SU1277067A1 - Adaptive control system for non-stationary linear object - Google Patents

Abstract

The invention relates to automatic control and can be used in automatic control systems for predominantly non-stationary processes. The invention makes it possible to increase the dynamic accuracy of adaptive object line control systems. The distinction of the invention, which ensures the achievement of the goal, is that the signals corresponding to the parameters of the tunable controller form a sequence by scaling the multidimensional signal, the components of which correspond to the parameters of the controller on the nominal mode, the first, second and third multidimensional signals. Moreover, the components of the first, second and third signals are obtained from signals that correspond to the actual parameters of the object and the parameters of the object in nominal (L mode. Invention can be widely used in adaptive systems for automatic control of linear objects. 1 hp, f-ly, 2 kp . J Od

Description

The invention relates to automatic control systems and can be used in the automatic control of technological processes with non-stationary parameters. The aim of the invention is to increase the dynamic accuracy of the systems. In Fig. 1, an adaptive control system of a non-stationary linear object is schematically depicted in Fig. 2 - shaper structure diagram. The adaptive control system of a linear object contains a control action measurement unit 1, a control object 2, a meter 3 of the output signal of the control object 2, an identification block 4 a block 5 of the adaptive control signal calculation 5. The output of the control measurement unit 1, the input of which is connected to the input of the control object 2, is connected to the first input of the identification unit 4, to the second input of which the output of the output signal meter 3 is connected, the output of the control object 2 is connected to the input of the output signal meter 3. In addition, the system includes the first 6 and second 7 blocks of formation, the block 8 of the reference parameters the first 9, the second 10, the third 11 and the fourth 12 matrix blocks of the multiplication matrix transposition unit 13 and the inversion matrix block 14. Adaptive control is made in the form of a PID controller with tunable parameters. The output of the meter 3 of the output signal of the control object 2 is connected to the signal input of the calculating signal block 5 of the adaptive control. The output of the first matrix multiplication unit 9, the first input of which is connected to the output of the second matrix multiplication unit 10, and the second to the output of the matrix transposition unit 13 and the first input of the third multiplication matrix unit 11 is connected to the first input of the fourth multiplication matrix unit 12. The output of the third matrix multiplication unit 11, the second input of which is connected to the output of the first formation unit b and to the input of the matrix understanding unit 13 via the inversion matrix unit 14 is connected to the second input of the fourth multiplication matrix unit 12, the output of which is connected to the parametric input of the signal calculation unit 5 adaptive control. The first output of the reference parameters block 8 is connected to the first input of the second formation block 7 and L to the second input of the first formation block 6, and the second output of the reference parameters block 8 is connected to the first input of the second matrix multiplication block 10, the second input of which is connected to the output of the second formation block 7 . The output of the Identification block 4 is connected from the first input of the first formation block 6 and to the second input of the second formation block 7, Each formation block 6 and 7 includes (d.2) the first 15 and second 16 cyclic shift registers, 2n + 2 first n - input adders 17, where n is the order of the control object, (2n + 2) n second adders 18, (2nj; 2) n first 19 and (2n + 2) second 20 multiplicators, the outputs of the first adders 17, each of n inputs of which are connected to the output of the corresponding second adder 18 are connected to the output of the forming unit and to the input of the first cyclic shift register 15, the output of which is connected to the corresponding output of the forming unit, and the input of the second cyclic shift register 16, the output of which is connected to the corresponding outputs of the forming unit, are connected to each input of each of the second adders 18 correspondingly connected first 19 and second 20 multiplication units, the first inputs of the first 19 and second 20 multiplication units being connected to the corresponding first inputs of the forming unit i and the second input of the first block 19 multiply - to the output of the second. The first multiplication unit 20, the second input of which is connected to the corresponding second input of the generation unit. The system works as follows. The control object and the PID controller in the frequency domain can be described by the following transfer functions. G (Is-A) B, is the transfer function where W. of the object, Wpp is the transfer function of the torus,. The adaptive control circuit achieves the system (1a) the dynamic characteristics of the reference model of the system, which can also be determined by the transfer functions of the reference object and the reference regulator. G “(IS- AI) G“. W „W. о -per - Me We represent W and W .. in the form According to the coefficients in section where a., Scientific research institute of the resolvent of the matrix A, A, respectively, b. , bj. are determined, through pairs of meters of the matrices A, A, B, B, G, C according to the Lever decomposition With regard to (1c), the control objective is represented as the relation Ev flbrsnc .. i 0V :: 0d 1.irO Пь ;. zpsmaz . d: i which is true for any S, if 2n + 2 equations are completed, which are obtained by equating the coefficients at the new powers of S in its left and right parts.

X is the state vector of the system of difference n, U is the control signal, u R and B are the matrix of the following form,

 , ..., „1, ve, Te (t

Coefficients aj, Ij: during the operation of an object can vary (2)

AT

 A, b

h

where A is the matrix of the following form.

a (t) e,

 diag 1, ..., 1

In-.

4-1

with a wide range. At the same time, in the nominal (calculated) mode, for example, when the system is started up, the parameters 31 of the control object have the values

b, j. (i € l, n). Dp security

Mi

well-known characteristics of the system of control 67) (.b, - a, b m, b;, + aJ) + C „, (a„ b M Mo obm1 / ICIoy - - - H-, h - - - - - G .. c-ha;, - b-s S The system (1g) can be put in the following matrix control MAY be mapped. LG. (1e) where G С,: G. G, l, and the matrix L, as follows from 1g It has a size () X. The second and third columns of it can be obtained from the first by a cyclic downward shift. The elements of the first column are determined according to the formula: 4.) -juv- / - Mao + ipi i where, obviously, the value of the elements whose indices are outside the interval are zero, (S 2 2n + l-jLi-i). -Vector G G,;. G, i.-G5l, la matrix 1, as follows from (1d), is defined in the same way as L, with the difference that bj is replaced by bj yamena by a. Mf) iH-n-f -ii Mi. The adaptation objectives reach, after the parametric input of the block 5, the parameter vector, which is the equation (1e):. G, L 4G (L4rL I G. Now we specify the relations (1e), 1g), revealing the relation b, b. with paraetra triplets of matrices (A, B, c1 A ,,, Bn, Cj,. Linear non-stationary object 2 of the board can be described by the following differential equation.

It is necessary that the parameters G,, G, GJ of the adaptive control signal calculation unit, which is the PID controller described by the equation

, (t) - GjEj (t) G3E ((t), (3) were equal to the nominal values

H1 ma mz, In equations (2)

Ej g - Y,

E, (

EE - EU), where g is the system control signal,

for G, ... Ojx is the output signal of the system.

Nominal values of parameters

M, CD W2

GI is stored in block 8 of reference parameters, to the first input of which information is given on the nominal values of the parameters a, .., a, b, ..., bn, and on the base, on the values GI,,, G,. At the output of each ju of the 2n + 2 first adders 17 of the first formation unit 6, a signal appears resulting from the summation of n signals, each of which is obtained by summing n signals of the form

l | u ajbs. .j.i (4)

where | u is the sequence number of the first adder, f e {1.2p +;);

ABOUT

Pe

T-Kn-H

2n-1 2.b-1 1.

where the elements l | M (i, s) are defined according to the formula {).

The structures of the first and second formation units are similar.

however, the output of the identification block 4 is connected to the first input of the generating unit 6, and the second input ь ..- 11 E: .., f. (i.s). ,,, ... (6)

(u (l, 2n + 2).

B is the result of i, -, L and signal G,: G from the second output of the block of 8 reference parameters

1 is the serial number of the second adder among n adders whose outputs are connected to the inputs of the corresponding pth first adder, S is the serial number of the second adder 18 among the n second adders connected to the i-th input of the 0th first adder 17.

bj.

In this case, the parameters

but

to

(i, j, k 1, n), whose index, for example S-i + 1, 2n + l-p-i) is less than one or greater than n, is equal to zero.

The implementation of signals of the form (4) is obtained by multiplying in the second block 20 the multiplication of the signal a, v /, - | uJi supplied about the corresponding second input of the first block 6

0 formation per signal a supplied from the first input of formation block 6. Further, the signal ,, |.,, In the first block 19 multiplies the house-; to signal

5 b .i, and takes the form specified in (4).

After summing up in the second 18 and first 17 adders and cycling the 0th shift in registers 15 and 16 on you-,

the course of the first formation unit 6 is given by a multidimensional signal of the following type,

L.H. (five) ,

 .r-1 i -1 ..

fMe (l,),

the first output of the reference parameter block 8, while the first output of the reference parameter block 8 is connected to the first input of the second formation block 7, and the output of the identification block B to the second output. Therefore, the output of the second block 7 of the formation takes place the signal

y-l i-1

through the system at the output of the fourth multiplication matrix block, the signal takes place

. 7 .12

-, t.

C (LG, (7) At the output of matrix 13 transposition, the signal .L occurs; at the output of the second multiplication matrix 10, the signal 1cG; at the output of the third multiplication matrix 11, the signal LL, which is then converted into an inversion matrix 14 the signal () which, being multiplied in the fourth matrix unit 12 multiplying by the signal L, coming from the output of the first matrix unit 9 multiplication, gives the signal G. The signal G is fed to the parametric input of the adaptive control signal calculating unit 5, you have compiled as indicated in Idea Pidregul torus.

When forming the parameters of the PID regulator in accordance with (7), the system is invariant with respect to parametric perturbations. The transfer function of the system can be represented as (1a), and the invariance condition is written

{in view of the equality of the transfer function

system to its nominal value.

770678

:, i.e. W, W, W ,,, (8) Open (7) and multiplying both sides of this equality by

T s - det (sI-A) det (sI-Ani), taking into account, 5 what f, f,.

C (sI-A) B (51 G s a, CA B) det (sI-A), 1--1 sH

will get

0,, J

: CI-s4c "- 5; & - 4. tt Afri ° 1 0 S i

(9)

Expression (9) is true for any s; therefore, the coefficients for the same power x s b of the right and left parts of x (9) are equal. Thus, relation (9) corresponds to 2p + 2 equations (by the number of different steppes s) that can be represented

as

LG. (10).

 G G ,, 7; G ;,; % V

Claims (2)

 Me M2n-1 2n 0 L L 2 -0 0 bn, Man-i Min-1 The regulator implements the procedure (7) or, equivalently, (10). Expression (10) is a condition of system invariance to parametric deviations, therefore, adjusting the controller in accordance with (7) ensures that the system is invariable to parametric deviations of the non-stationary linear control object (2). Formula of invention I. Adaptive control system of non-stationary linear object, containing control measurement unit, control object, object output signal meter b. s  Pri | yy control, identification unit, computing unit of the adaptive control signal, the output of the measuring unit of the controlling signal, whose input is connected to the input of the control object, 11 is connected to the first input of the identification unit, to the second input of which the output meter of the output signal is connected, output The control object is connected to the input of the output signal meter, characterized in that, in order to increase the dynamic accuracy of the system, it contains the first and second formation units, the unit of reference parameters, The first, second, third and fourth matrix multiplication blocks, the matrix transposition block and the inversion matrix block, the output meter of the output signal of the control object are connected to the signal input of the adaptive control signal calculation block, the output of the first multiplication matrix block, the first input of which is connected to the output of the second matrix block multiplication, and the second to the output of the matrix matching unit and the first input of the third matrix multiplication unit, is connected to the first input of the fourth matrix block and the multiplication, the output of the third matrix multiplication unit, the second input of ra, which is connected to the output of the first formation unit and to the input of the matrix transposition unit, through the inversion matrix unit is connected to the second input of the fourth matrix unit, the multiplication, output of which is connected to the parametric input of the signal calculation adaptive control, the first output of the block of reference parameters is connected to the first input of the second forming unit and to the second input of the first forming unit, and the second output of the unit When the standard parameters are connected to the first input of the second matrix multiplication unit, the second input of which is connected to the output of the second shaping unit, the output of the identification block is connected to the first input of the first block of the second 10 input and to the second shaping unit. 2. The system of claim 1, wherein the fuck formation contains, first and second cyclic shift, 2n + 2 first n-input adders (n is an order of the control object). (2p + 2) n second adders, (2p + 2) n first and (2p + 2) n second multiplication blocks, with the outputs of the first adders, each of whose n inputs are connected to the output of the corresponding second accumulator connected to the output of the forming unit and to the input of the first cyclic shift register, the output of which is connected to the corresponding output of the forming unit and to the input of the second cyclic shift register, the output of which is connected to the corresponding outputs of the forming unit, are connected to each input of each of the second adders correspondingly Suitable linking of the first and second multiplying units, wherein first inputs of first and second multiplier units connected to the respective inputs of the first forming unit and the second input of the first multiplying unit - to the exit of the second multiplying unit, the second input of which is connected to a corresponding second input of the imaging unit,