RU1807447C - Adaptive control system - Google Patents

Abstract

The invention relates to control systems with adaptation of controller parameters. The purpose of the invention is to increase accuracy, simplify and expand the scope of the system. The system contains six multipliers, four adders, a control object, a differentiator and three regulators. 1 ill.

Description

The invention relates to systems for controlling a non-stationary nonlinear object with additive interference arriving at the input of the system and inaccessible to measurement.

The purpose of the invention is to increase accuracy, simplify and expand the scope of the system.

Consider a non-stationary non-linear control object;

2 ai (x, ui.t) xO) + Ј, (t)

 b (x, u 1, t) u 1,

(1)

where ai, b are unknown nonlinear and non-stationary parameters of the object;

ui - scalar control;

Јr unknown interference.

The controller equation is chosen in the form

ul (t) m (t) u-k (t) (t) x. (2)

where ni (t), k (t) and ki (t) are customizable controller parameters;

x (t), x (t) n (t) are measurable output quantities and the input of the control system. We write the equation of the system:

OO

2 (x tui, t) x + | r (t). +.

.

+ a 1 (x, ui, t) + b (x, ui, t) x + (x, ui, t) + b (x, ui, t) k (t) ib (x, ui, t) m ( t) o + 2 | i (t). (3)

    - I about

We choose the equation of the reference model xjU (t) u. (4)

Further we denote Ј (t) A x-x / α, ai (x, ui, t) +

+ b (x, ui, t) ki (t) Ј + ki (t) a0 (x, u i, t) + b (x, u 1, t)

k (t) + Ak (t),

, b (x, ui, t) m (t) 1 + Am (t). (5)

c about h

t

I

ki (t) -A (ex + exdt),

to

In view of (5), from (3) and (4) we write e Am.u-Akx-Akix +

Y 8 |. (X.ui; t) x () + f Јl (t). (6) 5 m (t) 1-A (ex + -4iЈil + j udt). (and)

- P1 T l. tn

Od

I

I 2

ki (t) -A (ex + exdt),

to

We will adjust the controller parameters according to the principle of negative feedback

| k (t) -k (t0) + AkH (t), k (t0) 1 ki (t) ki (t0) + AkiH (t), ki (t0) o U (t) m (to) +. AmH (t). m (t0) 1. ()

To determine the values of AkH (t);. AkiH (t) n A mH (t) we compose the equation for the compensation of the discrepancy e (t) according to (6)

(t) u - AkH (t) x - AkiH (t) x. (8) Denote e AmH (t) u -Aki, (t) x -AkiH (t) x. (9) Choose a gradient

I AeЈn, (U)

and the parameter values will be considered such as to reduce the gradient (9) at each moment of time, for example, for the parametric increment AkH (t}:

AMO- -znrr + J-jsb

; .. From (11) taking into account (9) we write:

AkH (t) -A (cx + / Јxd (t).

to

Or finally with a lesson (7) we write the algorithm for adapting the parameters of the regulator

 k (t) 1 - A (f x H-), - (} k x d t),

The scheme of the proposed system is shown in the drawing.

The system contains multipliers 1-6, adders 7-10, control object 11, differentiator 12, and controllers 13-1.5, for example, PID controllers u (t} is the input signal of the system, x (t) is the output signal of the control object, Ј (t) is the interference, F (t) is the parametric interference.

The system operates as follows.

The input signal u (t) is supplied to the inputs of the multipliers 1 and 3 and to the summing input of the adder 7, to the subtracting input of which the output signal of the system x (t) is supplied. The signal e (t) from the output of adder 7 is supplied to the inputs of the multipliers 3,4 and 6, in which it is multiplied by u (t), x (t) and x (t), respectively. The result of multiplication from them goes to the inputs of the controllers 15, 13, and 14, respectively. Then, the signals from the outputs of the controllers 15,13 and 14 are fed to the inputs of the multipliers 1 and 2, respectively, through the adders 8 and 9, and directly to the input of the multiplier 5 (see. drawing). In multipliers x 1, 2 and 5, the signals received at the first inputs are multiplied with the signals u (t), x (t) n x (t), respectively. The signal x (t) is obtained by differentiating the signal x (t) in the differentiator 12. Thus, at the input of the control object 11, a signal obtained at the output of the adder 7 in the form (2), where the signals m (t), k (t) and ki (t) are defined in (13). ......

Claims (1)

The claims An adaptive control system containing a control object, three adders, a first controller and two multipliers, the output of the first multiplier connected to the input of the first controller, the output of which is connected to the first input of the first adder, the output of which is connected to the first input of the second multiplier, the output of which is connected with the first input of the second adder, the output of which is connected to the input of the control object, the output of which is connected to the output of the system, the first input of the first multiplier, the second input of the second multiplier and the first input the third adder, the output of which is connected to the second input of the first multiplier, while the first inputs of the second and the third adders are subtracting, characterized in that, in order to increase the accuracy and expand the scope of the system, it contains a fourth adder, a second and third regulators, a differentiator, and third to sixth multipliers, and the output of the control object through the differentiator is connected to the first inputs of the third and fourth multipliers, the input of the system is connected to the first inputs of the fifth and sixth multipliers and to the second input of the third adder, the output of which is connected to the second inputs of the third and fifth multiplier th outputs 0 5 which are connected to the inputs of the second and third controllers respectively, the output of the third controller is connected to the first input of the fourth adder, the output of which is connected to the second input of the sixth multiplier, the output of which is connected to the second input of the second adder, the third input of which is connected to the output of the fourth multiplier, the second the input of which is connected to the output of the second controller, while the second inputs of the first and fourth adders are connected to the input of value 1. and the third input of the second adder is subtracting.