RU2210800C2 - Self-adjusting control system for objects with control delay - Google Patents

Abstract

FIELD: technical cybernetics, systems controlling objects which parameters are unknown constant values or values slowly changing in time. SUBSTANCE: system includes object of adjustment, two units setting coefficients, four adders, four multipliers, three integrators, delay unit. EFFECT: potential for stabilization of adaptive system with presence 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 the adaptive stabilization system [1], which contains 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, if there is a control delay in the object, is the instability of the equilibrium position.

 The aim of the invention is to ensure the asymptotic stability of the equilibrium position of the system in the presence of a delay in the control object.

 The task is achieved in 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, entered delay unit by the value of τ, the second adder, the second unit for setting coefficients, the second integrator, the third adder, the third integrator, the third multiplier, h the fourth multiplier, the fourth adder, while the first input of the second adder is connected to the output of the fourth adder, the second input of the second adder is connected to the output of the delay unit, the third input of the second adder is connected to the output of the second coefficient setting unit, the output of the second adder is connected to the input of the second integrator, output which is connected to the first input of the third adder and to the input of the second unit for setting the coefficients, the second input of the third adder is connected to the output of the first adder, the output of the third adder is connected n with the second input of the first multiplier and with the first input of the third multiplier, the second input of the third multiplier is connected to the output of the first adder, the output of the third multiplier is connected to the input of the third integrator, the output of the third integrator is connected to the first input of the fourth multiplier, the second input of the fourth multiplier is connected to the output of the first the adder, the output of the fourth multiplier is connected to the second input of the fourth adder, and the first input of the fourth adder is connected to the output of the second multiplier, the output of the fourth adder is connected to the input of the delay unit, to the input of the control object and to the first input of the second adder, the output of the delay unit is connected to the second input of the second adder, to the second input of the second multiplier, to the first input of the first multiplier.

 The drawing shows a block diagram of a system.

The system contains a regulation object 1, a first block 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 second block for setting coefficients 9, a third adder 10, a third multiplier 11, the third integrator 12, the fourth multiplier 13, the fourth adder 14, the delay unit 15. The object of regulation is described by the equation
$\genfrac{}{}{0ex}{}{\text{dx}}{\text{dt}}$ = Ax + bu (t-τ), y = L ^* x, (1)
where x∈R ⁿ is the state vector of the regulatory object, L is the output matrix, y ₁ ,. . . , y _m are the outputs of the regulatory object, u is the scalar control action satisfying the equation
u = -χ (α $\genfrac{}{}{0ex}{}{\text{*}}{\text{0}}$ y) -ku (t-τ), (2)
where α ₀ - m is the dimensional vector of the coefficients of block 2 of setting the coefficients,
α $\genfrac{}{}{0ex}{}{\text{*}}{\text{0}}$ α (λ) is the Hurwitz quasi-polynomial of degree n-1 with a positive leading coefficient (α (λ) is the numerator of the transfer function of the control object);
y - m - dimensional vector of the output coordinates of the object.

где β>0 - число, γ>0 - число, z - выход дополнительного контура, динамика которого описывается уравнением
$\genfrac{}{}{0ex}{}{\text{dk}}{\text{dt}}$ = -a₀z+u-u(t-τ), (4)
где а₀>0 - число,
обеспечивает асимптотическую устойчивость системы.Using the Popov hypersensitivity criterion, it can be shown that the implemented tuning algorithm

where β> 0 is the number, γ> 0 is the number, z is the output of the additional circuit, the dynamics of which are described by the equation
$\genfrac{}{}{0ex}{}{\text{dk}}{\text{dt}}$ = -a ₀ z + uu (t-τ), (4)
where a ₀ > 0 is a number,
provides 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 from the i-th output of the object of regulation 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 summing unit 3. The signal from the output of the summing unit 3 comes to the second input of the third adder 10, to the second input of the third multiplier 11 and to the second input of the fourth multiplier 13, the signal from the output of the third adder 10 is supplied to the second input of the first multiplier 4 and to the first input of the third multiplier 11, 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 first input of the second multiplier 6, the signal from the output of the second multiplier 6 is fed to the first input of the fourth adder 14, the signal from the output of the third multiplier 11 goes to the input of the third integrator 12, the signal from the output of the third integrator 12 goes to the first input of the fourth multiplier 13, the signal from the output of the fourth multiplier 13 is fed to the second input of the fourth adder 14. The signal from the output of the fourth adder 14 goes to the input of the regulation object 1, to the first input of the second adder 7 and to the input of the delay unit 15, the signal from the output of the delay unit 15 goes to the second input of the second adder 7, to the first the first input of the first multiplier 4 and the second input of the second multiplier 6, 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 10 and to the input of the second block for setting coefficients 9, the signal the output of the second block specifying the coefficients 9 comes to the third input of the second adder 7.

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

Sources of information
1. Copyright certificate of the USSR 1019400, cl. G 05 B 13/02, 1983 (prototype).

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 block for setting coefficients, characterized in that the second adder, the second block for setting coefficients, and the second int are entered into the system grator, a third adder, a third multiplier, a third integrator, a fourth adder, the fourth multiplier; the first input of the second adder is connected to the output of the fourth adder, the second input is to the output of the delay unit, the third input is to the output of the second unit for setting the coefficients, the output of the second adder is connected to the input of the second integrator, the output of the second integrator is connected to the input of the second coefficient setting unit and to the first the input of the third adder, the second input of the third adder is connected to the output of the first adder, the output of the third adder is connected to the second input of the first multiplier and to the first input of the third multiplier, the first input of the first o the multiplier and the second input of the second multiplier are connected to the output of the delay unit, the output of the second multiplier is connected to the first input of the fourth adder, the second input of the third multiplier is connected to the output of the first adder, the output of the third multiplier is connected to the input of the third integrator, the output of the third integrator is connected to the first input of the fourth multiplier, the second input of the fourth multiplier is connected to the output of the first adder, the output of the fourth multiplier is connected to the second input of the fourth adder, the output of the fourth adder coupled to the input of the object of regulation and with the input of the delay unit.