SU1575152A1 - Adaptive control system - Google Patents

Abstract

The invention relates to automation and can be used in the management of dynamic objects. The purpose of the invention is to expand the field of application by increasing the number of control signals and increasing the accuracy of their formation for the respective executive bodies. The adaptive control system contains a control object 1, a block of 2 angle sensors and accelerometers, a discrete Kalman filter 3, a synchronization block 4, a functional coefficient adaptation block 5, a situation analysis block 6, an extrapolation block 7, an actuator position sensor block 8, an actuator block 9 bodies, switches 10-18, blocks 19 adaptive formation of the control signal. The purpose of the invention is achieved by the introduction of a block of 8 sensors of the position of the executive bodies, the switch 18 and the blocks 19 of the adaptive formation of a control signal whose number is less than the number of the executive bodies. 1 il.

Description

The invention relates to automation and can be used in the management of dynamic objects.

The purpose of the invention is to expand the field of application by increasing the number of control signals and increasing the accuracy of their formation for the respective executive bodies.

The drawing shows a block diagram of an adaptive control system.

The adaptive control system contains (Fig. 1) a control object 1, a block of 2 angle sensors and accelerometers, a discrete Kalman filter

3., synchronization unit 4, functional coefficients adaptation unit 5, situation analysis unit 6, extrapolation unit 7, position sensor unit 8

executive bodies, block. 9 actuators, switches 10-18, blocks 19 of adaptive control signal generation.

The adaptive signal control unit blocks 19 contain (Fig. 1) blocks 20 of the model of free movement of the control object, quadrators 21, blocks 22 for calculating the function L of Punov Bellman, blocks 23 for numerical differential

SL

ate

HS

3 15751524

Rotentirovaniya, switches 2L and 25, -,,

, e. I 1, respectively, the mobile unit 26 division. Ge

in - - the beginning and convo basis of the adaptive device,

   The interval of the control optical system is as follows: „„ “.

 h mizatsii.

ratios. The dynamics of the object. The optimal control 0 should

control and its executive orga-minimize the functional (2) on the re ... .a .... H: xeni (Oh, if there is a positive

function V (p, x ,,,

stationary difference equations m i g, i

“Woo about satisfying with the following condition H;

Viyam

XM + 1 VI V (1)

Bw UI + SL {V (1) SXM4 ,, mind „) - V (M, VyH) +

where x - n is the dimensional state vector, 5g t Tm n fxix 1 + ttt p p +

 Mob control), + lxp J Moore

y - r - dimensional position vector

executive bodies; + v () ii /; / 7)

v I - MH

Uf / - m - dimensional control vector g

A. - respectively, the matrix 20g.

the state of the object, the eff is r0 - | V ((p + l) ,, y ./.1) of the control efficiency K

and the position of the performer-- v (u x v) + Ghg vTl O +

organs .. + LXM

System quality is assessed by c25

using a discrete analogue of the criterion, t, t R TI ../ hM p / l

generalized work GT X (V) | (7 and

Suppose for any point

I xj yt 1, уЈ and some of its surroundingsL at p

{-it know the value of the optimal

+ xt utL QM XH + functions L of the Punov-Bellman V (p, x, yw),

F-Mo1- and m NC (and view r r

+ UTRMUM + +

Dr. L .. ,, 35 ..

„W ir il (This point corresponds to some- U u + i I

4g, oe value of optimal control

 Suppose that at the beginning of each Ge, Q y - positively semi-optimized tact of the work cycle, certain matrices are produced;

R - positive definite initial conditions in the free matrix model of the Jth motion of an opamp V - function L of Punov – Bell45

45

mana {Г хм 1 Г А // in

 C

d - differential, respectively - D

w / ln L ° E J

No

x "

Have

/and

Kj

(6)

 scalar function at the start of each measure

V the vector argument-50 equality of ment, m g 1 1 1 sI Y Y Y

 + L e-JT T TTd v (h + D /, x

r g Szii- / b: jB the power of equation (1) given point + 1, xjL, yjJ «) - V (p p. K6 x And some

point х l, fi У r (+1 J, которой which su- «/ (li, y) - the evaluation of signals

 R N I e -, there is a function

go traffic

five

H xm 1 G A // in

 C

 D

W / L L ° E J

x "

Have

/and

Kj

(6)

V ((p + 1), hm + 1, ug,)

 w

We expand the function V (jU + 1), x „ft, y + t) in Taylor series with respect to the vector

(fxn) 1 (Y (Uti) T 3 and with Accounting (7) we get

V ((K + 1), xM + f, yjM ,,) V ((p + 1),

HM v + PtGt 3VKf + D.,) + X f / s- +

° w / u + i

+ 1 Fri rr 3tv ((. YЈi)

+ 2 and sr m 4G

(Eun „)

15

Cpv

(9)

Substituting (9) into (0 and performing the vector differentiation with respect to and „, we obtain the optimal discrete control in the form

tl, -r2Ru + C V (fX + 1)) g L K F chl / and x 2 (3yp4i)

.with 1st wound ((H + 1, xЈ ,, y% .and) n

 ° MJCMaTy u

aum

} and "

Considering that

-M .. M

U ((c + 1) ,, y ") -, Vy / J.

-t)) T Q, yKp (n

we obtain that control (10) optimizes the functional (2) on solutions (1) and satisfies (3), W. Expression (11) taking into account (7) can be written as

v ((K + i, xpM, yp - vcK. - - (12)

Mr. G Ly and J

Sum both parts of (12) over p (from p0 to (1-1) and taking into account the equality

EI ((n + 1) ,, Um.) -, U ((m + O.kh +) y ((H + 1)., YЈt,) (15)

Zoom (x +

t II D,

157515 vCCH + 0 .. ,, yf ,,) nf,

-t y,,;

will get

)

+ +

)

)

)

ten

“H,.“ J.J-t J G “i: l +

t

f-1

. m

,

+ t (x) t (y;) (i3)

 - Mr J

Since any of the pc (1-O) can be chosen as the initial one, it follows from (13)

V ((p + 1), xJXt, yЈ,)

20 +

- Г (хГ) Т (У) (1) f

25 Thus, during the operation of the system, to determine the optimal discrete control on each and-th cycle, it is necessary to solve the equations of the free motion model of the OS under the initial conditions (7), calculate the function V ((p + 1), x,

y) according to (14), by numerical differentiation, determine the first and second partial 35 derivative functions V ((f + 1),,

Ј- ВЕКТ ° РУ С (хрТ (NP to calculate U., using the formula (S)) The controls 40 thus synthesized affect the executive organs of the object during the i-th cycle. The vector is measured by ((+1) -th cycle

condition and the calculation cycle is repeated. Numerical differentiation of the function V ((p + 1), x, y)

m by the vector y ,, + 1 can be produced using the formulas of difference approximation of partial derivatives, taking into account the left and right differences:

+

t II D,

/and

m

U V ((HjJ XjtMiyjiii

U ((And + 1),) 2U ((and + 1), x, 1, yЈ.,) + U ((m + 1),) (16)

(DO) / H

- small value; ABOUT

, is the norm of the matrix D ,, LH. m

V ((p + 1), xЈf,,) are functions calculated on the basis of (with the initial condition (xp + 1, yD);

x

m

V (p + 1), xJ + 1fyЈ, + rfDM) and VO (fH-l), Ј + 1 LU-I Dp) Functions, computed 2n

U ((M + 1), xp +,, y. +, + Ogr) - U ((and + 1, xЈ, Y%)

Substituting (15) and (16) into (10) we define the optimal discrete control in the form:

Р V ((fx + 1), Ј ,, y Ј, + o / DM) -2V ((,, y Јf) + V ((H + 1),, y, -JI)

where K -;

Therefore, when controlling (17) is implemented, the calculated values of the partial derivatives must be submitted to the division unit.

For dynamic objects, the coefficients of the quality matrix should change according to the change in the dynamic characteristics of the object. The implementation of this approach is implemented as follows. Based on (11) accounting (5) ,. (8) the expression of the quality matrix is determined by the expression

 GR:

at

° 1g G AI VI

E JV 0Г ЕГ

(18)

The matrix of the Lnunov – Bellman function can be determined from the expression

g 7 eGU ((m + 1) (19)

. ., -, H

(3

m

X (L + f

m

.W

)

which follows from (10) when accounting (8). Expressions (18), (19) form the basis for determining the matrix of quality Qr, an extended control object during system operation.

based on (14) under initial conditions (xЈt, yy ,, WDp) and (xЈ,,

for jut, -ofDp) respectively.

Thus, to calculate partial derivatives, it is necessary to solve the equations of the free motion model of the extended control object three times on the optimization interval under various initial conditions,

Substituting (15) and (16) into (10) we define the optimal discrete control in the form:

0

five

0

Adaptive control system works as follows.

Non-zero angles of rotation, linear accelerations and positions of executive bodies (MOs) are measured by a block of 2 angle sensors and accelerometers and a block of 8 sensors of the position of executive bodies, signals from the output. which are received respectively at the information input of the first switch 10, the start input of the synchronization block k and the information input of the switch 18. The synchronization block k starts to function, and its fifth output receives a signal at the control inputs of the switches 10, 18. opens them. The signals from the outputs of block 2 and block 8 are received through 5 cutors 10 and 18 to the input of the discrete Kalman filter 3, which goes into a decision mode and at its output generates signals — estimates of the parameters and states of the extended control object. These signals are sent to the information inputs of switches 15, 16, the third input of the functional coefficients adaptation block 5 and the second input of extrapolation unit 7, the first input of which receives the coefficients of the matrix Hz of the function L of Punov-Bellman for the previous control signal generation cycle

0

five

outputs of units 23 for numerically differentiating the differentiation of units 19 for adaptive formation of a control signal.

In block 7 of extrapolation, the signals of extrapolated values and coefficients of the matrix of the Punov-Bellman function L are formed. These signals from the output of the extrapolation unit 7 are fed to the second input of the adaptation unit 5 of the coefficients of the functional that implements the calculation of the coefficients of the quality matrix by expression (18). The signals from the output of block 5 are fed to the control input of the switch 16, the information input of the switch 17 and the control input according to the coefficients of the functional of the situation analysis block 6. Block 6 generates matrix coefficients

ai qm + (

AiVr O E

OX

xGGLAIM J N ° E J

and defines the conditions for its positive definiteness, in which it is possible to use the control obtained in the previous formation tact in its new tact. In the case of positive definiteness of the matrix I. At the output of block 6, a zero signal is generated permitting the use of the control obtained in the previous cycle, and in the opposite case a single inhibit signal is generated. In the case of a zero signal at the output of block 6, the switches 10, 11, 12. 13, 14, 17 are open, and blocks 20-22 are in the initial state. In the case of a single signal at the output of block 6, switches 10, 11, 12, 13, 14.17 are closed. In this case, the signals from the output of the block 5 of adaptation of the coefficients of the functional come through the key 17 to the inputs of the control of the rearrangement according to the coefficients of the quality functional of the blocks 22 for calculating the function L Punow-Bellman. At the same time, the signals for evaluating the states of the extended control object from the output of the discrete Kalman filter 3 through the switch 15 are fed to the information inputs of blocks 20 of the model of free motion of the control object, and from the fourth output of block 4 of synchronization 751521 °

In this case, through a switch 14, a signal is fed to the decision start inputs with nominal initial conditions of blocks 20 of the model of free movement of the control object, in which the state vector of the extended model is determined under nominal initial conditions. Then by sig

JQ link from the third output of the synchronization unit 4 through the switch 13 receives a signal to the decision trigger inputs with increased initial conditions of the blocks 20, in which a decision is made with initial conditions (HUH + 4b). And finally

The signal from the second output of the synchronization unit k, through the switch 12-20, receives a signal at the decision trigger inputs with reduced initial conditions of the blocks 20, in which the state vector is determined under the initial conditions (x and

74 M

y - VD). Signals from block outputs

20 obtained as a result of three solutions through the corresponding quadrants

21 enter information inputs of blocks 22, providing in each

respectively, the calculation of the three values of the function Punov-Bellman

35

), vf, y; r "

five

On three solutions of the model equation, free movement with initial conditions equal to the estimated angles, linear accelerations and the positions of the executive bodies and with their values reduced by a small constant value.

The signals from the outputs of the blocks 22 are fed to the inputs of the corresponding blocks 23 of the numerical differentiation, realizing the calculations of private pro-. derivative functions L of Punov-Bellman by formulas (15), (16). According to the signal from the fourth output of the synchronization block C, fed through the switch 14 to the control inputs of the switches 24, 25, the signals about the values of the first partial derivatives of the variable are read from the first outputs of the blocks 23 of the numerical differentiation through the switch 24 to the inputs

eleven

Divisible division blocks 26, and the signal O values of the second partial derivatives are read from the second outputs of block 23 through switch 25 to the inputs of the splitter blocks 26. In blocks 26, in accordance with (17), m-signals of the optimal discrete control are calculated, then fed to the corresponding executive signals organs of the block 9 of executive bodies whose action on the control object leads to a decrease in its angles and linear accelerations.

Thus, the adaptive control system, unlike the prototype, provides not identical control signals for all executive bodies, but corresponding ones, which allows to increase the number of control signals, as well as to improve their accuracy for the executive bodies by using position information organs.

invention formula

Adaptive control system containing sequentially connected block of executive bodies, object of control, block of angle sensors and accelerometers connected by an output to the information input of the first switch and a trigger input of the synchronization block, the first to fourth outputs of which are connected to the information inputs of the switches from the second to fifth and the fifth output - with the control input of the first switch, connected through the Kalman discrete filter connected in series, the sixth A switch, an adaptive control signal shaping unit to the input of the actuator unit, the first information input of the situation analysis block is connected to the second output of the adaptive control signal shaping unit, the first input of the functional coefficients adaptation block and through the extrapolation unit to the second input block adapting the coefficients of the functional connected by the third input to the second input of the extrapolation block,

one

12

five

five

0

five

0

five

0

five

a discrete Kalman filter and information input of the seventh switch, the output of which is connected to the second information input of the situation analysis block, and a control input to the output of the functional coefficients adaptation block, information input of the eighth switch and control input by the coefficients of the quality of the situation analysis block connected to the control inputs of the switches from the second to the sixth and eighth outputs of which are connected to the input of the control of the rearrangement according to the coefficients of the functional the quality of the adaptive control signal generation unit connected by the switching control input and the decision start input under nominal initial conditions with the output of the fifth switch, the decision start input with increased initial conditions, and the first control input of the operating modes with the output of the fourth switch, the decision start input with reduced initial conditions and the second input of operating mode control with the output of the third switch, the third input of operating mode control1 with the second output A switch, characterized in that, in order to expand the scope of application by increasing the number of control signals and improving the accuracy of their formation for the corresponding actuators, a block of actuators position sensors, a ninth switch, and additional blocks of adaptive shaping of the control signal, a number per unit less than the number of executive bodies, the output of the block of executive bodies through the series-connected block of the position sensor of the executive bodies and The second switch is connected to the second input of a discrete Kalman filter, the control inputs of the nine and first switches are combined, the inputs of the same name and the second outputs of the adaptive control signal generation units are combined, and their first outputs are connected to the corresponding inputs of the actuator unit.

Claims (1)

Claim An adaptive control system, comprising a series-connected block of executive bodies, a control object, a block of angle sensors and accelerometers connected to the information input of the first 52 discrete Kalman filter and the information input of the seventh switch, the output of which is connected to the second information input of the situation analysis unit, and the control input to the output of the functional coefficient adaptation block, the information input of the eighth switch and the control input by quality functional coefficients of the situation analysis unit, connected by the output to the control inputs of the switches from the second to the sixth and the eighth, the output of which 5 is connected to the adjustment control input according to the coefficients of the quality functional of the adaptive control signal generation unit, connected by the switching control input and the solution trigger input under nominal initial conditions with the output of the fifth switch, the input of the start of the solution under increased initial conditions and the first input of the control operation modes - with the output of the fourth switch, the input to start the solution under reduced initial conditions and the second input of the operating mode control · with the output [0 of the third switch, the third input of the operating mode control '- with the output of the second switch, characterized in that, in order to expand the scope of application due to the th switch and the start input of the synchronization unit, the outputs from the first to the fourth of which are connected to the information inputs of the switches, respectively, from the second to the fifth, and the fifth output is, with the control input of the first switch, sub connected through a sequentially connected discrete Kalman filter, sixth switch, adaptive control signal generation unit to the input of the executive • unit, the first information input of the situation analysis unit is connected to the second output of the adaptive control signal generation unit, the first input of the functional coefficient adaptation block and through the block extrapolation - to the second input of the block .adaptation of coefficients of the functional connected by the third input to the second input of the extrapolation block, the output of u the number of control signals 35 and increase the accuracy of their formation for the corresponding executive bodies, a block of sensors for positioning the executive bodies, the ninth switch and additional blocks for adaptive formation of the control signal, one less than the number of executive bodies, the output of the block of executive 45 bodies through series-connected a block of position sensors of the executive bodies and the ninth switch is connected to the second input of a discrete Kalman filter, controlling moves the first minutes of the ninth switches are united, and the second inputs of the same name zyhody blocks adaptively generating the control signal are combined, and their first outputs connected to respective inputs of unit 55 executive.