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Adaptive control system for dynamic objects with periodic coefficients and lag

Adaptive control system for dynamic objects with periodic coefficients and lag
IPC classes for russian patent Adaptive control system for dynamic objects with periodic coefficients and lag (RU 2450301):
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FIELD: physics.

SUBSTANCE: system, having a coefficient unit, a first adder unit, a first multiplier, a second adder unit, a delay unit, series-connected second multiplier and control object, also includes a second delay unit, a second coefficient unit, a lag unit, third, fourth and fifth adder units, third and fourth multipliers.

EFFECT: ensuring asymptotic stability of the equilibrium position of the investigated system for periodic action objects, having a known status time lag.

1 dwg

 

The invention relates to the technical Cybernetics and can be used to control periodic regimes of non-stationary dynamic objects containing the time-delay state.

The closest technical solution to the present invention is an adaptive control system for dynamic objects with periodic coefficients (RF Patent No. 2265873. Official Bulletin. "Inventions and utility models". - 2005, No. 34, prototype)containing a unit job of the coefficients, the first adder, the first multiplier, a second adder, the delay unit, connected in series to the second multiplier and the object of regulation, the outputs of which are connected to corresponding inputs of a unit job of the coefficients, the inputs of the first adder connected to the corresponding outputs of the unit job factors, the first input of the second adder connected to the output of the first multiplier, a second input to the output of the delay unit, the output of the second adder connected to the first input of the second multiplier and the input of the delay unit, the output of the first adder connected to the first and second inputs of the first multiplier and with the second 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 its failure to objects of regulation, containing the famous BP is the time delay for the state.

Technical problem which the claimed invention is directed, is to ensure the asymptotic stability of the equilibrium position of the system for periodic actions with a known temporal delay for the state.

The solution of this problem is due to the fact that in a system containing a unit job of the coefficients, the first summation block, the first multiplier, a second summation block, the delay unit, connected in series to the second multiplier and the object of regulation, according to the invention additionally introduced a second delay block, the second block set coefficients, block lag, third, fourth and fifth blocks of summation, third and fourth multipliers, the outputs of the object of regulation is connected to the corresponding inputs of the first unit of job factors, and unit delay, the outputs of which are connected to corresponding inputs of the second block set coefficients, the outputs of the first block of the task of the factors connected to respective inputs of the first unit summation, the output of the first summation block connected to the first and the second input of the first multiplier and to the second input of the second multiplier, the output of the first multiplier connected to the first input of the second summation block, W is the second input of the second summation block is connected to the output of the first delay unit, the output of the second summation block connected to the first input of the second multiplier and to the input of the first delay unit, the output of the second multiplier connected to the first input of the third summation block, the output of the second unit job factors connected to the corresponding inputs of the fourth block summation, the output of which is connected to the first and second inputs of the third multiplier and to the second input of the fourth multiplier, the output of the third multiplier connected to the first input of the fifth summation block, the second input is connected with the output of the second delay unit, the output of the fifth summation block connected to the first input of the fourth multiplier, and with the input of the second delay unit, the output of the fourth multiplier connected to the second input of the third summation block, the output of the third summation block is connected to the input of the regulation object.

The invention is illustrated in the drawing, which presents a block diagram of the system. The system contains the object of regulation 1, the first block of the task of the coefficients 2, the first summation block 3, the first multiplier 4, a second summation block 5, the first delay unit 6, the second multiplier 7, the third summation block 8, block lag 9, the second block set 10 coefficients, the fourth summation block 11, the third multiplier 12, the fifth summation block 13, the second delay unit 14, h is twenty multiplier 15, y1,...,ymthe outputs of the regulation object, u is a scalar control.

The object of the regulation is described by the equation:

where x(t) is the n-dimensional state vector of the object of the regulation;

A(t+T), D(t+T), b(t+T), respectively non-stationary matrix state matrix with delayed argument and the control vector, the elements of which are T-periodic functions of time;

y(t) is an m-dimensional vector of output coordinates of the regulation;

∗ the symbol of transposition;

L - matrix output;

τ - known temporary delay;

u(t) is a scalar control action that satisfies the relation:

where χper(t) - custom periodic coefficients contour adaptation;

α0that β0- m-dimensional vectors of coefficients of the first 2 and the second 10 blocks set coefficients, respectively, determined from the conditions:

,- Hurwitz polynomials of degree n-1 with positive higher coefficients, where α(λ) is the numerator of the transfer function of the object of regulation (1);

Using the methodology criteria giperustoichivost Vampirov, it can be shown that ensuring the asymptotic stability of system of regulation of the temperature is carried out by defining the settings of the regulator (2) in the form:

where γ0that γ1=const>0.

The system operates as follows.

The signals from the outputs of the object of regulation 1 go to corresponding inputs of a first block of the task of the coefficients 2 and the inputs of the delay unit 9. Within the first block of job factors 2 is the multiplication of the signal with the i-th input by a constant factor. The output signals of the first block set 2 coefficients are received at the respective inputs of the first summation block 3, where the fold. The output of the first summation block 3 goes to first and second inputs of the first multiplier 4, and the second input of the second multiplier 7. The output signal of the first multiplier 4 is supplied to the first input of the second summation block 5. To the second input of the second summation block 5 is fed the output signal of the first delay unit 6. The output of the second summation block 5 is input to the first delay unit 6 and the first input of the second multiplier 7, the output of which is fed to the first input of the third summation block 8. The output signals of the unit delay value τ 9 go to corresponding inputs of a second unit of job factors 10, inside of which are multiplied by the corresponding constant coefficients. The output signals of the unit job factors 10 on which are stated to corresponding inputs of a fourth summation block 11, where to fold. The output signal of the fourth block summation goes on first and second inputs of the third multiplier 12 and to the second input of the fourth multiplier 15. The output signal of the third multiplier 12 is supplied to the first input of the fifth summation block 13, to the second input of which is the output signal of the second delay unit 14. The output signal of the fifth summation block 13 is supplied to the first input of the fourth multiplier 15, and the input of the second delay unit 14. The output signal of the fourth multiplier 15 is supplied to the second input of the third summation block 8. The output of the third summation block 8 to the input of the object of regulation 1.

The technical result consists in ensuring the asymptotic stability of the equilibrium position of the system for periodic actions with a known temporal delay for the state.

This device can be implemented industrially based on standard components.

Adaptive control system for dynamic objects with periodic coefficients and delay containing block set coefficients, the first summation block, the first multiplier, a second summation block, the delay unit, connected in series to the second multiplier and the object of regulation, characterized in that additionally the introduction is by the second delay unit, the second block set coefficients, block lag, third, fourth and fifth blocks of summation, third and fourth multipliers, the outputs of the object of regulation is connected to the corresponding inputs of the first unit of job factors, and unit delay, the outputs of which are connected to corresponding inputs of the second unit job factors, the outputs of the first block of the task of the factors connected to respective inputs of the first unit summation, the output of the first summation block connected to the first and second inputs of the first multiplier and to the second input of the second multiplier, the output of the first multiplier connected to the first input of the second summation block, the second input the second summation block is connected to the output of the first delay unit, the output of the second summation block connected to the first input of the second multiplier and to the input of the first delay unit, the output of the second multiplier connected to the first input of the third summation block, the output of the second unit job factors connected to the corresponding inputs of the fourth block summation, the output of which is connected to the first and second inputs of the third multiplier and to the second input of the fourth multiplier, the output of the third multiplier connected to the first input of the fifth summation block, the second input is associated with you is a one second delay unit, the fifth output of the summation block connected to the first input of the fourth multiplier, and with the input of the second delay unit, the output of the fourth multiplier is connected to the second input of the third summation block, the output of the third summation block is connected to the input of the object of regulation.

 

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