RU2775514C1 - Control system based on the state of the control object with an observer and a state controller - Google Patents

Abstract

FIELD: automation.

SUBSTANCE: invention relates to automation and can be used in control systems of a priori uncertain non-stationary dynamic objects with state variables inaccessible to direct measurement. The essence of the invention consists in the fact that the control system for the state of the control object with an observer and a state controller includes a state observer, as which a digital filter for non-stationary signals is used, making it possible for a nonlinear process/system model to be used to assess the state of the controlled object and ensuring the stable operation of the control system under the conditions of non-stationary processes, while the setting effect for the control system is the required values of the state variables of the controlled object, for this purpose, the control system also contains: a controlled object, a delay unit, a state controller, a state error conversion unit, a Jacobi matrix correction unit, a control action formation unit, and an actuator unit. The introduction of additional units and a new connection scheme in the control system according to the state of the control object with an observer and a state controller made it possible to expand the functionality of the control system by using the system as the setting effect of the required values of the state variables of the controlled object and the use of a state observer, having the ability to use a nonlinear process/system model to assess the state of a controlled object and ensuring the stable operation of a control system for non-stationary dynamic objects with state variables inaccessible to direct measurement.

EFFECT: providing the possibility of controlling indefinite non-stationary dynamic objects with state variables inaccessible to direct measurement and having non-periodic external disturbances, using the required values of the state variables of the controlled object in the control process.

1 cl, 5 dwg

Description

The invention relates to automation and can be used in control systems for a priori indefinite non-stationary dynamic objects with state variables inaccessible to direct measurement.

The closest technical solution to the proposed one is a combined robust control system for a priori indefinite dynamic objects of periodic action with an observer (patent for invention 2528155, publication date 09/10/2014) [1], which contains: a state observer, a block for setting coefficients, the first block summation, the first multiplier, the second summing block, the delay block, the second multiplier and the control object connected in series, the third summing block. This system is designed to control a priori indefinite non-stationary dynamic objects with state variables inaccessible to direct measurement and having non-periodic external disturbances.

The disadvantage of such a control system is the use of a state observer in it, one of the inputs of which must receive a control signal that also arrives at the regulated object. There are control problems in the state space for which the state observer model partially or completely lacks information about the control signal (control action) and control coefficients. In this case, the driving force for the system is the required values of the state variables of the controlled object, expressed as a vector of the required state, and the elements of the output vector of the controlled object are the measured values of physical quantities to be estimated and transformed (for example, complexing) by the state observer in order to obtain the state vector .

The objective of the invention: improvement of the control system for uncertain non-stationary dynamic objects with state variables inaccessible to direct measurement under conditions of non-periodic external disturbances in order to expand the functionality of the system by using the system as a setting effect of the required values of the state variables of the controlled object.

The problem is solved by the fact that in the control system by the state of the control object with an observer and a state controller, containing a controlled object, the output of which is the system output vector, the state observer, the input of which is the system output vector from the output of the controlled object, the delay block, the control system by state controller with an observer and a state controller includes a state controller, a state error transformation block, a Jacobi matrix correction block, a block for generating control actions, a block of actuators, and the state observer is a digital filter for non-stationary signals, which is an extended Kalman filter, supplemented by an adaptive digital filter with the NLMS adaptation algorithm, and the input of the state observer at the initial time of the control system operation receives the initial Jacobi matrix of the observation function, while the input of the state observer from the output of the correction block of the Jacobian matrix post the corrected Jacobi matrix of the observation function drops, and the output of the state observer is the Jacobi matrix of the observation function, which is relevant at the previous moment of time, while the output of the state observer is the current vector of corrected values of the system state estimate and the vector of values of the a posteriori estimate of the system state, while at the input of the delay block the current vector of corrected values of the system state estimate comes from the output of the state observer, while the output of the delay block is the vector of corrected values of the system state estimate at the previous moment of time, and the current vector of corrected values of the system state estimate and the vector of values a posteriori assessment of the system state, while the input of the state controller from the output of the delay block receives a vector of corrected values of the system state assessment at the previous moment of time, and at the state controller stroke, the vector of required states is supplied, while the output of the state controller is the state error vector, and the state error vector is supplied to the input of the state error transformation block from the output of the state controller, and the corrected matrix is supplied to the input of the state error transformation block from the output of the Jacobi matrix correction block Jacobi function of observations, while the output of the block for transforming the state error is the error vector of the system output, and the input of the Jacobi matrix correction block from the output of the controlled object receives the system output vector, and the input of the Jacobi matrix correction block from the output of the state observer receives the Jacobi matrix of the observation function, actual at the previous moment of time, while the output of the correction block of the Jacobi matrix is the corrected Jacobi matrix of the observation function, and the vector o errors of the system output, and the diagonal matrix of gain coefficients, the vector of absolute values of the maximum values of the powers of the actions, the vector of the absolute values of the maximum values of the error of the system output, are supplied to the input of the block for the formation of control actions, while the output of the block for the formation of control actions is the vector of the powers of the actions and the vector of the directions of the actions, moreover, the input of the actuator block from the output of the block for generating control actions receives the power vector of actions and the vector of directions of influences, while the output of the block of actuators is force and/or kinematic actions directed at the controlled object and expressed as elements of the action vector.

The problem is also solved by the fact that the state controller includes: the first multiplication block, the input of which from the output of the state observer receives the current vector of corrected values of the system state assessment, and the input of the first multiplication block from the output of the adaptation block included in the state controller receives the diagonal matrix of element weights of the current vector of corrected values of the system state assessment obtained at the previous moment of time, while the output of the first multiplication block is the product of the diagonal matrix of weights of the elements of the current vector of corrected values of the system state assessment and the current vector of corrected values of the system state assessment; the second multiplication block, the input of which from the output of the state observer comes the vector of values of the a posteriori estimate of the state of the system, and the input of the second multiplication block from the output of the adaptation block included in the state controller receives the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimate of the state of the system, obtained in the previous time point, wherein the output of the second multiplication block is the product of the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimate of the state of the system and the vector of values of the a posteriori estimate of the state of the system; the first summation block, the input of which, from the output of the first multiplication block, is the product of the diagonal matrix of weights of the elements of the current vector of corrected values of the assessment of the state of the system and the current vector of corrected values of the assessment of the state of the system, and the input of the first summation block, from the output of the second multiplication block, is the product of the diagonal matrix of weights elements of the vector of values of the a posteriori estimate of the state of the system and the vector of values of the a posteriori estimate of the state of the system, while the output of the first summing block is the vector of the arithmetic mean weighted value, which is equal to the sum of two products: the product of the diagonal matrix of weights of the elements of the current vector of corrected values of the estimate of the state of the system and the current vector of corrected values estimates of the state of the system, the product of the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimate of the state of the system and the vector of values of the a posteriori assessing the state of the system; the first subtraction block, the input of which is the vector of the arithmetic weighted average value from the output of the first summation block, and the vector of required states is fed to the input of the first subtraction block, while the output of the first subtraction block is the state error vector, which is fed to the output of the state controller and to the input of the third the summation block included in the state controller, while the state error vector is equal to the difference of the vectors: the vector of the required states and the vector of the arithmetic mean weighted value; the second summation block, the input of which from the output of the state observer receives the current vector of corrected values of the assessment of the state of the system, and the input of the second summation block from the output of the delay block receives the vector of corrected values of the assessment of the state of the system at the previous point in time, while the output of the second summation block is the sum vectors: the current vector of adjusted values of the assessment of the state of the system and the vector of adjusted values of the assessment of the state of the system at the previous point in time; a division block, the input of which from the output of the second summation block receives the sum of the current vector of corrected values of the system state assessment and the vector of corrected values of the system state assessment at the previous point in time, while the output of the division block is the result of dividing by constant 2 the sum of the current vector of corrected values of the state assessment system and the vector of corrected values of the assessment of the state of the system at the previous point in time; the third summation block, the input of which from the output of the first subtraction block receives the state error vector, and the input of the third summation block from the output of the division block receives the result of dividing by constant 2 the sum of the current vector of corrected values of the system state assessment and the vector of corrected values of the system state assessment to the previous a point in time, wherein the output of the third summation block is the sum of the state error vector and the result of dividing by a constant 2 of the sum of the current vector of corrected values of the system state estimate and the vector of corrected values of the system state estimate at the previous point in time; the second subtraction block, the input of which from the output of the third summation block receives the sum of the state error vector and the result of division by a constant 2 of the sum of the current vector of corrected values of the system state assessment and the vector of corrected values of the system state assessment at the previous point in time, and the input of the second subtraction block receives the vector of required states, while the output of the second subtraction block is the error vector of the output of the state controller, which is equal to the difference of the vector of required states and the sum of the state error vector and the result of dividing by a constant 2 of the sum of the current vector of corrected values of the system state assessment and the vector of corrected values of the system state assessment to the previous moment of time; adaptation block, the input of which from the output of the second subtraction block receives the error vector of the output of the state controller, while the output of the adaptation block is the diagonal matrix of weights of the elements of the current vector of corrected values of the assessment of the state of the system, obtained at the previous point in time, and the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimates of the state of the system obtained at the previous time.

In the control system, a digital filter for non-stationary signals is used as a state observer, which is an extended Kalman filter, supplemented by an adaptive digital filter with the NLMS adaptation algorithm [2]. The digital filter for non-stationary signals allows using a non-linear process/system model to estimate the state of a controlled object and ensures stable operation of the control system for non-stationary dynamic objects with state variables that are not directly measurable. The control system, in addition to the controlled object (regulated object), the state observer, the delay block, includes: the state controller, the state error conversion block, the Jacobi matrix correction block, the block for generating control actions, the block of actuators, which allows the control system to use the required the values of the state variables of the managed object. This control system is a control system based on the state of the control object with an observer and a state controller.

The essence of the invention is illustrated by the drawing, where in Fig. 1 indicates the components of the control system according to the state of the control object with an observer and a state controller:

1 - managed object,

2 - state observer (digital filter for non-stationary signals [2]),

3 - delay block,

4 - state regulator,

5 - state error conversion block,

6 - Jacobi matrix correction block,

7 - block for the formation of control actions,

8 - block of actuators.

In FIG. 2 indicates the components of the state controller 4, which is part of the control system for the state of the control object with an observer and a state controller:

4-1 - the first multiplication block,

4-2 - second multiplication block,

4-3 - the first block of summation,

4-4 - the first subtraction block,

4-5 - the second summation block,

4-6 - division block,

4-7 - the third summation block,

4-8 - second subtraction block,

4-9 - adaptation block.

The technical result of the invention lies in the fact that the control system according to the state of the control object with an observer and a state regulator includes a state observer, which is used as a digital filter for non-stationary signals [2], which allows using a nonlinear process/system model to assess the state of the controlled object and ensuring stable operation of the control system under the conditions of action of non-stationary processes, while the master influence for the control system is the required values of the state variables of the controlled object, for which the control system also contains: a controlled object, a delay block, a state controller, a state error conversion block, a correction block Jacobian matrices, a block for generating control actions, a block of actuators, which allows the control system to control the state of the control object with an observer and a state controller to control uncertain non-stationary dynamic objects ami with state variables inaccessible to direct measurement under conditions of non-periodic external disturbances in order to expand the functionality of the control system.

The model of some controlled system is described by the expressions:

, (1)

, (one)

, (2)

, (2)

where:

x (k) - state vector, vector dimensionn;

u (k) is the vector of control actions, the dimension of the vectore;

y (k) - system output vector, vector dimensionm;

F (•) - some non-linear smooth vector function of the process (state change) with dimensionn, which has first-order partial derivatives with respect to all variables in the vicinity of some point ( x (k), u (k));

H (•) - some non-linear smooth vector function of observations with dimensionm, which has first-order partial derivatives with respect to all variables in the vicinity of some point ( x (k), u (k));

k - some current moment of time;

( k - 1) - the previous moment in time.

Let us assume that this nonlinear model of the controlled system is known and can be linearized using Jacobi matrices:

, (3)

, (3)

, (4)

, (four)

, (5)

, (5)

where:

- квадратная матрица Якоби частных производных функции процесса (изменения состояния) по аргументу x , размерность матрицы n×n;

- square Jacobi matrix of partial derivatives of the process function (change of state) with respect to the argument x , dimension of the matrix n × n ;

- прямоугольная матрица Якоби частных производных функции процесса (изменения состояния) по аргументу u , размерность матрицы n×e;

- rectangular Jacobi matrix of partial derivatives of the process function (change of state) with respect to the argument u , the dimension of the matrix is n × e ;

- прямоугольная матрица Якоби частных производных функции наблюдений по аргументу x (далее матрица Якоби функции наблюдений), размерность матрицы m×n;

- rectangular Jacobi matrix of partial derivatives of the observation function with respect to the argument x (hereinafter, the Jacobi matrix of the observation function), the dimension of the matrix is m × n ;

x ₁ , …, x _n - elements of the vector x of the state of the system;

u ₁ , …, u _e - elements of the vector u of control actions;

F ₁ (•), …, F _n (•) - elements of the vector function F (•);

H ₁ (•), …, H _m (•) are elements of the vector function H (•).

Using matrices (3), (4), (5), we rewrite expressions (1) and (2) [3, 4]:

, (6)

, (6)

, (7)

, (7)

where ( k + 1) is the point in time following the point in time k .

The control system based on the state of the control object with an observer and a state regulator works as follows.

размерностью m×n.The system output vector y ( k ) of dimension m from the output of controlled object 1 is fed to the input of state observer 2 - a digital filter for non-stationary signals, described in [2]. The vector y ( k ) is also supplied to the correction block of the Jacobian matrix 6 (Fig. 1). At the initial time of operation of the control system, the input of state observer 2 receives the initial Jacobi matrix of the observation function

dimension m × n .

, размерностью m×n (фиг. 1). At the input of state observer 2, the corrected Jacobi matrix of the observation function

, dimension m × n (Fig. 1) .

From the state observer 2 to the inputs of the state controller 4 come (Fig. 1):

- текущий вектор скорректированных значений оценки состояния системы в некоторый момент времени k [2],

- the current vector of corrected values of the assessment of the state of the system at some point in time k [2],

- вектор значений апостериорной (нескорректированной) оценки состояния системы [2].

- vector of values of a posteriori (uncorrected) assessment of the state of the system [2].

, актуальная в предыдущий момент времени (k – 1) и поступающая на вход блока коррекции матрицы Якоби 6 (фиг. 1).The output of state observer 2 is also the Jacobi matrix of the observation function used by state observer 2

, actual at the previous moment of time ( k – 1) and coming to the input of the Jacobi matrix correction block 6 (Fig. 1).

,

,

используются в качестве прямоугольной матрицы Якоби

уравнения наблюдений наблюдателя состояния 2 - цифрового фильтра для нестационарных сигналов [2].Jacobi matrices of observation functions

,

,

used as a rectangular Jacobian matrix

observation equations of state observer 2 - digital filter for non-stationary signals [2].

Block delay 3 (Fig. 1) performs the function of memory.

скорректированных значений оценки состояния системы в некоторый текущий момент времени k. Выходом блока задержки 3 является вектор

скорректированных значений оценки состояния системы в предыдущий момент времени (k – 1). С выхода блока задержки 3 вектор

поступает на вход регулятора состояния 4 (фиг. 1).The input of delay block 3 from the output of state observer 2 receives the current vector

adjusted values of the assessment of the state of the system at some current moment of time k . The output of delay block 3 is the vector

corrected values of the assessment of the state of the system at the previous time ( k - 1). From the output of the delay block 3 vector

enters the input of the state controller 4 (Fig. 1).

,

,

являются векторами оценки состояния

и имеют размерность n.Vectors

,

,

are state estimation vectors

and have dimension n .

In addition to the above data, the input of the state controller 4 receives the vector of required states X _T (k) dimensionn (Fig. 1, Fig. 2). Vector X _T (k) contains the required values of the state variables of managed object 1.

In addition to the previously indicated vectors and matrices, on the diagram of the state controller 4 (Fig. 2) are indicated:

- вектор среднего арифметического взвешенного значения векторов

,

с весами

,

соответственно, размерность вектора

– n;

- vector of arithmetic mean weighted value of vectors

,

with scales

,

respectively, the dimension of the vector

– n ;

- диагональная матрица весов элементов текущего вектора

скорректированных значений оценки состояния системы, полученная в предыдущий момент времени (k – 1), размерность матрицы - n×n;

- diagonal matrix of weights of elements of the current vector

corrected values of the assessment of the state of the system, obtained at the previous point in time ( k - 1), the dimension of the matrix is n × n ;

- диагональная матрица весов элементов вектора

значений апостериорной оценки состояния системы, полученная в предыдущий момент времени (k – 1), размерность матрицы - n×n;

- diagonal matrix of weights of vector elements

values of a posteriori assessment of the state of the system, obtained at the previous moment of time ( k - 1), the dimension of the matrix is n × n ;

- вектор ошибки выхода регулятора состояния, размерность вектора - n;

- error vector of the output of the state controller, vector dimension - n ;

- вектор ошибки состояния, размерность вектора - n;

- state error vector, vector dimension - n ;

k - some current moment of time;

( k – 1) - the previous moment in time.

поступает на вход первого блока умножения 4-1 и на вход второго блока суммирования 4-5 (фиг. 2).In state controller 4 vector

enters the input of the first multiplication block 4-1 and the input of the second summation block 4-5 (Fig. 2).

, поступающая с выхода блока адаптации 4-9 на вход первого блока умножения 4-1, умножается на вектор

, при этом выходом первого блока умножения
4-1 является произведение

, поступающее на вход первого блока суммирования 4-3 (фиг. 2).In the first block of multiplication 4-1 weight matrix

, coming from the output of the adaptation block 4-9 to the input of the first multiplication block 4-1, is multiplied by the vector

, while the output of the first multiplication block
4-1 is the product

, coming to the input of the first summation block 4-3 (Fig. 2).

поступает на вход второго блока умножения 4-2 регулятора состояния 4 (фиг. 2).Vector

enters the input of the second multiplication block 4-2 state controller 4 (Fig. 2).

, поступающая с выхода блока адаптации 4-9 на вход второго блока умножения 4-2, умножается на вектор

, при этом выходом второго блока умножения 4-2 является произведение

, поступающее на вход первого блока суммирования 4-3 (фиг. 2).In the second multiplication block 4-2 weight matrix

, coming from the output of the adaptation block 4-9 to the input of the second multiplication block 4-2, is multiplied by the vector

, while the output of the second multiplication block 4-2 is the product

, coming to the input of the first summation block 4-3 (Fig. 2).

и

, являющихся выходами первого блока умножения 4-1 и второго блока умножения 4-2 соответственно, при этом выходом первого блока суммирования 4-3 является сумма

, которая, в свою очередь, является вектором

среднего арифметического взвешенного значения, поступающего с выхода первого блока суммирования 4-3 на вход первого блока вычитания 4-4 (фиг. 2).In the first summation block 4-3 of the state controller 4, the summation of the products

and

, which are the outputs of the first multiplication block 4-1 and the second multiplication block 4-2, respectively, while the output of the first summation block 4-3 is the sum

, which in turn is a vector

arithmetic average weighted value coming from the output of the first summation block 4-3 to the input of the first subtraction block 4-4 (Fig. 2).

находится согласно выражению:Vector value

is found according to the expression:

. (8)

. (eight)

из вектора

, причем вектор

поступает на вход первого блока вычитания 4-4 с выхода первого блока суммирования 4-3, а вектор

поступает на вход первого блока вычитания 4-4 регулятора состояния 4, при этом полученная разность векторов

является вектором

ошибки состояния, который поступает на выход регулятора состояния 4 и на вход третьего блока суммирования 4-7 регулятора состояния 4 (фиг. 2).The first subtraction block 4-4 of state controller 4 performs vector subtraction

from vector

, and the vector

enters the input of the first subtraction block 4-4 from the output of the first summation block 4-3, and the vector

enters the input of the first subtraction block 4-4 of the state controller 4, while the resulting difference of the vectors

is a vector

state error, which is fed to the output of the state controller 4 and to the input of the third summation block 4-7 of the state controller 4 (Fig. 2).

ошибки состояния вычисляется, следуя выражению:Vector

status errors are calculated following the expression:

. (9)

. (9)

и

, поступающих на вход регулятора состояния 4, при этом выходом второго блока суммирования 4-5 является сумма

, поступающая на вход блока деления 4-6 (фиг. 2).In the second summation block 4-5 of the state controller 4, the summation of the vectors

and

coming to the input of the state controller 4, while the output of the second summation block 4-5 is the sum

, coming to the input of the division block 4-6 (Fig. 2).

, поступающей с выхода второго блока суммирования 4-5 на вход блока деления 4-6, при этом выходом блока деления 4-6 является результат данных вычислений

, который, в свою очередь, поступает на вход третьего блока суммирования
4-7 регулятора состояния 4 (фиг. 2).In the division block 4-6 of the state controller 4, the division by constant 2 of the sum is performed

coming from the output of the second summation block 4-5 to the input of the division block 4-6, while the output of the division block 4-6 is the result of these calculations

, which, in turn, is fed to the input of the third summation block
4-7 of the state controller 4 (FIG. 2).

и величины

, являющихся выходом первого блока вычитания 4-4 и выходом блока деления 4-6 соответственно, при этом выходом третьего блока суммирования 4-7 является сумма

, которая, в свою очередь, поступает с выхода третьего блока суммирования 4-7 на вход второго блока вычитания 4-8 регулятора состояния 4 (фиг. 2).In the third summation block 4-7 of the state controller 4, the summation of the value

and quantities

, which are the output of the first subtraction block 4-4 and the output of the division block 4-6, respectively, while the output of the third summation block 4-7 is the sum

, which, in turn, comes from the output of the third summation block 4-7 to the input of the second subtraction block 4-8 of the state controller 4 (Fig. 2).

, являющейся выходом третьего блока суммирования 4-7, из вектора

, поступающего на вход второго блока вычитания 4-8 регулятора состояния 4, причем полученная разность

является вектором

ошибки выхода регулятора состояния 4, при этом данный вектор

поступает с выхода второго блока вычитания 4-8 на вход блока адаптации 4-9 регулятора состояния 4 (фиг. 2).In the second subtraction block 4-8 of the state controller 4, the value is subtracted

, which is the output of the third summation block 4-7, from the vector

, coming to the input of the second subtraction block 4-8 of the state controller 4, and the resulting difference

is a vector

state controller output errors 4, while this vector

comes from the output of the second subtraction block 4-8 to the input of the adaptation block 4-9 of the state controller 4 (Fig. 2).

определяется следующим образом:Vector

is defined as follows:

. (10)

. (ten)

, поступающий с выхода второго блока вычитания 4-8, для формирования весовых матриц

и

(фиг. 2).Adaptation block 4-9 of the state controller 4 uses the vector

, coming from the output of the second subtraction block 4-8, for the formation of weight matrices

and

(Fig. 2).

и

(далее матрицы

и

) при условии, если хотя бы для одного i-го элемента вектора

справедливо выражение:Adaptation block 4-9 generates weight matrices

and

(hereinafter matrices

and

) provided that for at least one i -th element of the vector

the expression is correct:

, (11)

, (eleven)

where:

– абсолютное значение i-го элемента вектора

,

;

is the absolute value of the i -th element of the vector

,

;

– максимальное допустимое значение ошибки выхода регулятора состояния,

.

– the maximum allowable error value of the status controller output,

.

The operation algorithm of the adaptation block 4-9 consists in the sequential execution of calculations according to expressions (12 - 14):

, (12)

, (12)

where:

– величина некоторого шага алгоритма блока адаптации 4-9, соответствующего i-ому элементу вектора

,

;

- the value of a certain step of the algorithm of the adaptation block 4-9, corresponding to the i -th element of the vector

,

;

– максимальное значение шага алгоритма блока адаптации 4-9,

;

- the maximum value of the step of the adaptation block algorithm 4-9,

;

– постоянная скорость сходимости алгоритма блока адаптации 4-9,

;

- constant convergence rate of the adaptation block algorithm 4-9,

;

sign( x ) is a function to determine the sign of the argument x :

;

;

, (13)

, (13)

,where:

,

– i-ый элемент весовой диагональной матрицы

вида

– i -th element of the weight diagonal matrix

kind

,

,

.in this case, the condition

.

, (14)

, (fourteen)

where 1 is an n × n identity matrix.

,

, где 0 - нулевая матрица размерностью n×n.Initial conditions of the adaptation block algorithm 4-9:

,

, where 0 is an n × n zero matrix.

значения соответствующих им элементов весовой матрицы

будут уменьшаться, а значения соответствующих им элементов весовой матрицы

- увеличиваться.When condition (11) is satisfied for certain elements of the vector

values of the weight matrix elements corresponding to them

will decrease, and the values of the corresponding elements of the weight matrix

- increase.

и

, полученные в предыдущий момент времени (k – 1), поступают с выхода блока адаптации 4-9 на вход первого блока умножения 4-1 и вход второго блока умножения 4-2 соответственно (фиг. 2).Weight matrices

and

, obtained at the previous moment of time ( k - 1), come from the output of the adaptation block 4-9 to the input of the first multiplication block 4-1 and the input of the second multiplication block 4-2, respectively (Fig. 2).

The following is received at the input of the state error conversion block 5:

ошибки состояния размерностью n,- from the output of the state controller 4 - vector

state errors of dimension n ,

размерностью m×n (фиг. 1).- from the output of the Jacobi matrix correction block 6 - the corrected Jacobi matrix of the observation function

dimension m × n (Fig. 1).

ошибки состояния в вектор

ошибки выхода системы, следуя выражению:State error transformation block 5 produces vector transformation

status errors to vector

system exit errors, following the expression:

, (15)

, (fifteen)

where:

– вектор ошибки выхода системы, размерность вектора – m.

is the error vector of the system output, the dimension of the vector is m .

ошибки выхода системы (фиг. 1).From the output of the state error conversion block 5, the vector

system output errors (Fig. 1).

At the input of the correction block of the Jacobi matrix 6 are:

- from the output of controlled object 1 - the vector y ( k ) of the system output,

, актуальная в предыдущий момент времени (k – 1) (фиг. 1). Размерность матрицы

– m×n. - from the output of the observer of state 2 - the Jacobi matrix of the observation function used by the observer of state 2

, relevant at the previous moment of time ( k – 1) (Fig. 1). Matrix dimension

– m × n.

при работе системы управления. Исходными данными для рассматриваемого алгоритма являются: вектор y (k) выхода системы и матрица Якоби функции наблюдений

, актуальная в предыдущий момент времени (k – 1) и подлежащая коррекции (фиг. 1). Результат работы блока коррекции матрицы Якоби 6 – скорректированная матрица

. Каждый ненулевой элемент матрицы

является весовым коэффициентом (весом), определяющим вклад соответствующего этому весовому коэффициенту элемента вектора y (k) в результат преобразования информации, вычисляемого наблюдателем состояния 2. На фиг. 3 изображен пример матрицы

с расположением весовых коэффициентов на пересечениях её строк и столбцов: номера строк (отмечены индексами j,

) данной матрицы соответствуют номерам элементов векторов y (k) и

, а номера столбцов (отмечены индексами i,

) – номерам элементов векторов

,

,

и

. При условии, что n < m преобразованием информации является её комплексирование. Например, матрица

, изображенная на фиг. 3, задает комплексирование значений элементов y ₂(k), y ₃(k), y ₄(k), y ₅(k) и значений элементов y ₆(k), y ₇(k) вектора y (k) соответственно в значения элементов

и

вектора

. К элементам y ₀(k) и y ₁(k) вектора y (k) комплексирование не применяется, а значения этих элементов подвергаются только оценке, результаты которой помещаются соответственно в элементы

и

вектора

. Расположение ненулевых элементов в матрице

определяется задачей преобразования информации.Algorithm of the correction block of the Jacobi matrix 6 is shown in FIG. 4. The purpose of this block is the constant correction of the Jacobian matrix of the observation function

during operation of the control system. The initial data for the considered algorithm are: vector y (k) the system output and the Jacobi matrix of the observation function

, relevant at the previous point in time (k - 1) and subject to correction (Fig. 1). The result of the correction block of the Jacobi matrix 6 - corrected matrix

. Each non-zero element of the matrix

is a weight coefficient (weight) that determines the contribution of the vector element corresponding to this weight coefficient y (k) into the result of information transformation computed by state observer 2. In FIG. 3 shows an example of a matrix

with the location of weight coefficients at the intersections of its rows and columns: row numbers (marked with indicesj,

) of this matrix correspond to the numbers of elements of the vectors y (k) and

, and the column numbers (marked with indexesi,

) – numbers of elements of vectors

,

,

and

. Provided thatn <m the transformation of information is its integration. For example, matrix

shown in FIG. 3, specifies the aggregation of element values y ₂(k), y ₃(k), y _four(k), y ₅(k) and element values y ₆(k), y ₇(k) vector y (k) respectively into the values of the elements

and

vector

. To the elements y ₀(k) and y _one(k) vector y (k) no aggregation is applied, and the values of these elements are only evaluated, the results of which are placed respectively in the elements

and

vector

. Arrangement of non-zero elements in a matrix

is determined by the task of information transformation.

позволяет придать элементам вектора y (k) веса, пропорциональные значениям соответствующих элементов данного вектора. Процедура коррекции требуется при выполнении преобразования вектора y (k) и преобразования вектора

в условиях частичной или полной неопределенности диапазонов значений элементов вектора y (k) при низких величинах шумов, наложенных на выход системы y (k). Для процедуры коррекции необходима некоторая постоянная начальная матрица Якоби функции наблюдений

, содержащая по меньшей мере один ненулевой элемент. Чем ближе значения ненулевых элементов этой матрицы к искомым величинам весов, тем быстрее выполняется коррекция матрицы

.Matrix correction

allows you to give the elements of the vector y ( k ) weights proportional to the values of the corresponding elements of this vector. A correction procedure is required when performing a vector transformation y ( k ) and a vector transformation

under conditions of partial or complete uncertainty of the ranges of values of the elements of the vector y ( k ) at low values of noise imposed on the output of the system y ( k ). The correction procedure requires some constant initial Jacobi matrix of the observation function

, containing at least one nonzero element. The closer the values of non-zero elements of this matrix to the desired values of the weights, the faster the correction of the matrix is performed

.

Block diagram of the operation algorithm of the Jacobi matrix correction unit 6 is shown in FIG. 4. On the block diagram of the algorithm are indicated:

Y - one-dimensional array (vector) y ( k );

;J _Hx - two-dimensional array (matrix)

;

и хранит сумму значений элементов вектора y (k), соответствующих ненулевым элементам этого столбца матрицы

, размерность массива – n;COL_SUM - one-dimensional array (vector), each element of which corresponds to a certain column of the matrix

and stores the sum of the values of the elements of the vector y ( k ) corresponding to non-zero elements of this column of the matrix

, array dimension – n ;

и хранит количество ненулевых элементов этого столбца матрицы

, размерность массива – n;NONZERO_COUNT - one-dimensional array (vector), each element of which corresponds to a certain column of the matrix

and stores the number of non-zero elements of this matrix column

, array dimension – n ;

(номер строки массива COL_INPUTS соответствует номеру столбца матрицы

), размерность массива – n×m;COL_INPUTS - two-dimensional array (matrix), whose rows contain the values of the elements of the vector y ( k ), corresponding to non-zero elements of the matrix columns

(the row number of the COL_INPUTS array corresponds to the column number of the matrix

), the dimension of the array is n × m ;

(номер строки массива INPUT_INDEX соответствует номеру столбца матрицы

), размерность массива – n×m;INPUT_INDEX - two-dimensional array (matrix), the rows of which contain the numbers of elements of the vector y ( k ), corresponding to non-zero elements of the matrix columns

(the row number of the INPUT_INDEX array corresponds to the column number of the matrix

), the dimension of the array is n × m ;

index - a variable that stores the current column number of two-dimensional arrays INPUT_INDEX and COL_INPUTS;

i, j - variables that store the current numbers (indexes) of array elements;

соответственно;n, m - number of columns and rows of the matrix

respectively;

s is an extremely small positive value, s > 0.

вычисляются рекуррентно, используя среднее арифметическое их предыдущих значений и новых значений, полученных исходя из текущих величин элементов вектора y (k).Values of matrix elements

are calculated recurrently using the arithmetic mean of their previous values and new values obtained from the current values of the elements of the vector y ( k ).

, которая поступает на входы: наблюдателя состояния 2, блока преобразования ошибки состояния 5. Размерность матрицы

– m×n (фиг. 1). The result of the Jacobi matrix correction block 6 is the corrected Jacobi matrix of the observation function

, which enters the inputs of: state observer 2, state error transformation block 5. Dimension of the matrix

– m × n (Fig. 1) .

, и, задаваемые, исходя из конкретной задачи управления: диагональная матрица коэффициентов усиления K , вектор абсолютных величин максимальных значений мощностей воздействий u _max , вектор абсолютных величин максимальных значений ошибки выхода системы

, причем размерность векторов

,

, u _max – m, размерность матрицы K – m×m (фиг. 1). Матрица коэффициентов усиления K имеет вид:The inputs of the block for the formation of control actions 7 receive: from the block for converting the state error 5 - the error vector of the system output

, and, given on the basis of a specific control problem: a diagonal matrix of gains K , a vector of absolute values of the maximum values of the impact powers u _max , a vector of absolute values of the maximum values of the system output error

, and the dimension of the vectors

,

, u _max – m, dimension of the matrix K – m × m (Fig. 1) . The gain matrix K has the form:

,

,

where K ₀ , …, K _{m - 1} are some gain factors.

The output of the block for the formation of control actions 7 are:

мощностей воздействий, размерность вектора – m,- vector

impact powers, the dimension of the vector is m ,

направлений воздействий, размерность вектора – m (фиг. 1). - vector

directions of influences, the dimension of the vector is m (Fig. 1) .

The block diagram of the operation algorithm of the block for generating control actions 7 is shown in Fig. 5. On the block diagram of the algorithm are indicated:

- одномерный массив (вектор) ошибки выхода системы

, размерность массива – m;

- one-dimensional array (vector) of system output errors

, array dimension – m ;

K - two-dimensional array (matrix) K amplification factors, array dimension -m×m;

- одномерный массив (вектор) усиленной ошибки выхода системы

, размерность массива – m;

- one-dimensional array (vector) of enhanced system output error

, array dimension – m ;

, размерность массива – m;u _POW - one-dimensional array (vector) of the powers of actions

, array dimension – m ;

, размерность массива – m;u _DIR - one-dimensional array (vector) of impact directions

, array dimension – m ;

u _max - one-dimensional array (vector) of the absolute values of the maximum values of the impact powers u _max , each element of which contains the value of the maximum power of a certain actuator of the actuator block 8 corresponding to the element number of this array, the array dimension is m ;

- одномерный массив (вектор) абсолютных величин максимальных значений ошибки выхода системы

, размерность массива – m;

- one-dimensional array (vector) of the absolute values of the maximum values of the system output error

, array dimension – m ;

,

,

, u _max , u _POW , u _DIR ;i - a variable that stores: the current row number of the matrix K , the current numbers of the elements of the vectors

,

,

, u _max , u _POW , u _DIR ;

;j - a variable that stores the current column number of the matrix K , the current number of the vector element

;

,

,

, u _max , u _POW , u _DIR ;m - number of rows and columns of matrix K , elements of vectors

,

,

, u _max , u _POW , u _DIR ;

PrevDuty - a variable that stores the previous value of the impact power for some actuator;

AddDuty - a variable that stores the required change in the impact power for some actuator;

Duty - a variable that stores the required value of the impact power for some actuator;

operation | • | returns the absolute value of some number.

вычисляются умножением элементов двумерного массива K на элементы одномерного массива

аналогично произведению матрицы K на вектор

.Element values of a one-dimensional array

are calculated by multiplying the elements of a two-dimensional array K by the elements of a one-dimensional array

similarly to the product of the matrix K and the vector

.

The value of each element of the vector u _POW denotes the amount of power supplied to a certain actuator of the actuator block 8 of the control system. This value can be the duty cycle of the pulse width modulation (PWM) signal, for example, expressed as a percentage: from 0% to 100%. In this case, the PWM signal controls the operation of electronic power switches that regulate the supply of electricity to the actuators of the actuator block 8. The value of the power supplied to some i -th actuator is programmatically limited by the value of the i -th element of the vector u _max . The value of each element of the vector u _max is set based on the design of a particular actuator and the task of the control system.

The elements of the vector u _DIR contain the values of the directions of application of the supplied powers to the actuators of the actuator block 8 corresponding to the numbers of these elements. These directions can be: rotation of the motor shaft clockwise or counterclockwise, forward or reverse movement of the actuator. Each element of the vector u _DIR can take one of three values: -1 (actuator movement "backward"), 0 (actuator movement absent), 1 (actuator movement "forward"). The values of the elements of the vector u _DIR are designed to reverse the movements of the actuators using electronic power switches. To do this, the value of each i -th element u _{DIR i} is converted into a pair of binary numbers { A , B }, where A and B can take the following values:

1) when u _{DIR i} = -1 { A , B } = {0, 1}, 2) for u _{DIR i} = 0 { A , B } = {0, 0}, 3) for u _{DIR i} = 1 { A , B } = {1, 0}

The numbers A and B correspond to the control lines of the electronic power switches for reversing the movements of the actuators, and the binary values of these numbers correspond to the logic level voltages.

и направлений воздействий -

(фиг. 1). При этом управление каждым i-ым актюатором блока актюаторов 8 задается парой элементов данных векторов -

и

,

.From the output of the block for the formation of control actions 7 to the input of the block of actuators 8, control signals are received, expressed as two vectors of dimension m :

and directions of influences -

(Fig. 1). In this case, the control of each i -th actuator of the actuator block 8 is given by a pair of data elements of the vectors -

and

,

.

. Идеальным является случай, когда элементы вектора y (k) и соответствующие им элементы вектора p (k) хранят одни и те же физические величины. Предполагается, что работа каждого актюатора блока актюаторов 8 описана своей математической моделью.The controlled object 1 is subjected to some influences (force and/or kinematic) from the block of actuators 8, expressed as elements of the action vector p ( k ) with dimension m (Fig. 1). Each i -th actuator block of actuators 8 produces the impact p _i ( k ). To ensure the operation of a closed control system, it is required that there is an unambiguous relationship between changes in the elements of the vector p ( k ) and changes in the elements of the vector y ( k ), i.e. some element p _i ( k ) is associated with a certain element y _i ( k ),

. The ideal case is when the elements of the vector y ( k ) and the corresponding elements of the vector p ( k ) store the same physical quantities. It is assumed that the operation of each actuator of the actuator block 8 is described by its own mathematical model.

The combination of the state observer and the state regulator as part of the control system makes it possible to control uncertain non-stationary dynamic objects with state variables that are not directly measurable and have non-periodic external disturbances, using the required values of the state variables of the controlled object in the control process.

Thus, the introduction of additional blocks and a new connection scheme in the control system based on the state of the control object with an observer and a state controller made it possible to expand the functionality of the control system by using the system as a setting effect of the required values of the state variables of the controlled object and using a state observer that has the ability to use a nonlinear process/system models for assessing the state of a controlled object and ensuring stable operation of the control system for non-stationary dynamic objects with state variables inaccessible to direct measurement.

This device can be implemented industrially based on a standard element base.

Sources of information

1. Patent RU 2528155 IPC G05B 13/02, 2006.01, publ. 09/10/2014, Bull. No. 25 (prototype).

2. Patent RU 2747199 IPC H03H 17/04, H03H 21/00, 2006.01, publ. 29.04.2021, Bull. No. 13.

3. Pevzner L.D. Theory of control systems / M.: Publishing house of the Moscow State Mining University, 2002. - 472 p.

4. Gyorgy, K. The LQG Control Algorithms for Nonlinear Dynamic Systems / Procedia Manufacturing, vol. 32, 2019. – p. 553–563.

Claims (2)

1. A control system according to the state of the control object with an observer and a state controller, containing a controlled object, the output of which is the system output vector, the state observer, the input of which is the system output vector from the output of the controlled object, a delay block, characterized in that the control system state controller with an observer and a state controller includes a state controller, a state error transformation block, a Jacobi matrix correction block, a block for generating control actions, a block of actuators, and the state observer is a digital filter for non-stationary signals, which is an extended Kalman filter, supplemented by an adaptive digital filter with the NLMS adaptation algorithm, moreover, the initial Jacobi matrix of the observation function arrives at the input of the state observer at the initial time of the control system operation, while at the input of the state observer from the output of the correction block of the Jacobian matrix, the input gives the corrected Jacobi matrix of the observation function, and the output of the state observer is the Jacobi matrix of the observation function, relevant at the previous moment of time, while the output of the state observer is the current vector of corrected values of the system state estimate and the vector of values of the a posteriori estimate of the system state, while at the input of the delay block the current vector of corrected values of the system state estimate comes from the output of the state observer, while the output of the delay block is the vector of corrected values of the system state estimate at the previous moment of time, and the current vector of corrected values of the system state estimate and the vector of values a posteriori assessment of the state of the system, while the input of the state controller from the output of the delay block receives a vector of corrected values of the assessment of the state of the system at the previous moment of time, and at the input The state controller code receives the vector of required states, while the output of the state controller is the state error vector, and the input of the state error transformation block receives the state error vector from the output of the state controller, and the corrected matrix is supplied to the input of the state error transformation block from the output of the Jacobi matrix correction block Jacobi function of observations, while the output of the block for transforming the state error is the error vector of the system output, and the input of the Jacobi matrix correction block from the output of the controlled object receives the system output vector, and the input of the Jacobi matrix correction block from the output of the state observer receives the Jacobi matrix of the observation function, actual at the previous moment of time, while the output of the Jacobi matrix correction block is the corrected Jacobi matrix of the observation function, and the error vector system output curves, wherein the diagonal matrix of gain coefficients, the vector of absolute values of the maximum values of the powers of the actions, the vector of the absolute values of the maximum values of the error of the system output are fed to the input of the block for the formation of control actions, while the output of the block for the formation of control actions is the vector of the powers of the actions and the vector of the directions of the actions, moreover, the input of the actuator block from the output of the block for generating control actions receives the power vector of actions and the vector of directions of influences, while the output of the block of actuators is force and/or kinematic actions directed at the controlled object and expressed as elements of the action vector. 2. The control system according to the state of the control object with the observer and the state controller according to claim 1, characterized in that the state controller includes: the first multiplication block, the input of which from the output of the state observer receives the current vector of corrected values of the system state assessment, and on input of the first multiplication block from the output of the adaptation block included in the state controller, the diagonal matrix of weights of the elements of the current vector of corrected values of the assessment of the state of the system, obtained at the previous point in time, is received, while the output of the first multiplication block is the product of the diagonal matrix of weights of the elements of the current vector of the corrected values of the assessment the state of the system and the current vector of corrected values of the assessment of the state of the system; the second multiplication block, the input of which from the output of the state observer comes the vector of values of the a posteriori estimate of the state of the system, and the input of the second multiplication block from the output of the adaptation block included in the state controller receives the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimate of the state of the system, obtained in the previous time point, wherein the output of the second multiplication block is the product of the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimate of the state of the system and the vector of values of the a posteriori estimate of the state of the system; the first summation block, the input of which, from the output of the first multiplication block, is the product of the diagonal matrix of weights of the elements of the current vector of corrected values of the assessment of the state of the system and the current vector of corrected values of the assessment of the state of the system, and the input of the first summation block, from the output of the second multiplication block, is the product of the diagonal matrix of weights elements of the vector of values of the a posteriori estimate of the state of the system and the vector of values of the a posteriori estimate of the state of the system, while the output of the first summing block is the vector of the arithmetic mean weighted value, which is equal to the sum of two products: the product of the diagonal matrix of weights of the elements of the current vector of corrected values of the estimate of the state of the system and the current vector of corrected values estimates of the state of the system, the product of the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimate of the state of the system and the vector of values of the a posteriori assessing the state of the system; the first subtraction block, the input of which is the vector of the arithmetic weighted average value from the output of the first summation block, and the vector of required states is fed to the input of the first subtraction block, while the output of the first subtraction block is the state error vector, which is fed to the output of the state controller and to the input of the third the summation block included in the state controller, while the state error vector is equal to the difference of the vectors: the vector of the required states and the vector of the arithmetic mean weighted value; the second summing block, the input of which from the output of the state observer receives the current vector of corrected values of the assessment of the state of the system, and the input of the second summing block from the output of the delay block receives the vector of corrected values of the assessment of the state of the system at the previous point in time, while the output of the second summing block is the sum vectors: the current vector of adjusted values of the assessment of the state of the system and the vector of adjusted values of the assessment of the state of the system at the previous point in time; a division block, the input of which, from the output of the second summation block, receives the sum of the current vector of corrected values of the system state assessment and the vector of corrected values of the system state assessment at the previous point in time, while the output of the division block is the result of dividing by constant 2 the sum of the current vector of corrected values of the state assessment system and the vector of corrected values of the assessment of the state of the system at the previous point in time; the third summing block, the input of which from the output of the first subtraction block receives the state error vector, and the input of the third summing block from the output of the dividing block receives the result of dividing by constant 2 the sum of the current vector of corrected values of the system state assessment and the vector of corrected values of the system state assessment in the previous a point in time, wherein the output of the third summation block is the sum of the state error vector and the result of dividing by a constant 2 of the sum of the current vector of corrected values of the system state estimate and the vector of corrected values of the system state estimate at the previous point in time; the second subtraction block, the input of which from the output of the third summation block receives the sum of the state error vector and the result of division by a constant 2 of the sum of the current vector of corrected values of the system state assessment and the vector of corrected values of the system state assessment at the previous point in time, and the input of the second subtraction block receives the vector of required states, while the output of the second subtraction block is the error vector of the output of the state controller, which is equal to the difference of the vector of required states and the sum of the state error vector and the result of dividing by a constant 2 of the sum of the current vector of corrected values of the system state estimate and the vector of corrected values of the system state estimate to the previous moment of time; adaptation block, the input of which from the output of the second subtraction block receives the error vector of the output of the state controller, while the output of the adaptation block is the diagonal matrix of weights of the elements of the current vector of corrected values of the system state assessment obtained at the previous point in time, and the diagonal matrix of weights of the elements of the vector of values of the a posteriori estimates of the state of the system obtained at the previous point in time.

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