unit, a summing unit, a first multiplier, an integrator, a second multiplier connected in series, the outputs of the control object 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 coefficient setting unit, a delay unit by a value of τ is introduced, a second adder, a second integrator, a third adder, while the first input of the second adder is connected to the output of the second multiplier, the second input of the second adder is connected to the output of the second integrator, the third input of the second adder is connected to the output of the delay unit, the output of the second adder is connected to the input of the second integrator, the output of which is connected to the first input of the third adder and to the second input of the second adder, the second input of the third adder connected to the output of the first adder, the third input of the third adder is connected to the output of the second multiplier, the output of the third adder is connected to the second input of the first multiplier, the input of the delay unit is connected with the output of the second multiplier.

The invention is illustrated in the drawing, where figure 1 shows a block diagram of a system. The system contains a control object 1, a first unit for setting coefficients 2, a first adder 3, a first multiplier 4, a first integrator 5, a second multiplier 6, a second adder 7, a second integrator 8, a third adder 9, a delay unit 10. The control object is described by the equation

where x∈R ⁿ is the state vector of the control object, L is the output matrix, y ₁ , ..., y _m are the outputs of the control object, u is the scalar control action satisfying the equation

where α ₀ is the m-dimensional vector of coefficients of block 2 for setting coefficients, chosen from the condition

α ₀ * α (λ) - Hurwitz quasi-polynomial of degree n-1 with a positive leading coefficient (α (λ) - numerator of the transfer function of the control object);

y is the m-dimensional vector of the output coordinates of the object.

Using the criterion of hypersensitivity V.M.Popova it can be shown that the implemented tuning algorithm

where β> 0 is the number, ψ is the output of the additional circuit, the dynamics of which are described by the equation

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 summing unit 3. The signal from the output of the summing unit 3 comes to the second input of the third adder 9, to the first input of the first multiplier 4 and to the first input of the second multiplier 6, the signal from the output of the third adder 9 is supplied to the second input of the first multiplier 4, the signal from the output of the first multiplier 4 goes to the input of the first integrator 5, the signal from the output of the first integrator 5 goes to the second input of the second multiplier 6, the signal from the output of the second multiplier 6 is fed to the first the second input of the second adder 7, to the input of the delay unit 10, to the third input of the third adder 9 and to the input of the control object 1, the signal from the output of the delay unit 10 goes to the third input of the second adder 7, the signal from the output of the second adder 7 is fed to the input of the second integrator 8, the signal from the output of the second integrator 8 is fed to the first input of the third adder 9 and to the second input of the second adder 7.

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

The technical result of the claimed invention lies in the possibility of stabilization of the adaptive system in the presence of objects with a delay in control.

Claims (1)

Adaptive stabilization system in the presence of objects with a delay in control, containing the first block for setting the coefficients, the first adder, series-connected first multiplier, the first integrator, the second multiplier, the outputs of the control object are connected to the corresponding inputs of the first block for setting the coefficients, the inputs of the first adder are connected to the corresponding outputs the first unit for setting coefficients, the output of the first multiplier is connected to the input of the first integrator, the output of the first integrator is connected to about the second input of the second multiplier, characterized in that a second adder, a second integrator, a third adder, a delay unit are introduced into the system; the first input of the second adder is connected to the output of the second multiplier, the second input is connected to the output of the second integrator, the output of the second adder is connected to the second input of the second adder and to the first input of the third adder , the second input of the third adder is connected to the output of the first adder, the third input of the third adder is connected to the output of the second multiplier, the output of the third adder is connected to the second input of the first multiplier, the first course of the first multiplier and the second multiplier first input connected to the output of the first adder, the second multiplier output is connected to a first input of the second adder, a third input of the third adder to the input of the delay unit and the input of the controlled object.