RU1827664C - Self-adjusting control system with standard model - Google Patents

Abstract

The invention relates to control systems. The purpose of the invention is to improve the accuracy of the system, this is achieved by the fact that the system further comprises two exponentiation blocks, a first differentiator, a third multiplier and a second differentiator, a fourth multiplier and a fourth differentiator and a fifth differentiator and a third adder connected in series. 1 ill.

Description

The invention relates to control systems, and in particular, to control systems for a non-stationary object with a reference model synthesized based on the second L Punov method.

The purpose of the invention is to improve the accuracy of a non-stationary object control system.

This goal is achieved in that a self-tuning control system with a reference model further comprises a matrix amplifier, an adder, five differentiators, two exponentiation units and two multipliers.

Consider a non-stationary control object for simplicity and first order, but do not lose generality:

(p -a (t) p + b (t) gi

0)

where k (x) and nr) (t) are variable parameters that can be configured using the tuner,

g (t) is the input signal.

From (1) and (2) we write the equation of the control system

(t) + k (t) b (t) p + b (t) m (t) g. (3) We choose the equation of the reference model

l

(p p m + bg (4)

where a, b const О

p m (t.) - the output signal of the model. Denote

AND

00

go about

f-a (t) + k (t) b (t) + a Д k (t) b (t) m (t) - b - A m (t)

(5)

 where (f (t) is the output of the control object, g1 (t) is the control,

a (t), b (t) are variable coefficients.

And the management is presented in the form

gi (t) k (t) p + m (t) g,

(2)

Then, taking into account (5), from (3) and (4) we write

aef

the equation for the error is Ј - p (t) - f M (t): Ј -a e + A k (t) p + A m (t) g (6)

31827664 A

Denote 2rH dfed) V

DgptrMedG11 egdt.

c - A k (t) (p + Д m (t) g a s + e (7) to

 .ps where e a Ј + k

We choose the function A Punova 5 d d and d.

v - 0 5 (e2 + ktr2 + A mTp2), (8) AmH (t), and the value of customizable pairs is vv. . meters of the torus can be represented as

where AktP (t) and A mTp (t) are the required values (g irfrt - | cЫ - A Ut)

no current parametric deviations, 1 and A V. l A, Ak (t) and A m (t), respectively, and write SA mw A

derivative function A Punova05)

l j. l 2 l1 .1. l Am / t If we write the values AkH (t) and

v her + DKTO AKTD + Dttr Dttr (),

n vm and v 5 A mM (t) through their current values

We find the value of the derivative e from (7) A. m, m l (. -.

in the following form Jα, | f S ((I)

e - Ak, P «+ Д k, p p + Д Л, Р0 Д + nhpg and with (, 5) (, 6) and (5) we write for (Д

/ mm proportional law in the adaptation circuit

In view of (10), we write the derivative φW + А Ь 1® A k (t) b (t) - а + A k (t),

v -e (AkTp Aktp + А rfhpa-f А 25 (b (tXm (t) - Я) Am (t) b + Д m (t}

mTpg) + Akrp AkTp + A mTp Attr 0U

vvvv v Open loop error adaptation

Ch. Ak (t) and Д m (t) can be written in the form

If we now put the value 0 in the form 30 b (t) + k (b) b (t) + a - A k (t) - vI b {t} m (t0) - b Am (t),

t (18)

v "-0.5 (e pfn + (eg) 2 + AkTp J A ktpdt + and in closed from (17) we obtain for Д k3 (t) and

"OAm3 (t)

tv

+ AmTp / AmTpdt (12)

to

crest

n 1,2

Ak3 (t)

Ak (t)

.- Am (t)

it is necessary that the equal is fulfilled .- Am (t)

40

DG D-AkTpee, (19)

/ Д гптоД Anhpeg, In the case of proportional-differential differential-integral law in the circuit

J AkTp / fikrpdt - Д krpee, adaptations when changing the input signal

to45 g (t) and parameters of the control object a (t) and

A v. dd b (t) in the latter will be both static and

DttrPttrL-- And so on. And dynamic error, so you can

e k --fe ep) 2t 1 formulate the following statement:

ea Dt TR Cheagp The considered adaptive control system VV. 50 will be stable if deviations

parameters Дка (0 and Д m3 (t) will be such, And9 (13) we will immediately receive algorithms that the system with parameters

parameters i. .

i-a + Ak3 (t) a3 (t).

(.., 55 | b + Am3 (t) b3 (t)

Д kTp - - {е у)) 201 - Я- / (е p} di (14) (20)

 will satisfy the conditions of stability

Raussa - Hurwitz.

Thus, algorithms (14) allow

crest

Ak3 (t)

Ak (t)

.- Am (t)

- provide in the loop adaptation of the parameters,

-to limit the rate of change of the parameters of the control object.

This is evidenced by the derivative function of A Punov (12), which directly shows the convergence of algorithms (14) both in signal mismatch and in parametric.

Algorithms (14) were synthesized for the case where both zeros (t) and poles (2, 3) are adjusted.

In addition, in the synthesis of algorithms (14), it is not necessary to solve a system of equations for determining the components of the matrix P (2, 3), which greatly simplifies the synthesis,

The drawing shows a functional diagram of the control system, where the following notation is accepted: comparison blocks 1,2, adders 3,4,5, differentiators 6. 7, 8, 9, 10, amplifiers 11, 12,13, integrators 14,15. multiplication blocks 16.1 18.19, variable gain blocks 20, 21, non-stationary control object 22, reference model 23, power blocks 24 and 25.

The system operates as follows.

The input signal g (t) is input to the comparison unit 1, to the second input of which, through the variable gain block 20, the output signal p ($ of the control object is received. The control error signal from the output of the comparison block 1 through the variable gain 21 is control is input to the control object 22.

The signal g (t) is also transmitted through the reference model 23 of the system to the subtracting input of the comparison unit 2, where it is compared with the output signal of the object p (i.e.).

The discrepancy signal from the output of the comparator 2 Ј (t) serves to generate tuning signals for the parameters k (t) and m (t). The meaning of installing blocks of the functional diagrams 8, 9, 10, 11, 3, 4, 13. 15, 18. Sep 19 and 25 from the parameter adaptation algorithm is the first equation of the system of equations (14), and the second equation of this system is implemented by blocks 5, 6 , 7, 12, 14, 16, 17, 24 and the connections between them.

From the outputs of the adders to the settings inputs, respectively, D tn (0 go to the settings inputs, respectively blocks

20 and 21 with a variable gain. The gain of the blocks 20 and

21 are adjusted in such a way as to compensate for the parametric deviations Дк (т.) And Д m (t), which will be equal to zero when е О

Claims (1)

The claims A self-adjusting control system with a reference model, comprising a 5 reference model, the output of which is connected to the input of the system and the first input of the first multiplier unit, the output of which is connected to the input of the first integrator, the output of the first unit with a variable gain of 10 is connected to the first input of the first comparison unit, the control object, the output of which is the output of the system, the second comparison unit connected by the first input ic to the output of the reference model, the second 5 a multiplication unit connected by an output to the input of the second integrator, two amplifiers and a second unit with a variable gain, characterized in that, five differentiators are inserted into it, three 0 adder, two exponentiation blocks, the third and fourth blocks of multiplication, the third amplifier, the input of the system is connected to the input of the first differentiator and the second input of its comparison unit, connected by a valuable output through the second block with a variable gain to the input of the control object, the output of which is connected with the first input of the second block of multiplication, the information input of the first 0 unit with a variable gain, the input of the second differentiator and the second input of the second comparison unit, the output of which through the third amplifier and the third differentiator is connected respectively to the first and second inputs of the first adder, the outputs of the first and second differentiators are connected to the first inputs of the third and fourth blocks, respectively multiplication, the second inputs of which are connected to the output of the first adder and the second inputs of the first and second multiplication blocks, connected by the outputs through the first and second blocks and exponentiation sootvetst5 Wein to the inputs of the first and second amplifiers, the outputs of the third and fourth multiplying units, respectively connected to the inputs of the fourth and fifth differentiators, the outputs of which are connected to first inputs 0, respectively, of the second and third adders, connected by the outputs to the control inputs of the second and first blocks with a variable gain, respectively, the second and third inputs of the second 5 adder are connected to the outputs of the first amplifier and the first integrator, respectively, the second and third input of the third adder are connected to the outputs a second amplifier and a second integrator, respectively.