RU2530278C1 - Combined robust control system for a priori indefinite objects of intermittent action with lagging - Google Patents

Abstract

FIELD: machine building.

SUBSTANCE: system includes two coefficient setting units, a lag unit, six adders, four multipliers, two delay units and a controlled object.

EFFECT: provision for stability at controlling unstable objects with non-periodical external disturbances and lagging as per the state.

1 dwg

Description

The invention relates to technical cybernetics and can be used in control systems of a priori indefinite non-stationary dynamic objects of periodic action with a state lag.

The closest technical solution to the proposed one is an adaptive control system for dynamic objects with periodic coefficients and delay (RF Patent No. 2450301, Official Gazette “Inventions and Utility Models.” - 2012, No. 13, prototype), containing the first and second blocks for setting the coefficients, delay unit, first, second, third, fourth and fifth summing blocks, first, second, third and fourth multipliers, first and second delay blocks and an object of regulation, the outputs of which are simultaneously connected to the corresponding inputs of the first block for setting the coefficients and the inputs of the block for delay, the outputs of the first block for setting the coefficients are connected to the inputs of the first block of summation, the output of which is connected to both inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the first input of the second summing block, the output of which connected to the first input of the second multiplier and the input of the first delay unit, the output of the first delay unit is connected to the second input of the second summing unit, the output of the second o the multiplier is connected to the first input of the third summing unit, the outputs of the delay unit are connected to the corresponding inputs of the second coefficient setting unit, the outputs of which are connected to the corresponding inputs of the fourth summing unit, the output of which is connected to both 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 summing unit, the output of which is connected to the first input of the fourth multiplier and the input of the second delay unit, the output of the second of the second delay unit is connected to the second input of the fifth summing unit, the output of the fourth multiplier is connected to the second input of the third summing unit, the output of which is connected to the input of the control object.

However, the disadvantage of this system is the loss of performance in case of instability of an a priori indefinite control object, as well as the presence of parameters that are non-periodic functions of time.

The objective of the invention is to expand the functionality of the system, in particular ensuring stability when controlling unstable objects with non-periodic external disturbances and state lag.

The solution to this problem is achieved by the fact that in a combined robust control system for a priori indefinite objects of periodic action with delay, containing the first and second blocks for setting coefficients, a delay block, the first, second, third, fourth and fifth summation blocks, the first, second, third and the fourth multipliers, the first and second delay units, the control object whose outputs are simultaneously connected to the corresponding inputs of the first unit for setting the coefficients and the inputs of the unit are delayed ia, the outputs of the first coefficient setting block are connected to the inputs of the first summing block, the output of which is connected to both inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the first input of the second summing block, the output of which is connected to the input of the first delay block, the output of the first the delay unit is connected to the second input of the second summing unit, the output of the second multiplier is connected to the first input of the third summing unit, the outputs of the delay unit are connected to the corresponding by the inputs of the second coefficient setting block, the outputs of which are connected to the corresponding inputs of the fourth summing block, the output of which is connected to both inputs of the third multiplier and to the second input of the fourth multiplier, the output of the third multiplier is connected to the first input of the fifth summing block, the output of which is connected to the first input of the fourth the multiplier and the input of the second delay unit, the output of the second delay unit is connected to the second input of the fifth summing unit, the output of the fourth multiplier is connected to the second ode third summing unit, an output connected to an input of the controlled object, is additionally introduced sixth summing unit having a first input coupled to the output of the first multiplier, a second input with the output of the second summing unit, and the output of the sixth summing unit connected to the first input of the second multiplier.

The inclusion in the system of an additional summing unit allows you to build a workable control system for unstable dynamic objects of periodic action with non-periodic external perturbations and delayed state.

The invention is illustrated in the drawing, where Fig.1 shows a block diagram of a control system. The system comprises: regulation object 1, first coefficient setting unit 2, first summing unit 3, first multiplier 4, second summing unit 5, first delay unit 6, second multiplier 7, third summing unit 8, delay unit 9, second coefficient setting unit 10 , the fourth summing block 11, the third multiplier 12, the fifth summing block 13, the second delay block 14, the fourth multiplier 15, the sixth summing block 16, y ₁ , ..., y _m are the outputs of the control object, u is the scalar control action, f are external perturbations of the regulatory object ligation.

The object of regulation is described by the equations

$$\frac{dx\left(t\right)}{dt}=A\left(t+T\right)xD\left(t+T\right)x\left(\tau -t\right)+b\left(t+T\right)u\left(t\right),y\left(t\right)=L^{T}x\left(t\right),(\mathrm{one})$$

where x (f) is the n-dimensional vector of state variables of the regulatory object;

A (t + t) is an unstable state matrix;

D (t + T) is a non-stationary matrix with a delayed argument;

b (t + T) is the non-stationary control vector;

T is the period of changing the parameters of the matrices and the vector of the object;

f (t) is a vector of external constantly acting disturbances satisfying the condition

$$f^T\left(t\right)=\left[0...\mathrm{,\; 0,}{f}_n\left(t\right)\right];f_n\left(t\right)=|\; |\; |f_{Pe{R}_n}\left(t\right)+f_{nePe{R}_n}\left(t\right)|\; |\; |\le f_n^2=const>0;(2)$$

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

L is the output matrix;

τ is the known time delay;

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

$$u\left(t\right)=-{\chi }_{\mathrm{one}}\left(t\right)\left({\alpha }_0^{T}y\left(t\right)\right)-{\chi }_2\left(t\right)\left({\beta }_0^{T}y\left(t-\tau \right)\right),(3)$$

where χ ₁ (t), χ ₂ (f) are custom coefficients of the adaptation loop;

α ₀ , β ₀ are the w-dimensional vectors of the coefficients of the first 2 and second 9 blocks for setting the coefficients, respectively, chosen from the conditions: α ₀ α (λ), β ₀ α (λ) are Hurwitz polynomials of degree (n-1) with positive coefficients ; α (λ) is the numerator of the transfer function of the regulatory object (1), (2).

Using the methodology of V. M. Popov’s criterion of hyperastability, it can be shown that by synthesizing the settings of the controller parameters (3) in the form (4), the dissipative stability of the control system is

$$\begin{array}{cc}\begin{array}{l}{\chi }_{\mathrm{one}}\left(t\right)={\chi }_{\mathrm{one}PeR}\left(t\right)+{\chi }_{\mathrm{one}R\mathrm{but}b}\left(t\right),\\ {\chi }_{\mathrm{one}PeR}\left(t\right)={\chi }_{\mathrm{one}PeR}\left(t\right)-{\gamma }_0{\left({\alpha }_0^{T}y\left(t\right)\right)}^2,{\chi }_{\mathrm{one}R\mathrm{but}b}\left(t\right)=-\gamma \left({\alpha }_0^{T}y\left(t\right)\right),\\ {\chi }_2\left(t\right)={\chi }_2\left(t-T\right)-{\gamma }_2{\left(B_0^{T}y\left(t-\tau \right)\right)}^2,\end{array}& (\mathrm{four})\end{array}$$

where γ ₀ , γ ₁ , γ ₂ are some positive constant values. The system operates as follows.

The signals from the outputs of the control object 1 simultaneously arrive at the corresponding inputs of the first block for setting the coefficients 2 and the delay unit 9. Inside the first block for setting the coefficients 2, the ith signal is multiplied by a constant coefficient α _i , i = 1, ..., m. The output signals of the first block for setting coefficients 2 go to the inputs of the first block of summation 3, inside which are added. The signal from the output of the first summing unit 3 is fed to both inputs of the first multiplier 4 and to the second input of the second multiplier 7. The output signal of the first multiplier 4 with the corresponding coefficients is fed to the first input of the second summing unit 5 and to the first input of the sixth summing unit 16. The output signal the second summing unit 5 is simultaneously fed to the input of the first delay unit 6 and to the second input of the sixth summing unit 16. The output signal of the first delay unit 6 goes to the second input of the second summing unit 5. The signal from The ode of the sixth summing unit 16 is supplied to the first input of the second multiplier 7, the output signal of which is supplied to the first input of the third summing unit 8. The signals from the output of the delay unit 9 are supplied to the corresponding inputs of the second unit for setting the coefficients 10, inside which are multiplied by the corresponding constant coefficients D. The output signals of the second block for setting coefficients 10 go to the corresponding inputs of the fourth block of summation 11, where they add up. The signal from the output of the fourth summing block 11 is simultaneously fed to both inputs of the third multiplier 12, as well as to the second input of the fourth multiplier 15. The output signal of the third multiplier 12 with an appropriate coefficient goes to the first input of the fifth summing block 13, the output signal of which is fed to the input of the second the delay unit 14 and the first input of the fourth multiplier 15. The output signal of the second delay unit 14 goes to the second input of the fifth summing unit 13. The signal from the output of the fourth multiplier 15 goes to the second input of the third block summation 8, the output signal of which is supplied to the input of the regulatory object 1.

The technical result is to ensure the stability of the system when controlling unstable a priori indefinite dynamic objects with non-periodic external disturbances and state lags. This device can be implemented industrially based on a standard elemental base.

Claims (1)

Combined robust control system for a priori indefinite objects of periodic action with delay, containing the first and second blocks for setting coefficients, a delay block, the first, second, third, fourth and fifth blocks of summation, the first, second, third and fourth multipliers, the first and second delay blocks , an object of regulation, the outputs of which are simultaneously connected to the corresponding inputs of the first block for setting coefficients and the inputs of the delay unit, the outputs of the first block for setting coefficients inens with the inputs of the first summing unit, the output of which is connected to both inputs of the first multiplier and the second input of the second multiplier, the output of the first multiplier is connected to the first input of the second summing unit, the output of which is connected to the input of the first delay unit, the output of the first delay unit is connected to the second input of the second the summing unit, the output of the second multiplier is connected to the first input of the third summing unit, the outputs of the delay unit are connected to the corresponding inputs of the second unit for setting the coefficients, the moves of which are connected to the corresponding inputs of the fourth summing block, the output of which is connected to both inputs of the third multiplier and to the second input of the fourth multiplier, the output of the third multiplier is connected to the first input of the fifth summing block, the output of which is connected to the first input of the fourth multiplier and the input of the second delay block, the output of the second delay unit is connected to the second input of the fifth summing unit, the output of the fourth multiplier is connected to the second input of the third summing unit, the output of which it is single with the input of the control object, characterized in that a sixth summing unit is additionally introduced, the first input of which is connected to the output of the first multiplier, the second input with the output of the second summing unit, and the output of the sixth summing unit is connected to the first input of the second multiplier.