RU2488155C1 - Adaptive control system for priori undefined objects with self-adjustment of dynamic corrector - Google Patents

Abstract

FIELD: physics.

SUBSTANCE: system, which includes a coefficient unit, series-connected adder unit, first multiplier, integrator, second multiplier and control object, further includes a series dynamic corrector and a functional unit, and a coefficient unit and an adder unit are also excluded from the system. The output of the control object is connected to the first and second inputs of the first adder and the second input of the second adder; the output of the first multiplier is connected to the input of the integrator, the output of which is connected to the input of the functional unit and the first input of the second multiplier; the output of the second multiplier is connected to the first input of the series dynamic corrector, the second input of which is connected to the output of the functional unit; the output of the series dynamic corrector is connected to the input of the control object.

EFFECT: broader functional capabilities of the system, providing asymptotic stability when controlling a priori undefined linear dynamic objects with a relative order of the transfer function greater than one.

3 dwg

Description

The invention relates to automatic control systems and can be used in the construction of adaptive control systems for a priori indefinite linear dynamic objects with a relative transfer function order greater than unity.

The closest technical solution to the proposed one is a self-adjusting control system (A.S. 1019400 USSR, Bulletin of discoveries and inventions. - 1983, No. 19, prototype), which contains a unit for setting coefficients, series-connected summing unit, a first multiplier, an integrator, a second multiplier, the regulation 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 coefficient setting unit, the output of the summing unit is connected with the first and second input of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the input of the integrator, the output of which 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.

However, the disadvantage of this system is the loss of performance in the case of control of a priori indefinite linear dynamic objects, the relative order of the transfer function of which exceeds unity.

The technical problem, the solution of which the claimed invention is directed, is to expand the functionality of the system, i.e. ensuring asymptotic stability when controlling a priori indefinite linear dynamic objects with a relative order of the transfer function greater than unity.

The solution of this problem is achieved due to the fact that a sequential dynamic corrector and a functional block are additionally introduced into the system containing the coefficient setting block, the summation unit, the first multiplier, the integrator, the second multiplier and the control object, and the coefficient setting block is also excluded from the system and a summing unit, wherein the output of the control object is connected to the first and second inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier The amplifier is connected to the input of the integrator, the output of which is connected to the input of the functional block and the first input of the second multiplier, the output of the second multiplier is connected to the first input of the serial dynamic corrector, the output of the functional block is connected to its second input, the output of the serial dynamic corrector is connected to the input of the control object.

By introducing a sequential dynamic corrector and a functional block, the asymptotic stability of the adaptive system is ensured in the case of control of a priori indefinite linear dynamic objects with a relative transfer function order exceeding unity.

- сигнал настраиваемого коэффициента динамического корректора, u - сигнал управления, $$\overline{u}$$

- выходной сигнал последовательного динамического корректора.The invention is illustrated in the drawing, where figure 1 shows a block diagram of a control system; figure 2 shows a block diagram of a functional block; figure 3 illustrates a block diagram of a sequential dynamic corrector. The system contains: control object 1, first multiplier 2, integrator 3, second multiplier 4, function block 5, sequential dynamic corrector 6, y - output signal of the control object, χ - adaptive controller tuning signal, $$\overline{\chi }$$

- signal of the adjustable coefficient of the dynamic corrector, u - control signal, $$\overline{u}$$

- output signal of a sequential dynamic corrector.

The regulation object (OP) has a relative order ρ = (n-m)> 1 and is described using the transfer function

$$W_{OP}\left(s\right)=\frac{\alpha \left(s\right)}{\beta \left(s\right)}=\frac{{\alpha }_0{s}^m+{\alpha }_{\mathrm{one}}{s}^{m-\mathrm{one}}+...+{\alpha }_{m-\mathrm{one}}s+{\alpha }_m}{s^n+{\beta }_{\mathrm{one}}{s}^{n-\mathrm{one}}+...+{\beta }_{n-\mathrm{one}}s+{\beta }_n},\left(\mathrm{one}\right)$$

where s is a complex variable;

α (s) are Hurwitz polynomials of degree m;

β (s) is a polynomial of degree n with an arbitrary arrangement of roots;

α _j = α _j (ξ), β _i = β _i (ξ) (j = 0, 1, ..., m; i = 1, 2, ..., n) are constant numbers;

ξ is a set of unknown parameters belonging to some known set Ξ.

A sequential dynamic corrector (MPC) consists of k (k = ρ-1 = (n-m) -1) series-connected high-speed elastic links, each of which is described by a differential equation

$$\frac{d\tilde{y}\left(t\right)}{dt}+\tilde{\chi }\left(t\right)\tilde{y}\left(t\right)=\tilde{\chi }\left(t\right)\left[T\frac{du\left(t\right)}{dt}+u\left(t\right)\right],\left(2\right)$$

- соответственно входной и выходной сигналы упругого звена;where u (t), $$\tilde{y}\left(t\right)$$

- respectively, the input and output signals of the elastic link;

T> 0 is the time constant;

- параметр, настаиваемый в соответствии с алгоритмом $$\tilde{\chi }\left(t\right)$$

- parameter that can be set in accordance with the algorithm

$$\tilde{\chi }\left(t\right)={\psi }_0+{\psi }_{\mathrm{one}}\left|\chi \left(t\right)\right|,\left(3\right)$$

where ψ ₀ , ψ ₁ > 1 are some numbers;

χ (t) is the adjustable coefficient of the adaptive controller specified by the ratio

$$u\left(t\right)=-\chi \left(t\right)y\left(t\right),\left(\mathrm{four}\right)$$

where y (t) is the scalar output of OP (1).

Using the hyperstability criterion of V.M. Popov, it can be shown that the implementation of the adaptive controller tuning algorithm (4) in the form

$$\frac{d\chi \left(t\right)}{dt}=h_0{y}^2\left(t\right),\left(5\right)$$

where h ₀ > 0 is a number; will provide asymptotic stability of the considered control system.

The system operates as follows.

с выхода ФБ 5. Входной сигнал χ ФБ 5 (структурная схема представлена на фиг.2) поступает на вход блока выделения модуля 7, сигнал с выхода которого с соответствующим коэффициентом идет на первый вход блока суммирования 8, на второй вход блока суммирования 8 подается постоянный сигнал с выхода задающего блока 9, сигнал $$\tilde{\chi }$$

с выхода блока суммирования 8 поступает на выход ФБ 5.The scalar signal y from the output of OP 1 is fed to both inputs of the first multiplier 2 and to the second input of the second multiplier 4, the output signal of the first multiplier 2 with the corresponding coefficient goes to the input of the integrator 3, the output signal of which (χ) simultaneously arrives at the first input of the second multiplier 4 and the input of the functional block (FB) 5, the signal from the output of the second multiplier 4 goes to the first input of the MPC 6, to the second input of which a signal $$\tilde{\chi }$$

from the output of the FB 5. The input signal χ FB 5 (the block diagram is shown in Fig. 2) is fed to the input of the allocation unit of module 7, the output signal of which with the corresponding coefficient goes to the first input of the summing unit 8, a constant input to the second input of the summing unit 8 the signal from the output of the master unit 9, the signal $$\tilde{\chi }$$

from the output of the summing unit 8 is fed to the output of the FB 5.

со второго входа ПДК 6 одновременно подается на вторые входы умножителей 11_h (h=1, 2, …, k), на первые входы которых поступает сигнал с выхода блоков суммирования 10_h, выходные сигналы умножителей 11_h одновременно поступают на входы интеграторов 12_h и с соответствующими коэффициентами на вторые входы блоков суммирования 13_h, выходные сигналы интеграторов 12_h поступают на первые входы блоков суммирования 13_h и на вторые входы блоков суммирования 10_h, сигналы с выходов блоков суммирования 13_r (r=1, 2, …, k-1) поступают на первые входы блоков суммирования 10_f (f=2, 3, …, k), выходной сигнал блока суммирования 13_k подается на выход ПДК 6, сигнал $$\overline{u}$$

с выхода ПДК 6 поступает на вход OP 1.The signal u from the first input of MPC 6 (the structural diagram is presented in figure 3) goes to the first input of the summing unit 10 ₁ , the signal $$\tilde{\chi }$$

from the second input of the MPC 6 is simultaneously fed to the second inputs of the multipliers 11 _h (h = 1, 2, ..., k), the first inputs of which receive a signal from the output of the summing units 10 _h , the output signals of the multipliers 11 _h simultaneously arrive at the inputs of the integrators 12 _h and with the corresponding coefficients at the second inputs of the summing blocks 13 _h , the output signals of the integrators 12 _h are fed to the first inputs of the summing blocks 13 _h and the second inputs of the summing blocks 10 _h , the signals from the outputs of the summing blocks 13 _r (r = 1, 2, ..., k-1) go to the first inputs of the summing blocks 10 _f (f = 2, 3, ..., k), the output signal of the summing unit 13 _k is fed to the output of the MPC 6, the signal $$\overline{u}$$

from the output of the MPC 6 goes to the input OP 1.

The technical result consists in expanding the functionality of the system, namely, in providing asymptotic stability when controlling a priori indefinite linear dynamic objects with a relative transfer function order greater than unity.

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

Claims (1)

An adaptive control system for a priori indefinite objects with self-tuning of a dynamic corrector, comprising a first multiplier, an integrator, a second multiplier and a control object, characterized in that a sequential dynamic corrector and a functional unit are additionally introduced, while the output of the control object is connected to the first and second inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the input of the integrator, the output of which is connected to the input of the functional block OK and the first input of the second multiplier, the output of the second multiplier is connected to the first input of the dynamic corrector, the input of the function block is connected to the input of the module selection unit, the output of which is connected to the first input of the summing unit, the second input of which is connected to the output of the master unit, the output of the summing unit is connected to the second input of the dynamic corrector, the first input of the dynamic corrector is connected to the first input of the summing unit, the second input of the dynamic corrector is connected to the second inputs of the multipliers, the first inputs of which are connected to the outputs of the summing blocks (except the last), the outputs of the multipliers are simultaneously connected to the inputs of the integrators and the second inputs of the subsequent summing blocks, the outputs of the integrators are connected to the second inputs of the previous summing blocks and to the first inputs of the subsequent summing blocks, the outputs of which are connected to the first inputs summing blocks, the output of the last summing block corresponds to the output of the dynamic corrector, which is connected to the input of the regulatory object.

Images