CN110298124B - Industrial control system actuator parameter estimation method based on filtering - Google Patents
Industrial control system actuator parameter estimation method based on filtering Download PDFInfo
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Abstract
The invention discloses a filtering-based industrial control system actuator parameter estimation method, and belongs to the field of manufacturing process control. The method comprises the steps of obtaining a linear model of a pneumatic servo motor in an actuator of the industrial control system, obtaining vertex coordinates of an initial convex polyhedron, carrying out average triangulation on the convex polyhedron at the moment k-1, calculating the variance of the size of a simplex for each subdivision mode, storing vertex coordinates of all the simplices corresponding to the subdivision mode with the minimum variance into a cell body at the moment k, updating to obtain the vertex coordinates of the convex polyhedron at the moment k according to the intersection condition of each simplex in the cell body at the moment k and a hyperplane wrapping area at the moment k, and averaging all the coordinates of the convex polyhedron at the moment k to obtain an estimated value of an estimated parameter; the problems of low accuracy and low efficiency of the traditional parameter estimation method are solved; the method and the device have the advantages that the accuracy and the efficiency of estimating the parameters of the pneumatic servo motor are improved.
Description
Technical Field
The embodiment of the invention relates to the field of manufacturing process control, in particular to a filtering-based industrial control system actuator parameter estimation method.
Background
With the rapid development of scientific technology in recent years, the research of a servo system has a new breakthrough, and the servo system is widely applied to the fields of industrial control, aerospace, laser processing, household appliances and the like. Because the servo motor has the nonlinear phenomena of dead zones, saturation, friction, gaps and the like in practical application, the key for controlling the servo system is to select a simple and effective mathematical model to accurately describe the servo system.
The nonlinear parameter estimation can well solve the problem of inaccuracy in the linear model description servo system, and can provide a basis for later-stage fault diagnosis. The traditional system parameter estimation considers that noise is a random variable subject to known or parameterizable probability distribution, and a unique parameter estimation value is obtained on the basis of the random variable.
Disclosure of Invention
In order to solve the problems in the prior art, the embodiment of the invention provides a filtering-based industrial control system actuator parameter estimation method. The technical scheme is as follows:
in a first aspect, a method for estimating actuator parameters of an industrial control system based on filtering is provided, and the method includes:
obtaining a nonlinear second-order dynamic model of a pneumatic servo motor in an actuator of an industrial control system:
acquiring a linearization model of the pneumatic servo motor according to the nonlinear second-order dynamic model:
obtaining an initial convex polyhedron S0Vertex coordinates of (2), initial convex polyhedron S0The method comprises the steps of including a true value of a parameter to be estimated of a pneumatic servo motor;
for convex polyhedron S at k-1 momentk-1Carrying out average triangulation to obtain a plurality of subdivision modes, wherein each subdivision mode corresponds to a plurality of simplex shapes;
aiming at each subdivision mode, the method comprises the following steps of,obtaining the variance of the sizes of the simplices, storing the vertex coordinates of all the simplices corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkPerforming the following steps;
cell body Z according to time kkPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkVertex coordinates of (2), hyperplane wrap area H+(k) The method is determined according to input data and output data of a pneumatic servo motor;
convex polyhedron S for k momentskAveraging all the vertex coordinates to obtain an estimated value of the parameter to be estimated;
wherein X represents servomotor rod displacement, PsIndicating the pressure in the pneumatic servomotor chamber, AeDenotes the diaphragm area, m denotes the mass bar, kxDenotes the spring and diaphragm constants, kvDenotes the valve constant, l is a constant;
φkrepresenting the observed vector of the pneumatic servomotor, ekRepresenting an unknown but bounded sequence of noise,
in order to be a known lower bound of noise,
is the known upper bound of noise;
ykrepresenting the output data of the pneumatic servomotor, ukInput data representing the pneumatic servo motor, the input data and the output data being known;
θ*representing the true value of the parameter vector theta to be estimated, theta*Unknown;
k＝1,2...,n；
optionally, when the vertex coordinates of the convex polyhedron are two-dimensional coordinates, the simplex obtained by average triangulation is a triangle;
aiming at each subdivision mode, acquiring the variance of the sizes of the simplex forms, and storing the vertex coordinates of all the simplex forms corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn, comprising:
aiming at each subdivision mode, calculating the area of each simplex according to the vertex coordinates of each simplex, and calculating the variance of the area of the simplex according to the areas of all the simplices;
storing the vertex coordinates of all the simplex shapes corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn (1).
Optionally, when the vertex coordinates of the convex polyhedron are three-dimensional coordinates, the simplex obtained by average triangulation is a tetrahedron;
aiming at each subdivision mode, acquiring the variance of the sizes of the simplex forms, and storing the vertex coordinates of all the simplex forms corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn, comprising:
aiming at each subdivision mode, calculating the volume of each simplex according to the vertex coordinates of each simplex, and calculating the variance of the volume of the simplex according to the volumes of all the simplices;
storing the vertex coordinates of all the simplex shapes corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn (1).
Optionally, when the vertex coordinates of the convex polyhedron are two-dimensional coordinates, the simplex obtained by average triangulation is a triangle;
cell body Z according to time kkPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkIncludes:
overclad area H according to time k+(k) Defining two parallel hyperplanes H1(k) And H2(k) The limiting equation of (1);
cell body Z according to time kkDetermining a linear equation where the sides of the triangle are located according to the vertex coordinates of each triangle;
for cell body Z at time kkEach triangle in (1) connecting two parallel superbeamsPlane H1(k) And H2(k) The limiting equation and the linear equation of the triangle side to obtain the hyperplane wrapping area H+(k) Coordinates of the intersection point with the straight line;
determining the wrapping area H in the hyperplane according to the coordinates of the intersection point+(k) Outer vertex coordinates and in hyperplane wrap region H+(k) Inner vertex coordinates, to be in the hyperplane envelope region H+(k) Convex polyhedron S with inner vertex coordinates as k timekThe vertex coordinates of (2);
wherein the content of the first and second substances,
optionally, when the vertex coordinates of the convex polyhedron are three-dimensional coordinates, the simplex obtained by average triangulation is a tetrahedron;
cell body Z according to time kkPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkIncludes:
overclad area H according to time k+(k) Defining two parallel hyperplanes H1(k) And H2(k) The limiting equation of (1);
cell body Z according to time kkDetermining the linear equation of the edge of each tetrahedron according to the vertex coordinates of each tetrahedron;
soma Z for time kkEach tetrahedron in (A) has two parallel hyperplanes H1(k) And H2(k) The limiting equation and the linear equation of the edges of the tetrahedron are obtained to obtain the hyperplane wrapping area H+(k) Coordinates of the intersection point with the straight line;
determining the wrapping area H in the hyperplane according to the coordinates of the intersection point+(k) Outer vertex coordinates and in hyperplane wrap region H+(k) Inner vertex coordinates, to be in the hyperplane envelope region H+(k) Convex polyhedron S with inner vertex coordinates as k timekThe vertex coordinates of (2);
wherein the content of the first and second substances,
the technical scheme provided by the embodiment of the application has the following beneficial effects:
by obtaining a nonlinear second-order kinetic model of a pneumatic servo motor in an actuator of an industrial control system, converting the nonlinear second-order kinetic model into a linear model, obtaining vertex coordinates of an initial convex polyhedron comprising a true value of a parameter to be estimated of the pneumatic servo motor, carrying out mean triangulation on the convex polyhedron at the moment k-1 to obtain a plurality of subdivision modes, wherein each subdivision mode corresponds to a plurality of simplex shapes, calculating the variance of the sizes of the simplex shapes aiming at each subdivision mode, storing the vertex coordinates of all the simplex shapes corresponding to the subdivision mode with the smallest variance into a cell body at the moment k, updating to obtain the vertex coordinates of the convex polyhedron at the moment k according to the intersection condition of each simplex shape in the cell body at the moment k and a hyperplane wrapping area at the moment k, and averaging all the coordinates of the convex polyhedron at the moment k, obtaining an estimation value of the estimation parameter; the problems of low accuracy and low efficiency of the traditional parameter estimation method are solved; the accuracy and the efficiency of estimating the parameters of the pneumatic servo motor in the actuator of the industrial control system are improved, and the effect of guaranteeing the follow-up fault diagnosis is provided.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow diagram illustrating a method for filter-based estimation of an actuator parameter of an industrial control system according to an exemplary embodiment.
Detailed Description
To make the objects, technical solutions and advantages of the present application more clear, embodiments of the present application will be described in further detail below with reference to the accompanying drawings.
Definitions referred to in the examples of the present application:
if a polyhedron S is present, if
λ∈[0 1]If z ═ λ x + (1- λ) y ∈ S, S is called a convex polyhedron.
In the embodiment of the application, the convex polyhedron is used for approximating the parameter feasible region of the pneumatic servo motor in the actuator of the industrial control system.
Referring to fig. 1, a flow chart of a method for estimating actuator parameters of an industrial control system based on filtering according to an embodiment of the present application is shown. As shown in FIG. 1, the filter-based industrial control system actuator parameter estimation method may include the steps of:
The nonlinear second-order dynamic model of the pneumatic servo motor in the industrial control system actuator is as follows:
wherein X represents servomotor rod displacement, PsIndicating the pressure in the pneumatic servomotor chamber, AeDenotes the diaphragm area, m denotes the mass bar, kxDenotes the spring and diaphragm constants, kvDenotes the valve constant, l is a constant.
And 102, acquiring a linearization model of the pneumatic servo motor according to the nonlinear second-order power model.
The formula (1) is collated and simplified to obtain:
where cvp (t) represents the amount of control pressure.
Using y (t) instead of x (t), u (t) instead of cvp (t), and considering system noise e (t), we get:
Establishing a linear model of the pneumatic servo motor according to the formula (3):
wherein k is an integer, k is 1,2 …, n.
ekRepresenting an unknown but bounded sequence of noise,
in order to be a known lower bound of noise,
known as the upper bound of noise. Optionally, ek∈U[-0.01,0.01]。
ykRepresenting the output data of the pneumatic servomotor, ukInput data representing the pneumatic servo motor, the input data and the output data being known. Optionally, uk∈N(0,1)。
θ*Representing the true value of the parameter vector theta to be estimated, theta*Is unknown.
φkRepresenting the observed vector of the pneumatic servo motor.
When observing the vector phik＝[yk-1,…,yk-n]TWhen the formula (4) represents an Autoregressive (AR) model;
when observing the vector
Equation (4) represents a controlled Autoregressive (ARX) model; n is na+nb，naIndicating the number of output data, nbIndicating the number of input data.
Initial convex polyhedron S0Contains the true value theta of the parameter vector to be estimated of the pneumatic servo motor*I.e. theta*∈S0。
Optionally, an initial convex polyhedron S0Taking a convex polyhedron with each side parallel to the coordinate axis or a convex polyhedron with other shapes.
The vertex coordinates of the initial convex body are set in advance according to actual conditions.
And determining the dimension of the vertex coordinate of the initial convex polyhedron according to the dimension of the parameter to be estimated.
In the embodiment of the present application, two cases, that is, two-dimensional coordinates and three-dimensional coordinates, are considered as vertex coordinates.
According to the formula (3), the parameter to be estimated of the pneumatic servo motor can be estimated according to different conditions, for example, if the parameter to be estimated is in the parameter vector theta
When estimation is carried out, the vertex coordinates of the initial convex polyhedron are two-dimensional coordinates; if it is to be estimated in the parameter vector theta
When estimation is carried out, the vertex coordinates of the initial convex polyhedron are four-dimensional coordinates.
When estimating the parameters of the pneumatic servo motor, the following steps 104 to 106 may be cyclically performed to obtain the convex polyhedron S at the time kkAnd cell body Z at time k +1k+1。
Convex polyhedron S at acquisition moment kkConvex polyhedron S at time k-1k-1It is known that a convex polyhedron S is taken according to the moment k-1k-1The cell body Z at the k moment can be obtained by utilizing average triangulationk，k＝1,2…,n。
104, aligning the convex polyhedron S at the k-1 momentk-1And carrying out average triangulation to obtain a plurality of subdivision modes, wherein each subdivision mode corresponds to a plurality of simplex shapes.
At the beginning, for an initial convex polyhedron S0And carrying out average triangulation.
If the vertex coordinates of the convex polyhedron are two-dimensional coordinates, the simplex obtained after the average triangulation is a triangle; if the convex polyhedron has m two-dimensional coordinates, the number of subdivision modes obtained after average triangulation is as follows:
if the vertex coordinates of the convex polyhedron are three-dimensional coordinates, the simplex obtained after the average triangulation is tetrahedral; if the convex polyhedron has m three-dimensional coordinates, the number of subdivision modes obtained after average triangulation is as follows:
such as: the convex polyhedron has 4 two-dimensional coordinates, the convex polyhedron is a quadrangle on the coordinate plane, and according to the subdivision principle, 2 subdivision modes are provided, each subdivision mode corresponds to 2 simplex shapes, and the simplex shapes are triangles.
105, acquiring the variance of the sizes of the simplices aiming at each subdivision mode, and storing the vertex coordinates of all the simplices corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn (1).
Initial soma Z0Is an empty cell body.
Each row in the cell is all the vertex coordinates of a simplex.
The cell body is equivalent to a second-order matrix, the number of the simplex determines the row number of the cell body, and the number of the vertex coordinates of the convex polyhedron determines the column number of the cell body.
When the simplex is triangular, the size of the simplex refers to the area of the simplex; when the simplex is tetrahedral, the size of the simplex refers to the volume of the simplex.
For each subdivision mode, the size of each simplex corresponding to each subdivision mode is calculated, and then the variance of the sizes of the simplices is calculated.
Hyperplane wrap area H+(k) Is determined according to the input data and the output data of the pneumatic servo motor.
Hyperplane wrap area H+(k) Is composed of 2 parallel hyperplanes H in parameter space1(k) And H2(k) Defined spatial area:
simplex and hyperplane wrapped region H+(k) There are three relationships:
1. the simplex is all in the hyperplane wrapping area;
2. the simplex is all outside the hyperplane wrapping area;
3. the simplex intersects the hyperplane wrap-around region.
Will wrap area H in the hyperplane+(k) Inner vertex coordinates as a convex polyhedron S at time kkThe vertex coordinates of (2).
Convex polyhedron S at moment kkAny one of the vertexes ofThe standard is a possible value of the parameter to be estimated, the mean value of all vertex coordinates is calculated, and the mean value is used as an estimated value of the parameter to be estimated to be output.
In summary, in the embodiment of the present application, a nonlinear second-order kinetic model of a pneumatic servo motor in an actuator of an industrial control system is obtained, the nonlinear second-order kinetic model is converted into a linear model, vertex coordinates of an initial convex polyhedron are obtained, the initial convex polyhedron includes a true value of a parameter to be estimated of the pneumatic servo motor, the convex polyhedron at the time k-1 is subjected to average triangulation, a plurality of subdivision modes are obtained, each subdivision mode corresponds to a plurality of simplex shapes, for each subdivision mode, a variance of the sizes of the simplex shapes is calculated, vertex coordinates of all the simplex shapes corresponding to the subdivision mode with the smallest variance are stored in a cell at the time k, according to the intersection condition of each simplex shape in the cell at the time k and a hyperplane wrapping area at the time k, the vertex coordinates of the convex polyhedron at the time k are updated, and an average value is calculated for all coordinates of the convex polyhedron at the time k, obtaining an estimation value of the estimation parameter; the problems of low accuracy and low efficiency of the traditional parameter estimation method are solved; the accuracy and the efficiency of estimating the parameters of the pneumatic servo motor in the actuator of the industrial control system are improved, and the effect of guaranteeing the follow-up fault diagnosis is provided.
In an alternative embodiment based on the embodiment shown in fig. 1, the parameter vector to be estimated is known according to equation (3)
Parameter(s)
At denominator, parameter
Located in the numerator, to improve the efficiency of estimating the parameter to be estimated, the parameter may be estimated
And parameters
Since the parameters are estimated separately, the following two cases can be included when the above steps 104 to 106 are executed:
one, one pair of parameters
And performing parameter estimation, wherein the coordinates of the top end of the convex polyhedron are two-dimensional coordinates, and the simplex obtained by average triangulation is a triangle.
For convex polyhedron S at k-1 momentk-1And carrying out average triangulation to obtain a plurality of subdivision modes, wherein each subdivision mode corresponds to a plurality of simplex shapes, and each simplex shape is a triangle.
Aiming at each subdivision mode, acquiring the variance of the sizes of the simplex forms, and storing the vertex coordinates of all the simplex forms corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn (1).
Specifically, for each subdivision mode, calculating the area of each simplex according to the vertex coordinates of each simplex; from the areas of all the simplex, the variance of the simplex areas is calculated.
When the simplex is a triangle, the coordinates of the vertex of the triangle (a) are known1,b1)、(a2,b2)、(a3,b3) The area v of the triangle can be calculated according to the following formula:
and (3) calculating the variance of the area of the triangle according to the calculated areas of all the triangles for each subdivision mode:
vjithe area of the ith simplex obtained in the jth subdivision is shown,
the average value of the areas of all the simplex obtained in the j subdivision mode is shown; r isjThe variance of the simplex size in the j-th subdivision mode when the average triangulation is performed is shown, and r is a two-dimensional coordinate when the coordinates of the top end of the convex polyhedron are two-dimensional coordinatesjIs the variance of the simplex area. After the variance of the sizes of the simplex corresponding to each subdivision mode is calculated, the vertex coordinates of all the simplex corresponding to the subdivision mode with the minimum variance are stored into the cell body Z at the moment kkIn (1).
Cell body Z according to time kkPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkThe vertex coordinates of (2).
In particular, the overclad area H according to the time k+(k) Defining two parallel hyperplanes H1(k) And H2(k) The defining equation of (1).
When the simplex is triangular, the cell body Z is determined according to the k timekDetermining the linear equation of the side of each triangle according to the vertex coordinates of each triangle.
The vertex coordinates (a) of the triangle are known1,b1)、(a2,b2)、(a3,b3) Taking one side as an example, the equation of a straight line where one side is located is determined as follows:
soma Z for time kkEach triangle in (1) are connectedThe two parallel hyperplanes H1(k) And H2(k) The limiting equation and the linear equation of the triangle side to obtain the hyperplane wrapping area H+(k) Coordinates of the intersection with the straight line.
Namely, the simultaneous formula (6), the formula (7) and the formula (10), the hyperplane wrapping area H can be obtained+(k) Coordinates of the intersection with the straight line.
For time k soma ZkThe vertex coordinates of all triangles in the table are determined according to the intersection point coordinates+(k) Outer vertex coordinates and in hyperplane wrap region H+(k) Inner vertex coordinates, to be in the hyperplane envelope region H+(k) Convex polyhedron S with inner vertex coordinates as k timekThe vertex coordinates of (2).
Two, to the parameter
And performing parameter estimation, wherein the coordinates of the top end of the convex polyhedron are three-dimensional coordinates, and the simplex obtained by average triangulation is a tetrahedron.
For convex polyhedron S at k-1 momentk-1And carrying out average triangulation to obtain a plurality of subdivision modes, wherein each subdivision mode corresponds to a plurality of simplex shapes, and each simplex shape is a tetrahedron.
Aiming at each subdivision mode, acquiring the variance of the sizes of the simplex forms, and storing the vertex coordinates of all the simplex forms corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn (1).
Specifically, for each subdivision mode, calculating the area of each simplex according to the vertex coordinates of each simplex; from the areas of all the simplex, the variance of the simplex areas is calculated.
When the simplex is a tetrahedron, the coordinates of the vertices of the tetrahedron (a) are known1,b1,c1)、(a2,b2,c2)、(a3,b3,c3)、(a4,b4,c4) The volume v' of the tetrahedron can be calculated according to the following formula:
and (3) calculating the variance of the volume of the tetrahedron according to the calculated volumes of all the tetrahedrons aiming at each subdivision mode:
v'jithe volume of the ith simplex obtained in the jth subdivision is shown,
the average value of the areas of all the simplex obtained in the j subdivision mode is shown; r isjThe variance of the simplex size in the j-th subdivision mode when the average triangulation is performed is shown, and r is the three-dimensional coordinate when the coordinates of the top end of the convex polyhedron are three-dimensional coordinatesjIs the variance of the simplex volume. After the variance of the sizes of the simplex corresponding to each subdivision mode is calculated, the vertex coordinates of all the simplex corresponding to the subdivision mode with the minimum variance are stored into the cell body Z at the moment kkIn (1).
Cell body Z according to time kkPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkThe vertex coordinates of (2).
In particular, the overclad area H according to the time k+(k) Defining two parallel hyperplanes H1(k) And H2(k) The defining equation of (1).
When the simplex is tetrahedral, the cell body Z is determined by the time kkThe coordinates of the vertices of each tetrahedron determine the linear equation where the edges of the tetrahedron lie.
The vertex coordinates (a) of the tetrahedron are known1,b1,c1)、(a2,b2,c2)、(a3,b3,c3)、(a4,b4,c4) Taking one side as an example, the parameter equation form of the linear equation where one side is located is determined as follows:
wherein t is a parameter.
Soma Z for time kkEach tetrahedron of (a), the two parallel hyperplanes H being connected1(k) And H2(k) The limiting equation and the linear equation of the edges of the tetrahedron are obtained to obtain the hyperplane wrapping area H+(k) Coordinates of the intersection with the straight line.
Will exceed the plane H1(k) And H2(k) Written in the form of a dot-law equation:
(n1,n2,n3) Expressing any point on the plane, and respectively rewriting the formula (6) and the formula (7) into a dot method equation form according to the formula (13).
By simultaneously establishing equations (13) and (14), the parameter t:
substituting the formula (15) into the formula (13) to obtain the hyperplane wrapping area H+(k) Coordinates of the intersection with the straight line.
For time k soma ZkThe vertex coordinates of all tetrahedrons in (1) are determined according to the intersection point coordinates to form a hyperplane wrapping area H+(k) Outer vertex coordinates andand in the hyperplane wrapping region H+(k) Inner vertex coordinates, to be in the hyperplane envelope region H+(k) Convex polyhedron S with inner vertex coordinates as k timekThe vertex coordinates of (2).
Convex polyhedron S at moment kkAfter the vertex coordinates of (c), the convex polyhedron S at the moment kkAnd averaging all the vertex coordinates to obtain an estimated value of the parameter to be estimated.
It should be noted that: the above-mentioned serial numbers of the embodiments of the present invention are merely for description and do not represent the merits of the embodiments.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program instructing relevant hardware, where the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (5)
1. A method for filter-based industrial control system actuator parameter estimation, the method comprising:
obtaining a nonlinear second-order dynamic model of a pneumatic servo motor in an actuator of an industrial control system:
obtaining a linearization model of the pneumatic servo motor according to the nonlinear second-order dynamic model:
obtaining an initial convex polyhedron S0The vertex coordinates of (1), the initialConvex polyhedron S0The method comprises the steps of including a true value of a parameter to be estimated of a pneumatic servo motor;
for convex polyhedron S at k-1 momentk-1Carrying out average triangulation to obtain a plurality of subdivision modes, wherein each subdivision mode corresponds to a plurality of simplex shapes;
aiming at each subdivision mode, acquiring the variance of the sizes of the simplex forms, and storing the vertex coordinates of all the simplex forms corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkPerforming the following steps;
cell body Z according to the k timekPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkThe hyperplane wrap region H+(k) The method is determined according to input data and output data of the pneumatic servo motor;
for the convex polyhedron S at the k momentkAveraging all the vertex coordinates to obtain an estimated value of the parameter to be estimated;
wherein X represents servomotor rod displacement, PsIndicating the pressure in the pneumatic servomotor chamber, AeDenotes the diaphragm area, m denotes the mass bar, kxDenotes the spring and diaphragm constants, kvDenotes the valve constant, l is a constant;
φkrepresenting the observed vector of the pneumatic servomotor, ekRepresenting an unknown but bounded sequence of noise,
in order to be a known lower bound of noise,
is the known upper bound of noise;
ykrepresenting the output data of the pneumatic servomotor, ukRepresenting input data of pneumatic servomotors, ukE N (0,1), the input data andthe output data is known;
θ*representing the true value of the parameter vector theta to be estimated, theta*Unknown;
k＝1,2…,n；
2. the filter-based industrial control system actuator parameter estimation method of claim 1, wherein when the vertex coordinates of the convex polyhedron are two-dimensional coordinates, the simplex resulting from the average triangulation is a triangle;
the variance of the sizes of the simplex shapes is obtained for each subdivision mode, and the vertex coordinates of all the simplex shapes corresponding to the subdivision mode with the minimum variance are stored into the cell body Z at the moment kkIn, comprising:
aiming at each subdivision mode, calculating the area of each simplex according to the vertex coordinates of each simplex, and calculating the variance of the area of the simplex according to the areas of all the simplices;
storing the vertex coordinates of all the simplex shapes corresponding to the subdivision mode with the minimum variance into the cell body Z at the moment kkIn (1).
3. The filter-based industrial control system actuator parameter estimation method of claim 1, wherein the simplex resulting from the average triangulation is a tetrahedron when the vertex coordinates of the convex polyhedron are three-dimensional coordinates;
the variance of the sizes of the simplex shapes is obtained for each subdivision mode, and the vertex coordinates of all the simplex shapes corresponding to the subdivision mode with the minimum variance are stored into the cell body Z at the moment kkIn, comprising:
aiming at each subdivision mode, calculating the volume of each simplex according to the vertex coordinates of each simplex, and calculating the variance of the volume of the simplex according to the volumes of all the simplices;
when vertex coordinates of all simplex corresponding to the subdivision mode with the minimum variance are stored in kCarved cell body ZkIn (1).
4. The filter-based industrial control system actuator parameter estimation method of claim 1 or 2, wherein when the vertex coordinates of the convex polyhedron are two-dimensional coordinates, the simplex obtained by the average triangulation is a triangle;
the cell body Z according to the k timekPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkIncludes:
overclad area H according to time k+(k) Defining two parallel hyperplanes H1(k) And H2(k) The limiting equation of (1);
cell body Z according to time kkDetermining a linear equation where the sides of the triangle are located according to the vertex coordinates of each triangle;
for cell body Z at time kkEach triangle of (a) connecting the two parallel hyperplanes H1(k) And H2(k) The limiting equation and the linear equation of the triangle side to obtain the hyperplane wrapping area H+(k) Coordinates of the intersection point with the straight line;
determining the wrapping area H in the hyperplane according to the coordinates of the intersection point+(k) Outer vertex coordinates and in hyperplane wrap region H+(k) Inner vertex coordinates, to be in the hyperplane envelope region H+(k) Convex polyhedron S with inner vertex coordinates as k timekThe vertex coordinates of (2);
wherein the content of the first and second substances,
5. the filter-based industrial control system actuator parameter estimation method of claim 1 or 3, wherein when the vertex coordinates of the convex polyhedron are three-dimensional coordinates, the simplex obtained by the average triangulation is a tetrahedron;
the cell body according to the k timeZkPer simplex and at time k, a hyperplane envelope H+(k) Updating the convex polyhedron S to obtain the k momentkIncludes:
overclad area H according to time k+(k) Defining two parallel hyperplanes H1(k) And H2(k) The limiting equation of (1);
cell body Z according to time kkDetermining the linear equation of the edge of each tetrahedron according to the vertex coordinates of each tetrahedron;
soma Z for time kkEach tetrahedron of (a), the two parallel hyperplanes H being connected1(k) And H2(k) The limiting equation and the linear equation of the edges of the tetrahedron are obtained to obtain the hyperplane wrapping area H+(k) Coordinates of the intersection point with the straight line;
determining the wrapping area H in the hyperplane according to the coordinates of the intersection point+(k) Outer vertex coordinates and in hyperplane wrap region H+(k) Inner vertex coordinates, to be in the hyperplane envelope region H+(k) Convex polyhedron S with inner vertex coordinates as k timekThe vertex coordinates of (2);
wherein the content of the first and second substances,
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