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

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.

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The invention relates to automatic control systems and can be used to build adaptive control systems priori uncertain linear dynamic objects with relative order transfer function, a large unit.

The closest technical solution to the present invention is a self-tuning control system (A.S. 1019400 the USSR, Bulletin of discoveries and inventions. - 1983, No. 19, prototype)containing block job factors, connected in series summation block, the first multiplier, an integrator, a second multiplier, the object of regulation, the outputs of which are connected to the corresponding inputs of the unit job factors, inputs summation block connected to the corresponding outputs of unit assignments coefficients, the output of the summation block is connected to the first and the second input of the first multiplier and the second input of the second multiplier, the output of the first multiplier 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 connected to the input of the regulation object.

However, the disadvantage of this system is the loss of efficiency in case management a priori uncertain linear dynamic objects, the relative order of a transfer function which exceeds unity

Technical problem which the claimed invention is directed, is to expand the functionality of the system, i.e. ensuring the asymptotic stability in the management of a priori uncertain linear dynamic objects with relative order transfer function, a large unit.

The solution of this problem is due to the fact that in a system containing a block of job factors, connected in series summation block, the first multiplier, an integrator, a second multiplier and the object of regulation, additionally introduces incremental dynamic corrector and functional unit, also are excluded from the system unit assignments coefficients and the summation block with the object of regulation is connected with the first and second inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier connected to the input of the integrator, the output of which is connected to the input of the function block and the first input of the second multiplier, the output of the second multiplier connected to the first input serial dynamic corrector, to the second input of which is connected to the output of the function block, the output of serial dynamic corrector is connected to the input of the regulation object.

By introducing a sequential dynamic the static corrector and functional unit ensures asymptotic stability of adaptive systems in control, a priori uncertain linear dynamic objects with a relative order of transfer functions greater than one.

The invention is illustrated in the drawing, in which figure 1 presents the block diagram of the control system; figure 2 shows a block diagram of the functional unit; figure 3 illustrates a block diagram of the sequential dynamic offset. The system contains: the object of regulation 1, the first multiplier 2, the integrator 3, the second multiplier 4, a functional block 5, serial dynamic corrector 6, y is an output signal of the object of regulation, χ - signal tuning adaptive controller,$$\stackrel{}{x}$$- signal custom dynamic coefficient corrector, u is the control signal,$$\stackrel{}{u}$$- output signal serial dynamic offset.

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

$$W_{OP}\left(s\right)=\frac{\alpha \left(s\right)}{\beta \left(s\right)}=\frac{{\alpha }_0{s}^m+{\alpha }_1{s}^{m-1}+...+{\alpha }_{\mathrm{m\; <mo>\; -\; </mo>\; <mn>\; 1\; </mn>}}s+{\alpha }_m}{s^n+{\beta }_1{s}^{n-1}+...+{\beta }_{n-1}s+{\beta }_n},\left(1\right)$$

where s is a complex variable;

α(s) - Gurvitz a polynomial of degree m;

β(s) is a polynomial of degree n with arbitrary location of the roots;

α_j=α_j(ξ), β_i=β_i(ξ) (j=0, 1, ..., m; i=1, 2, ..., n) is a constant number;

ξ is the set of unknown parameters that belong to some known set Ξ.

Serial dynamic corrector (MPC) consists of k (k=ρ-1=(n-m)-1) of series-connected high-speed UE is ugogo links, each of which is described by the differential equation

$$\frac{d\stackrel{}{y}\left(t\right)}{dt}+\stackrel{}{x}\left(t\right)\stackrel{}{y}\left(t\right)=\stackrel{}{x}\left(t\right)\left[T\frac{du\left(t\right)}{dt}+u\left(t\right)\right],mtext>\left(2\right)$$

where u(t),$$\stackrel{}{y}\left(t\right)$$respectively the input and output signals of the elastic element;

T>0 is the time constant;

$$\stackrel{}{x}\left(t\right)$$- the option insist in accordance with the algorithm

$$\stackrel{}{x}\left(t\right)={\psi }_0+{\psi }_1\left|x\left(t\right)\right|,\left(3\right)$$

where ψ₀, ψ₁>1 - some numbers;

χ(t) - custom coefficient adaptive controller specified ratio

where y(t) is a scalar output OP (1).

Using the criterion of giperustoichivost Vampirov it can be shown that the implementation of the algorithm tuning adaptive controller (4) in the form

where h₀>0 - number; ensure asymptotic stability of the control system.

The system operates as follows.

Scalar signal y output from the OP-1 is fed to both inputs of the first multiplier 2 and to the second input of the second multiplier is 4, you are the one signal of the first multiplier 2, with the corresponding coefficient is input and the integrator 3, the output signal of which (χ) simultaneously supplied to the first input of the second multiplier 4 and to the input of function block (FB) 5, the signal from the output of the second multiplier 4 is at the first input of the MPC 6, to the second input of which is applied a signal$$\stackrel{}{x}$$output FB 5. The input signal FB χ 5 (structural diagram presented in figure 2) is fed to the input of block allocation module 7, the output of which with the corresponding coefficient is at the first input of the summation block 8, to the second input of the summation block 8 is supplied to a constant output signal from the setting unit 9, a signal$$\stackrel{}{x}$$from the output of the summation block 8 is output FB 5.

The signal u from the first entrance MPC 6 (structural diagram presented on figure 3) goes to the first input of the summation block 10₁signal$$\stackrel{}{x}$$from the second entrance MPC 6 is simultaneously supplied to the second inputs of the multipliers 11_h(h=1, 2, ..., k), the input of which receives the output signal from summation blocks 10_hthe output signals of the multipliers 11_hsimultaneously arrive at the inputs of the integrators 12_hand with the corresponding coefficients on the second input of the summation blocks 13 _hthe output signals of the integrators 12_hcome to the first inputs of summation blocks 13_hand second input blocks of summation 10_hthe signals from outputs of summation blocks 13_r(r=1, 2, ..., k-1) are fed to the first inputs of summation blocks 10_f(f=2, 3, ..., k), the output signal of the summation block 13_kapplied to the output of MPC 6, a signal$$\stackrel{}{u}$$output MPC 6 is fed to the input of OP 1.

The technical result is to expand the functionality of the system, namely in ensuring the asymptotic stability in the management of a priori uncertain linear dynamic objects with relative order transfer function, a large unit.

This device can be implemented industrially based on standard components.

Adaptive control system for a priori uncertain objects with dynamic self-adjustment of the offset containing the first multiplier, an integrator, a second multiplier and the object of regulation, characterized in that it further introduced a sequential dynamic corrector and function block with the object of regulation is connected with the first and second inputs of the first multiplier and the second input of the second multiplier, Ihad first multiplier connected to the input of the integrator, the output of which is connected to the input of the function block and the first input of the second multiplier, the output of the second multiplier connected to the first input of the dynamic offset, input function block connected to the input of the unit selection module, the output of which is connected to the first input of the summation block, the second input is connected to the output of the master unit, the output of the summation block is connected to a second input of the dynamic corrector, the first input of the dynamic corrector connected to the first input of the summation block, the second input of the dynamic corrector is connected with the second inputs of the multipliers, the first inputs of which are connected to the outputs of summation blocks (except the last), the outputs of the multipliers at the same time connected with the inputs of the integrators and the second inputs of subsequent blocks summation, the outputs of the integrators are connected to second inputs of the previous blocks of summation and to the first inputs of subsequent blocks summation, the outputs of which are connected with the first inputs of blocks summation, the output of the last block of the summation corresponds to the dynamic output of the corrector, which is connected to the input of the object of regulation.