CN114385964A - State space model calculation method, system and equipment of multivariate fractional order system - Google Patents

State space model calculation method, system and equipment of multivariate fractional order system Download PDF

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CN114385964A
CN114385964A CN202111509919.XA CN202111509919A CN114385964A CN 114385964 A CN114385964 A CN 114385964A CN 202111509919 A CN202111509919 A CN 202111509919A CN 114385964 A CN114385964 A CN 114385964A
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赵东东
阎石
孙卫国
周兴文
李艺昌
胡洋
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Abstract

The invention discloses a method, a system and equipment for calculating a state space model of a multivariate fractional order system, wherein the method for calculating the state space model of the multivariate fractional order system comprises the following steps: acquiring a rational transfer matrix of the multivariate fractional order system, and constructing a polynomial transfer matrix according to the rational transfer matrix; extracting a polynomial transfer vector of a polynomial transfer matrix; constructing a directed graph meeting a preset condition according to the polynomial transfer vector; determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, the preset construction vector, the polynomial transfer vector, the preset first relational expression and the preset corresponding relation; determining a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix; and determining a state space model corresponding to the rational transfer matrix according to the second model parameter, a preset algorithm and a preset model relation. The invention can generate a state space model with much lower internal dimension than the existing method.

Description

State space model calculation method, system and equipment of multivariate fractional order system
Technical Field
The invention relates to the technical field of model prediction, in particular to a state space model calculation method, a state space model calculation system and state space model calculation equipment of a multivariate fractional order system.
Background
Fractional calculus belongs to a mathematical tool, in the aspect of control science, a fractional calculus equation can be used for well performing mathematical description on a fractional control system and performing dynamic and stable performance analysis on the system on the basis, and the fractional calculus has unique logic and grammatical rules just like a new language. Among them, the multivariate fractional order system has been widely used in various fields such as industrial automation, economics, and abnormal diffusion in semi-infinite waves.
One of the fundamental problems of the multivariate fractional order system is the realization of a state space model, i.e. the establishment of the state space model by means of a transfer matrix, and since the internal dimension of the fractional order state space model has a direct relationship with the computational complexity and hardware implementation cost of the system, it is desirable that the internal dimension of the state space model is as low as possible. However, it is often very difficult to obtain a minimal state space model of a multivariate fractional order system, in essence unlike the conventional integer case.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art. Therefore, the invention provides a state space model calculation method of a multivariate fractional order system, which can calculate and obtain a state space model with small internal dimension.
The invention also provides a state space model calculation system of the multivariate fractional order system.
The invention also provides the electronic control equipment.
The invention also provides a computer readable storage medium.
In a first aspect, an embodiment of the present invention provides a state space model calculation method for a multivariate fractional order system, including:
acquiring a rational transfer matrix of a multivariate fractional order system, and constructing a polynomial transfer matrix according to the rational transfer matrix;
extracting a polynomial transfer vector of the polynomial transfer matrix;
constructing a directed graph meeting a preset condition according to the polynomial transfer vector;
determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, a preset construction vector, the polynomial transfer vector, a preset first relation and a preset corresponding relation;
determining a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix;
and determining a state space model corresponding to the rational transfer matrix according to the second model parameter, a preset algorithm and a preset model relational expression.
The state space model calculation method of the multivariate fractional order system in the embodiment of the invention at least has the following beneficial effects: the concept of a directed graph is introduced, the directed graph is associated with a polynomial transfer vector of a multi-element fractional order system for the first time, then a second model parameter of the polynomial transfer matrix is calculated according to the first model parameter and the polynomial transfer matrix after a first model parameter of the polynomial transfer vector is calculated, and then a state space model of the multi-element fractional order system is obtained by substituting a preset algorithm and a preset model relation according to the second model parameter.
According to another embodiment of the present invention, a method for calculating a state space model of a multivariate fractional order system, the obtaining a rational transfer matrix of the multivariate fractional order system, and constructing a polynomial transfer matrix according to the rational transfer matrix, includes:
acquiring a rational transfer matrix of the multivariate fractional order system;
converting the rational transfer matrix into a preset right-fraction matrix form to obtain a right-fraction matrix;
and determining a polynomial transfer matrix according to the right fractional matrix.
According to another embodiment of the present invention, the method for calculating a state space model of a multivariate fractional order system, the extracting polynomial transfer vectors of the polynomial transfer matrix includes:
extracting each column vector in the polynomial transfer matrix to obtain a plurality of column vectors;
determining the polynomial transfer vector from the plurality of column vectors.
According to another embodiment of the present invention, a state space model calculation method for a multivariate fractional order system, where a directed graph is composed of a finite set of nodes and an edge set, and the directed graph satisfying a preset condition is constructed according to a polynomial transfer vector, includes:
constructing the directed graph in which the finite set of nodes and the edge set satisfy a preset condition according to the polynomial transfer vector.
According to another embodiment of the present invention, the method for calculating a state space model of a multivariate fractional order system, where determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, a preset constructed vector, the polynomial transfer vector, a preset first relation and a preset corresponding relation includes:
corresponding to the preset construction vector according to the directed graph to determine a first vector matrix and a second vector matrix;
according to the polynomial transfer vector, representing the polynomial transfer vector by a preset first relational expression to determine a third directional model coefficient and a fourth directional model coefficient;
determining a first directed model coefficient and a second directed model coefficient according to the first vector matrix, the second vector matrix and a preset corresponding relation;
and determining a first model parameter corresponding to the polynomial transfer vector according to the first directed model coefficient, the second directed model coefficient, the third directed model coefficient and the fourth directed model coefficient.
According to another embodiment of the present invention, the method for calculating a state space model of a multivariate fractional order system, determining a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix includes:
obtaining column vectors of the polynomial transfer matrix to obtain a plurality of polynomial column vectors;
calculating the first model parameters of the polynomial column vectors to obtain first model parameters;
and obtaining the second model parameters corresponding to the polynomial transfer matrix according to the plurality of first model parameters.
According to another embodiment of the present invention, the method for calculating a state space model of a multivariate fractional order system, wherein determining the state space model corresponding to the rational transfer matrix according to the second model parameter, the preset algorithm and the preset model relation includes:
substituting a first polynomial model coefficient, a second polynomial model coefficient, a third polynomial model coefficient and a fourth polynomial model coefficient in the second model parameter into the preset algorithm to obtain a first model coefficient, a second model coefficient, a third model coefficient and a fourth model coefficient;
and substituting the first model coefficient, the second model coefficient, the third model coefficient and the fourth model coefficient into the preset model relational expression to obtain the state space model corresponding to the rational transfer matrix.
In a second aspect, an embodiment of the present invention provides a state space model computing system of a multivariate fractional order system, including:
the acquisition module is used for acquiring a rational transfer matrix of the multivariate fractional order system and constructing a polynomial transfer matrix according to the rational transfer matrix;
an extraction module for extracting polynomial transfer vectors of the polynomial transfer matrix;
the construction module is used for constructing a directed graph meeting a preset condition according to the polynomial transfer vector;
the first parameter calculation module is used for determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, a preset construction vector, a preset first relational expression and a preset corresponding relation;
the second parameter calculation module is used for determining second model parameters corresponding to the polynomial transfer matrix according to the first model parameters and the polynomial transfer matrix;
and the state space model construction module is used for determining the state space model corresponding to the rational transfer matrix according to the second model parameter, a preset algorithm and a preset model relational expression.
The state space model calculation system of the multivariate fractional order system in the embodiment of the invention at least has the following beneficial effects: the concept of a directed graph is introduced, the directed graph is associated with a polynomial transfer vector of a multi-element fractional order system for the first time, then a second model parameter of the polynomial transfer matrix is calculated according to the first model parameter and the polynomial transfer matrix after a first model parameter of the polynomial transfer vector is calculated, and then a state space model of the multi-element fractional order system is obtained by substituting a preset algorithm and a preset model relation according to the second model parameter.
In a third aspect, an embodiment of the present invention provides an electronic control apparatus including:
at least one processor, and,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform a method of state space model computation for a multivariate fractional order system as set forth in the first aspect.
In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium storing computer-executable instructions for causing a computer to perform the method for state space model computation for a multivariate fractional order system as set forth in the first aspect.
Additional features and advantages of the application will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by the practice of the application. The objectives and other advantages of the application may be realized and attained by the structure particularly pointed out in the written description and drawings.
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FIG. 1 is a flowchart illustrating a state space model calculation method for a multivariate fractional order system according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart diagram illustrating a state space model calculation method for a multivariate fractional order system according to another embodiment of the present invention;
FIG. 3 is a flow chart illustrating a state space model calculation method for a multivariate fractional order system according to another embodiment of the present invention;
FIG. 4 is a flowchart illustrating a state space model calculation method for a multivariate fractional order system according to another embodiment of the present invention;
FIG. 5 is a flowchart illustrating a state space model calculation method for a multivariate fractional order system according to another embodiment of the present invention;
FIG. 6 is a flowchart illustrating a state space model calculation method for a multivariate fractional order system according to another embodiment of the present invention;
FIG. 7 is a flowchart illustrating a state space model calculation method for a multivariate fractional order system according to another embodiment of the present invention;
FIG. 8 is a block diagram of a state space model calculation system for a multivariate fractional order system according to an embodiment of the present invention;
fig. 9 is a block diagram of an embodiment of an electronic control device according to the present invention.
Reference numerals: 100. an acquisition module; 200. an extraction module; 300. building a module; 400. a first parameter calculation module; 500. a second parameter calculation module; 600. a state space model building module; 700. a processor; 800. a memory.
Detailed Description
The concept and technical effects of the present invention will be clearly and completely described below in conjunction with the embodiments to fully understand the objects, features and effects of the present invention. It is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments, and those skilled in the art can obtain other embodiments without inventive effort based on the embodiments of the present invention, and all embodiments are within the protection scope of the present invention.
In the description of the present invention, if an orientation description is referred to, for example, the orientations or positional relationships indicated by "upper", "lower", "front", "rear", "left", "right", etc. are based on the orientations or positional relationships shown in the drawings, only for convenience of describing the present invention and simplifying the description, but not for indicating or implying that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and thus should not be construed as limiting the present invention.
In the description of the embodiments of the present invention, if "a number" is referred to, it means one or more, if "a plurality" is referred to, it means two or more, if "greater than", "less than" or "more than" is referred to, it is understood that the number is not included, and if "greater than", "lower" or "inner" is referred to, it is understood that the number is included. If reference is made to "first" or "second", this should be understood to distinguish between features and not to indicate or imply relative importance or to implicitly indicate the number of indicated features or to implicitly indicate the precedence of the indicated features.
One basic problem of the multivariate fractional order system is the implementation of a state space model, i.e. the establishment of the state space model by means of a transfer matrix. Since the internal dimension of the fractional order state space is directly related to the computational complexity and hardware implementation cost of the system. It is therefore desirable to achieve a state space model with as low an internal dimension as possible. However, unlike the conventional integer case, it is often very difficult to obtain a minimal state space model implementation of a multivariate fractional order system. It is therefore desirable to implement a fractional order state space model with minimal internal dimensions.
Need to explain: when an actual control system is designed, for a complex actual system, the modeling by using a fractional calculus equation is simpler and more accurate than that by using an integer model. The fractional calculus refers to a mathematical model of which the order of differentiation and integration can be arbitrary or fractional calculus, and can more accurately describe the dynamic response of an actual system. Fractional calculus belongs to a basic mathematical tool, in the aspect of control science, a fractional calculus equation can be used for well describing a fractional control system and analyzing the dynamic and stable performance of the system on the basis, and the fractional calculus has unique logic and grammatical rules like a new language.
The state space model is a dynamic time domain model, and takes the implicit time as an argument. State space model the new method for estimating a vector value state space model proposed by Aoki et al can obtain a so-called internal equilibrium state space model, any low order approximation model can be obtained without re-estimation as long as the corresponding elements in the system matrix are removed, and the obtained low order approximation model is also stable as long as the original model is stable.
A directed graph is a graph composed entirely of directed edges. Directional, as the name suggests, has a direction. The number of arcs in the directed graph starting at v is called the run-out of v and is denoted as d+(v) (ii) a The number of arcs with v as the end point is called the degree of entry of v and is denoted as d-(v) (ii) a The sum of the out-degree and in-degree of the vertex v is denoted as d (v).
The terms used in the present application are explained below.
The set N + represents a set of positive integers including 0, RmRepresenting m-dimensional real column vector space, A for matrix ATRepresents the transpose of matrix A, [ A ]]i,j(or a)i,j) The (i, j) th element of a is represented and the vector is represented in bold. I isnAnd 0nRespectively representing an n × n identity matrix and a zero matrix.
The state space model of a multivariate fractional order system can be described as:
Δαx(t)＝Ax(t)+Bu(t) (1)
y(t)＝Cx(t)+Du(t) (2)
wherein u (t) e Rq，y(t)∈RpAre input and output vectors, x (t) e RnIs a state vector of the form:
Figure BDA0003404856570000071
Figure BDA0003404856570000072
d is a real matrix of suitable dimensions, 0<αi1, m is a fractional order
Figure BDA0003404856570000073
Operator
Figure BDA0003404856570000074
The fractional order derivative is defined based on the Caputo fractional order derivative. Alpha is alphaiI 1.. m corresponding sub-state vectors are formed by
Figure BDA0003404856570000075
And (4) defining. Dimension of the state vector x (t)
Figure BDA0003404856570000076
Referred to as the internal dimensions of the state space model of the multivariate fractional order system. m-dimensional vector n ═ n1,...,nm]Also referred to as the internal dimensions of the state space model of the multivariate fractional order system. (1) The coefficients corresponding to the state space models in (2) and (2) can be simply expressed as (A, B, C, D; n).
In a first aspect, referring to fig. 1, an embodiment of the present invention discloses a state space model calculation method for a multivariate fractional order system, including:
s100, acquiring a rational transfer matrix of the multivariate fractional order system, and constructing a polynomial transfer matrix according to the rational transfer matrix;
s200, extracting a polynomial transfer vector of the polynomial transfer matrix;
s300, constructing a directed graph meeting preset conditions according to the polynomial transfer vector;
s400, determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, the preset construction vector, the polynomial transfer vector, the preset first relational expression and the preset corresponding relation;
s500, determining a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix;
s600, determining a state space model corresponding to the rational transfer matrix according to the second model parameter, the preset algorithm and the preset model relational expression.
A rational transfer matrix of a multivariate fractional order system is obtained, and then a polynomial transfer matrix is constructed according to the rational transfer matrix. Determining a polynomial transfer vector through a polynomial transfer matrix, constructing a directed graph meeting preset conditions through the polynomial transfer vector, after obtaining the directed graph, determining a corresponding vector value according to the directed graph and a preset construction vector, determining a corresponding relational expression according to the polynomial transfer vector and a preset first relational expression, and determining a first model parameter of the polynomial transfer vector according to the corresponding vector value, the corresponding relational expression and the preset corresponding relation, wherein the first model parameter is also an initial model parameter and does not represent a model parameter of a multivariate fractional order system. And determining a second model parameter corresponding to the polynomial transfer matrix through the first model parameter, the polynomial transfer vector, the polynomial transfer matrix and a preset model parameter relation, wherein the second model parameter is not the model parameter of the multivariate fractional order system, but the model parameter is further obtained according to the first model parameter, finally determining the model parameter of the multivariate fractional order system according to the second model parameter and a preset algorithm, and then determining the state space model of the rational transfer matrix according to the model parameter of the multivariate fractional order system and the preset model relation, namely obtaining the state space model of the multivariate fractional order system. Therefore, the concept of the directed graph is introduced and is firstly associated with the polynomial transfer vector of the multivariate fractional order system, the operation of calculating the second model parameter of the polynomial transfer matrix is given, the operation of calculating the first model parameter of the polynomial transfer vector is also given, and finally the state space model of the rational transfer matrix is obtained, so that the state space model with much lower internal dimensionality than that of the existing method is generated.
In order to mathematically derive the state space model in the formula (1), a polynomial transfer matrix needs to be constructed, and a sequence f (t) is set, wherein t is more than or equal to 0. The Z transformation of the sequence f (t) is defined as
Figure BDA0003404856570000081
Where Z can be considered a unit delay operator. The p × q dimensional transfer matrix of formula (1) can be easily obtained by Z-transforming the state space model in formula (1) assuming that the boundary condition is zero:
H(z)＝CZ(In-AZ)-1B+D (5)
wherein the content of the first and second substances,
Figure BDA0003404856570000091
the state space model implementation problem of the multivariate fractional order system can be described as: given a rational transfer matrix of a multivariate fractional order system, find matrices A, B, C, D and the internal dimension n such that (5) holds.
Wherein the base fraction order is alpha1,...,αmOf multivariate fractional order polynomial zβCan represent
Figure BDA0003404856570000092
In the formula of gamma1,...,γmIs a non-negative integer. The multivariate fractional order polynomial can be expressed as
Figure BDA0003404856570000093
Wherein
Figure BDA0003404856570000094
For a multivariate fractional order monomial, k ∈ {0, 1., l }. The order set of the multivariate fractional order polynomial p (z) is defined as:
Figure BDA0003404856570000095
if d (0) ≠ 0, it is said that the multivariate fractional order transfer function h (z) ═ n (z)/d (z) is causal. H (z) is said to be causal if all elements of the multivariate fractional order transfer matrix H (z) are causal.
Referring to fig. 2, in some embodiments, step S100 includes:
s110, acquiring a rational transfer matrix of the multivariate fractional order system;
s120, converting the rational transfer matrix into a preset right-fraction matrix form to obtain a right-fraction matrix;
and S130, determining a polynomial transfer matrix according to the right fractional matrix.
Acquiring a rational transfer matrix of the multivariate fractional order system, then obtaining a right-fraction matrix by using the rational transfer matrix in a preset right-fraction matrix form, and then determining the polynomial transfer matrix according to parameters of the right-fraction matrix. A further calculated polynomial transfer matrix can thus be obtained by means of the rational transfer matrix.
Specifically, the rational transfer matrix of the multivariate fractional order system is H (z), which is expressed in the form of a preset right-fraction matrix
Figure BDA0003404856570000096
Then the polynomial transfer matrix obtained from the right-part matrix is:
Figure BDA0003404856570000097
if the rational transfer matrix is:
Figure BDA0003404856570000098
the rational transfer matrix is only a rational transfer matrix formed by rational formulas, and the base fractional order of the rational transfer matrix is alpha1,α2,α3Then decomposing the rational transfer matrix into a preset right-fraction matrix form
Figure BDA0003404856570000101
The polynomial transfer matrix is reconstructed as follows:
Figure BDA0003404856570000102
therefore, the polynomial transfer matrix obtained by the formulas (9) and (10) is accurate and simple.
For example, in an aircraft drive system, the two most important components for the aircraft drive system are a hydraulic actuator and an electro-hydrostatic actuator, and therefore the rational transfer function of the multivariate fractional system of the electro-hydrostatic actuator is:
Figure BDA0003404856570000103
having a base fraction of order alpha1＝0.1,α2＝0.3,α3The following is the process of implementing its state space model using the method of the present embodiment, 0.5. First, the rational transfer matrix is written as a base fractional order alpha1,α2,α3In the form of:
Figure BDA0003404856570000104
then, a polynomial transfer matrix is constructed according to the right fractional matrix, wherein the polynomial transfer matrix is as follows:
Figure BDA0003404856570000105
therefore, the operation of obtaining the polynomial transfer matrix by calculating the rational transfer function of the multivariate fractional order system is simple.
Referring to fig. 3, in some embodiments, step S200 includes:
s210, extracting each column vector in the polynomial transfer matrix to obtain a plurality of column vectors;
and S220, determining a polynomial transfer vector according to the plurality of column vector matrixes.
If the polynomial transfer matrix is obtained, extracting each column vector in the polynomial transfer matrix to obtain a plurality of column vectors, and then obtaining the polynomial transfer vector according to the plurality of column vectors. If the polynomial transfer matrix is Hp(z) obtaining a polynomial transfer vector of by each column vector in the polynomial transfer matrix
Figure BDA0003404856570000106
Wherein
Figure BDA0003404856570000107
Is HpA column vector formed by the k-th column elements of (z), k being 1.
Specifically, if the polynomial transfer matrix is as in formula (10), the polynomial transfer vector is extracted, in this embodiment, the polynomial transfer matrix is formed by only one column vector, and the obtained polynomial transfer vector is:
Figure BDA0003404856570000111
therefore, the polynomial transfer vector obtained by the polynomial transfer matrix is easy to calculate.
For example, in the present embodiment, a polynomial transfer matrix is obtained:
Figure BDA0003404856570000112
the polynomial transfer vector is thus extracted by the polynomial transfer matrix, which in this example consists of only one column vector, thus obtaining the polynomial transfer vector as:
Figure BDA0003404856570000113
referring to fig. 4, in some embodiments, the directed graph is composed of a finite set of nodes and an edge set, and step S300 includes:
s310, constructing a directed graph of which the finite set of nodes and the edge set meet preset conditions according to the polynomial transfer vector.
The directed graph G is composed of a finite set V of nodes and a side set epsilon V multiplied by V, wherein the side set epsilon is an ordered pair (w, V) of the nodes, w is not equal to V epsilon V, w is called a leader of V for one side (w, V) epsilon, and V is a successor of w. Two preset conditions are provided, and the two preset conditions are as follows:
(a)
Figure BDA0003404856570000114
(b) for each V ∈ V (V ≠ 0), V has a leader w such that V ∈ V ≠ αi+ w holds, where w ∈ V, i ∈ {1,.., m }.
The node V in the finite set may be decomposed into: v ═ {0 }. and ═ V-1∪…∪Vm (12)
Wherein, Vi＝{v∈V|v＝αi+w,w∈V},i＝1,...,m (13)
And the set of edges ε is decomposed as:
ε＝ε1∪…∪εm (14)
wherein epsiloni＝{(w,v)|v∈Vi},i＝1,...,m. (15)
Therefore, the polynomial transfer vector is input to the preset condition (a), and then the initialization is performed, and the initialization operation is performed according to the following formula:
Figure BDA0003404856570000115
according to the preset condition (b), for
Figure BDA0003404856570000121
The following process is carried out until
Figure BDA0003404856570000122
If v ═ αiIf + w, w ∈ V, i ∈ {1,.. the m } holds, then update Vi＝Vi∪{v},εi＝εi∪{(w,v)},
Figure BDA0003404856570000123
Otherwise, find an i e { 1.,. m } such that w-v- αiWherein w can be represented as
Figure BDA00034048565700001220
Then update Vi＝Vi∪{v},εi＝εi∪{(w,v)},
Figure BDA0003404856570000125
Therefore, let ε equal to ε1∪...∪εmTo output G ═ V, epsilon.
Specifically, since the polynomial transfer vector is as in equation (11), and then initialized, we obtain:
V＝order(hp(z))＝{0,α2,2α1,α2+α3,α1+α2+α3} (17)
Figure BDA0003404856570000126
Figure BDA0003404856570000127
to pair
Figure BDA0003404856570000128
Performing iterations until
Figure BDA0003404856570000129
For the
Figure BDA00034048565700001210
Can be expressed as v ═ α2+0,0 ∈ V, i ═ 2. So that the following steps are updated:
Figure BDA00034048565700001211
Figure BDA00034048565700001212
for the
Figure BDA00034048565700001213
Cannot be expressed as v ═ αiIn the form of + w, w ∈ V, i ∈ {1, ·, m }, we choose i ═ 1 such that w ═ V- αi＝2α1-α1＝α1Can be expressed as w ═ γ1α1,γ11. So that the following steps are updated:
Figure BDA00034048565700001214
Figure BDA00034048565700001215
Figure BDA00034048565700001216
Figure BDA00034048565700001217
in the same way, until
Figure BDA00034048565700001218
The following can be obtained finally:
V1＝{α1,2α1,α1+α2+α3}、V2＝{α2}、V3＝{α2+α3,2α1+α3},、ε1＝{(0,α1),(α1,2α1),(α2+α3),(α1+α2+α3)}、ε2＝{(0,α2)}、ε3＝{(α2,α2+α3),(2α1,2α1+α3)}、
Figure BDA00034048565700001219
let epsilon equal to epsilon1∪ε2∪ε3It is possible to obtain:
ε＝{(0,α1),(α1,2α1),(α2+α3,α1+α2+α3),(0,α2),(α2,α2+α3),(2α1,2α1+α3)}
thus, a polynomial transfer vector h is obtained by V, εpThe directed graph G of (z) is (V, e).
For example, by V, ε we get a polynomial transfer vector of:
Figure BDA0003404856570000131
then substituting equation (17) to equation (25) according to the polynomial transfer vector yields:
V＝{0,α1,α3,2α3，3α3,4α3,2α3+α2,3α3+α2,4α3+α1,4α3+2α1,3α3+α2+α1}
ε＝ε1∪ε2∪ε3
＝{(0,α1),(4α3,4α3+α1),(4α3+α1,4α3+2α1),(3α3+α2,3α3+α2+α1),(2α3,2α3+α2),(3α3,3α3+α2),(0,α3)，(α3,2α3),(2α3,3α3),(3α3,4α3)}
therefore, a directed graph can be obtained by substituting the polynomial transfer vector into the formula (17) to the formula (25).
Referring to fig. 5, in some embodiments, step S400 includes:
s410, corresponding to a preset construction vector according to the directed graph to determine a first vector matrix and a second vector matrix;
s420, representing the polynomial transfer vector by a preset first relational expression to determine a third directional model coefficient and a fourth directional model coefficient;
s430, determining a first directed model coefficient and a second directed model coefficient according to the first vector matrix, the second vector matrix and a preset corresponding relation;
and S440, determining a first model parameter corresponding to the polynomial transfer vector according to the first directed model coefficient, the second directed model coefficient, the third directed model coefficient and the fourth directed model coefficient.
Wherein, predetermine and construct the vector and include:
Figure BDA0003404856570000132
Figure BDA0003404856570000141
here ViAnd εiRespectively corresponding to a formula (12) and a formula (14), corresponding to a preset construction vector v, w through a directed graph to obtain a first vector matrix and a second vector matrix, and then, carrying out polynomial transfer vector according to a preset first relational expressionExpressing to obtain a third directional model coefficient and a fourth directional model coefficient, and presetting a first relation as hp(z)＝Cpv+DpWherein, CpAnd DpAre respectively formed by1(z),...,hpThe coefficients and constants of (z). The first directed model coefficient is APThe second directed model coefficient is BPFirst, set up Ap＝0n×n,Bp＝0n×1，
Figure BDA0003404856570000142
If it is
Figure BDA0003404856570000143
Then order
Figure BDA0003404856570000144
Here, the
Figure BDA0003404856570000145
A component corresponding to w; otherwise find a t such that
Figure BDA0003404856570000146
Is established to
Figure BDA0003404856570000147
Therefore, a first directed model coefficient and a second directed model coefficient are obtained, and a first model parameter (A) corresponding to the polynomial transfer vector is determined from the first directed model coefficient, the second directed model coefficient, the third directed model coefficient, and the fourth directed model coefficientp,Bp,Cp,Dp；n)。
Specifically, according to the directed graph:
Figure BDA0003404856570000148
ε＝{(0,α1),(α1,2α1),(α2+α3,α1+α2+α3),(0,α2),(α2,α2+α3),(2α1,2α1+α3)}
according to the digraph, corresponding to a preset construction vector to obtain a first vector matrix and a second vector matrix as follows:
Figure BDA0003404856570000149
the vector is transferred according to the polynomial expression and is expressed by a preset first relation to obtain:
Figure BDA00034048565700001410
thus, the third and fourth directed model parameters are:
Figure BDA00034048565700001411
initialization
Figure BDA00034048565700001412
Because of the fact that
Figure BDA00034048565700001413
Order to
Figure BDA00034048565700001414
For the
Figure BDA00034048565700001415
Because, finding t ═ 1 satisfies
Figure BDA0003404856570000151
Thus making
Figure BDA0003404856570000152
In the same way
Figure BDA0003404856570000153
By the way, canObtaining:
Figure BDA0003404856570000154
thus, Ap(3,5)＝1,Bp(4)＝1,Ap(5,4)＝1,ApSince (6,2) is 1, the first and second directed model coefficients are obtained as follows:
Figure BDA0003404856570000155
for example, the known directed graph is:
V＝{0,α1,α3,2α3，3α3,4α3,2α3+α2,3α3+α2,4α3+α1,4α3+2α1,3α3+α2+α1}
ε＝ε1∪ε2∪ε3
＝{(0,α1),(4α3,4α3+α1),(4α3+α1,4α3+2α1),(3α3+α2,3α3+α2+α1),(2α3,2α3+α2),(3α3,3α3+α2),(0,α3)，(α3,2α3),(2α3,3α3),(3α3,4α3)}
obtaining the following result according to the corresponding relation between the preset construction vector and the directed graph:
Figure BDA0003404856570000156
n＝[4 2 4]
the polynomial transfer vector is then expressed in a preset first relation as:
Figure BDA0003404856570000157
therefore, the third and fourth directed model coefficients are obtained as:
Figure BDA0003404856570000161
then initialize Ap＝010×10,Bp＝010×1To a
Figure BDA0003404856570000162
When it is due to
Figure BDA0003404856570000163
So that Bp(1) 1. For the
Figure BDA0003404856570000164
When the temperature of the water is higher than the set temperature,
Figure BDA0003404856570000165
find t 10 so that
Figure BDA0003404856570000166
Is established, so that
Figure BDA0003404856570000167
For the
Figure BDA0003404856570000168
When the temperature of the water is higher than the set temperature,
Figure BDA0003404856570000169
find t 2 so that
Figure BDA00034048565700001610
Is established, so that
Figure BDA00034048565700001611
For the
Figure BDA00034048565700001612
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700001613
find t 6 so that
Figure BDA00034048565700001614
Is established, so that
Figure BDA00034048565700001615
For the
Figure BDA00034048565700001616
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700001617
find t 8 so that
Figure BDA00034048565700001618
Is established, so that
Figure BDA00034048565700001619
For the
Figure BDA00034048565700001620
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700001621
find t equal to 9 so that
Figure BDA00034048565700001622
Is established, so that
Figure BDA00034048565700001623
For the
Figure BDA00034048565700001624
When it is due to
Figure BDA00034048565700001625
So that Bp(7) 1. For the
Figure BDA00034048565700001626
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700001627
find t 7 so that
Figure BDA00034048565700001628
Is established, so that
Figure BDA00034048565700001629
For the
Figure BDA00034048565700001630
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700001631
find t 8 so that
Figure BDA00034048565700001632
Is established, so that
Figure BDA00034048565700001633
For the
Figure BDA00034048565700001634
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700001635
find t equal to 9 so that
Figure BDA00034048565700001636
Is established, so that
Figure BDA00034048565700001637
Finally, the first directed model coefficient and the second directed model coefficient are obtained as follows:
Figure BDA00034048565700001638
thus passing through AP、BP、CP、DPThe first model parameter, which yields the polynomial transfer vector, is (A)P,Bp,CP,DP；n)。
Referring to fig. 6, in some embodiments, step S500 includes:
s510, obtaining column vectors of a polynomial transfer matrix to obtain a plurality of polynomial column vectors;
s520, calculating first model parameters of the polynomial column vectors to obtain a plurality of first model parameters;
s530, obtaining second model parameters corresponding to the polynomial transfer matrix according to the plurality of first model parameters.
The method comprises the steps of obtaining a plurality of polynomial column vectors by obtaining column vectors of a polynomial transfer matrix, calculating the polynomial column vectors by the same method of calculating first model parameters according to the polynomial transfer vectors, obtaining a plurality of first model parameters corresponding to the polynomial column vectors, determining second model parameters according to the first model parameters, and if only one column vector of the polynomial transfer matrix exists, calculating that the first model parameters of the column vectors are consistent with the first model parameters of the polynomial column vectors, so that the first model parameters are equal to the second model parameters.
Wherein the second model parameter obtained by the first model parameters of the polynomial column vectors is
Figure BDA0003404856570000171
Wherein the content of the first and second substances,
Figure BDA0003404856570000172
wherein k is 1.
Specifically, since the polynomial transfer matrix is as follows:
Figure BDA0003404856570000173
therefore, there is only one polynomial column vector of the polynomial transfer matrix, and in this embodiment, the second model parameter of the polynomial transfer matrix is equal to the first model parameter, then (a)R,BR,CR,DR；n)＝(AP,Bp,CP,DP；n)。
For example, the polynomial column vector of the polynomial transfer matrix corresponding to the multivariate fractional order system of the electro-hydrostatic actuator in this embodiment is equal to the polynomial transfer vector, and because h isp(z)＝Hp(z)＝HR(z) so that the polynomial transfer matrix Hp(z) and HRThe first model parameter and the second model parameter of (z) are (A)R,BR,CR,DR；n)＝(AP,Bp,CP,DP；n)。
Referring to fig. 7, in some embodiments, step S600 includes:
s610, substituting a first polynomial model coefficient, a second polynomial model coefficient, a third polynomial model coefficient and a fourth polynomial model coefficient in second model parameters into a preset algorithm to obtain a first model coefficient, a second model coefficient, a third model coefficient and a fourth model coefficient;
and S620, substituting the first model coefficient, the second model coefficient, the third model coefficient and the fourth model coefficient into a preset model relational expression to obtain a state space model corresponding to the rational transfer matrix.
In the present embodiment, since the polynomial column vector of the polynomial transfer matrix coincides with the polynomial transfer vector, the second model parameter is the same as the first model parameter. Wherein, the preset algorithm is as follows:
Figure BDA0003404856570000181
Figure BDA0003404856570000182
Figure BDA0003404856570000183
therefore, the first, second, third and fourth model coefficients are substituted into equations (31) to (33) according to the first, second, third and fourth polynomial model coefficients in the second model parameters to obtain the first, second, third and fourth model coefficients. The preset model relations are as shown in the formulas (1) and (2), so that the state space model of the rational transfer matrix can be obtained by substituting the first model coefficient, the second model coefficient, the third model coefficient and the fourth model coefficient obtained from the formulas (31) to (33) into the formulas (1) and (3), namely the state space model of the multivariate fractional order system is obtained, and the state space calculation of the multivariate fractional order system is simple and accurate.
In particular, since the polynomial column vector of the polynomial transfer matrix is only one, the polynomial transfer matrix is not limited to two columns
Figure BDA0003404856570000184
Therefore, the third model coefficient and the fourth model coefficient obtained from the formula (31) are
CN＝[ 12 11 13 140 p 0 p p p],DN＝[p10]
CD＝[ 23 21 22 230 0 p p p p],DD＝[p20]
By the formula
Figure BDA0003404856570000185
The first model coefficient, the second model coefficient, the third model coefficient and the fourth model coefficient of the rational transfer matrix h (z) required in this example are calculated as follows:
Figure BDA0003404856570000191
Figure BDA0003404856570000192
Figure BDA0003404856570000193
n＝[3 1 2]. Therefore, the obtained state space model of the multivariate fractional order system is simple and accurate.
For example, by
Figure BDA0003404856570000194
Obtaining a third model coefficient and a fourth model coefficient:
CN＝[0 0 0 -0.1 0 0 0 0 0 0],DN＝[0]
CD＝[-8.3 0.9 3.7 0 15.4 0 0 0 -2.8 0],DD＝[1]
by calculation of formula
Figure BDA0003404856570000195
The first model coefficient, the second model coefficient, the third model coefficient and the fourth model coefficient are further obtained by calculation as follows:
Figure BDA0003404856570000196
C＝[0 0 0 -0.1|0 0|0 0 0 0],D＝[0]；n＝[4 2 4]
therefore, the state space model of h (z) can be obtained by substituting the above A, B, C, D into the equations (1) and (2).
The state space model calculation method of the multivariate fractional order system according to the embodiment of the invention is described in detail in a specific embodiment with reference to fig. 1 to 7. It is to be understood that the following description is only exemplary, and not a specific limitation of the invention.
By calculating the multivariate fractional order system of the electric hydrostatic actuating mechanism, the transfer function of the multivariate fractional order system is firstly obtained as follows:
Figure BDA0003404856570000201
its base fraction order alpha1＝0.1,α2＝0.3,α3First, a rational transfer function matrix is written 0.5Fractional order of composition alpha1,α2,α3In the form of (a) a (b),
Figure BDA0003404856570000202
constructing a polynomial transfer matrix:
Figure BDA0003404856570000203
the polynomial transfer vector is extracted through the polynomial transfer matrix, in this example, the polynomial transfer matrix is composed of only one column vector, and the obtained polynomial transfer vector is:
Figure BDA0003404856570000204
then, the vector h is transmitted according to the polynomialp(z) construct directed graph G ═ V, epsilon):
V＝{0,α1,α3,2α3，3α3,4α3,2α3+α2,3α3+α2,4α3+α1,4α3+2α1,3α3+α2+α1}
ε＝ε1∪ε2∪ε3
＝{(0,α1),(4α3,4α3+α1),(4α3+α1,4α3+2α1),(3α3+α2,3α3+α2+α1),(2α3,2α3+α2),(3α3,3α3+α2),(0,α3)，(α3,2α3),(2α3,3α3),(3α3,4α3)}
the first vector matrix and the second vector matrix are obtained by corresponding the directed graph with a preset construction vector as follows:
Figure BDA0003404856570000211
n＝[4 2 4]
then h is putp(z) is represented by hp(z)＝Cpv+DpIn the form of:
Figure BDA0003404856570000212
Figure BDA0003404856570000213
Figure BDA0003404856570000214
initialization Ap＝010×10,Bp＝010×1To a
Figure BDA0003404856570000215
When it is due to
Figure BDA0003404856570000216
So that Bp(1) 1. For the
Figure BDA0003404856570000217
When the temperature of the water is higher than the set temperature,
Figure BDA0003404856570000218
find t 10 so that
Figure BDA0003404856570000219
Is established, so that
Figure BDA00034048565700002110
For the
Figure BDA00034048565700002111
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700002112
find t 2 makesTo obtain
Figure BDA00034048565700002113
Is established, so that
Figure BDA00034048565700002114
For the
Figure BDA00034048565700002115
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700002116
find t 6 so that
Figure BDA00034048565700002117
Is established, so that
Figure BDA00034048565700002118
For the
Figure BDA00034048565700002119
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700002120
find t 8 so that
Figure BDA00034048565700002121
Is established, so that
Figure BDA00034048565700002122
For the
Figure BDA00034048565700002123
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700002124
find t equal to 9 so that
Figure BDA00034048565700002125
Is established, so that
Figure BDA00034048565700002126
For the
Figure BDA00034048565700002127
When it is due to
Figure BDA00034048565700002128
So that Bp(7) 1. For the
Figure BDA00034048565700002129
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700002130
find t 7 so that
Figure BDA00034048565700002131
Is established, so that
Figure BDA00034048565700002132
For the
Figure BDA00034048565700002133
When the temperature of the water is higher than the set temperature,
Figure BDA00034048565700002134
find t 8 so that
Figure BDA00034048565700002135
Is established, so that
Figure BDA00034048565700002136
For the
Figure BDA0003404856570000221
When the temperature of the water is higher than the set temperature,
Figure BDA0003404856570000222
find t equal to 9 so that
Figure BDA0003404856570000223
Is established, so that
Figure BDA0003404856570000224
Finally we get the first model parameters:
Figure BDA0003404856570000225
because of hp(z)＝Hp(z)＝HR(z) so that the first model parameter and the second model parameter are equal, e.g., (A)R,BR,CR,DR；n)＝(AP,Bp,CP,DP；n)。
By
Figure BDA0003404856570000226
Obtaining:
CN＝[0 0 0 -0.1 0 0 0 0 0 0],DN＝[0]
CD＝[-8.3 0.9 3.7 0 15.4 0 0 0 -2.8 0],DD＝[1]
by calculation of formula
Figure BDA0003404856570000227
The calculation can yield:
Figure BDA0003404856570000228
C＝[0 0 0 -0.1|0 0|0 0 0 0],D＝[0]；n＝[4 2 4]
thus, a state space model (A, B, C, D; n) of the rational transfer matrix is finally obtained
In a second aspect, referring to fig. 8, an embodiment of the present invention further discloses a state space model calculation system of a multivariate fractional order system, including: the system comprises an acquisition module 100, an extraction module 200, a construction module 300, a first parameter calculation module 400, a second parameter calculation module 500 and a state space model construction module 600; the obtaining module 100 is configured to obtain a rational transfer matrix of the multivariate fractional order system, and construct a polynomial transfer matrix according to the rational transfer matrix; the extracting module 200 is configured to extract a polynomial transfer vector of the polynomial transfer matrix; the construction module 300 is configured to construct a directed graph satisfying a preset condition according to the polynomial transfer vector; the first parameter calculation module 400 is configured to determine a first model parameter corresponding to a polynomial transfer vector according to the directed graph, a preset construction vector, a preset first relation, and a preset corresponding relationship; the second parameter calculation module 500 is configured to determine a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix; the state space model building module 600 is configured to determine a state space model corresponding to the rational transfer matrix according to the second model parameter, the preset algorithm, and the preset model relation.
The rational transfer matrix of the multivariate fractional order system is obtained through the obtaining module 100, the polynomial transfer vector of the rational transfer matrix is extracted through the extracting module 200, the constructing module 300 constructs a directed graph meeting preset conditions according to the polynomial transfer vector, then a first model parameter corresponding to the polynomial transfer vector can be determined according to the directed graph, the preset constructed vector, the preset first relational expression and the preset corresponding relation, a second model parameter corresponding to the polynomial transfer matrix is obtained through calculation according to the polynomial transfer matrix and the first model parameter, and finally a state space model corresponding to the rational transfer matrix is determined according to the second model parameter, the preset algorithm and the preset model relational expression, namely the state space model of the multivariate fractional order system is determined, so that the state space model of the multivariate fractional order system is obtained through calculation, and is simple and accurate.
The specific calculation process of the state space model calculation system of the multivariate fractional order system refers to the state space model calculation method of the multivariate fractional order system in the first aspect, and therefore details are not repeated here.
In a third aspect, referring to fig. 9, an electronic control apparatus, comprising:
at least one processor 700, and,
a memory 800 communicatively coupled to the at least one processor 700; wherein the content of the first and second substances,
the memory 800 stores instructions executable by the at least one processor 700 to enable the at least one processor 700 to perform a method of state space model computation for a multivariate fractional order system as described in the first aspect.
The electronic control equipment can be mobile terminal equipment or non-mobile terminal equipment. The mobile terminal equipment can be a mobile phone, a tablet computer, a notebook computer, a palm computer, vehicle-mounted terminal equipment, wearable equipment, a super mobile personal computer, a netbook, a personal digital assistant, CPE, UFI (wireless hotspot equipment) and the like; the non-mobile terminal equipment can be a personal computer, a television, a teller machine or a self-service machine and the like; the embodiments of the present invention are not particularly limited.
The electronic device may include a processor 700, an external memory interface, and an internal memory.
Processor 700 may include one or more processing units, such as: processor 700 may include an Application Processor (AP), a modem processor, a Graphics Processing Unit (GPU), an Image Signal Processor (ISP), a controller, memory 800, a video codec, a Digital Signal Processor (DSP), a baseband processor, and/or a neural-Network Processing Unit (NPU), among others. The different processing units may be separate devices or may be integrated in one or more processors 700.
A memory 800 may also be provided in the processor 700 for storing instructions and data. In some embodiments, memory 800 in processor 700 is a cache memory. The memory 800 may hold instructions or data that have just been used or recycled by the processor 700. If the processor 700 needs to use the instruction or data again, it can be called directly from the memory 800. Avoiding repeated accesses reduces the latency of the processor 700, thereby increasing the efficiency of the system.
In a fourth aspect, a computer-readable storage medium stores computer-executable instructions for causing a computer to perform the method for state space model computation for a multivariate fractional order system as set forth in the first aspect.
The above-described embodiments of the apparatus are merely illustrative, wherein the units illustrated as separate components may or may not be physically separate, i.e. may be located in one place, or may also be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment.
One of ordinary skill in the art will appreciate that all or some of the steps, systems, and methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as is well known to those of ordinary skill in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, Digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by a computer. In addition, communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media as known to those skilled in the art.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention. Furthermore, the embodiments of the present invention and the features of the embodiments may be combined with each other without conflict.

Claims (10)

1. A state space model calculation method of a multivariate fractional order system is characterized by comprising the following steps:
acquiring a rational transfer matrix of a multivariate fractional order system, and constructing a polynomial transfer matrix according to the rational transfer matrix;
extracting a polynomial transfer vector of the polynomial transfer matrix;
constructing a directed graph meeting a preset condition according to the polynomial transfer vector;
determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, a preset construction vector, the polynomial transfer vector, a preset first relation and a preset corresponding relation;
determining a second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix;
and determining a state space model corresponding to the rational transfer matrix according to the second model parameter, a preset algorithm and a preset model relational expression.
2. The method of claim 1, wherein the obtaining a rational transfer matrix of the multivariate fractional order system and constructing a polynomial transfer matrix according to the rational transfer matrix comprises:
acquiring a rational transfer matrix of the multivariate fractional order system;
converting the rational transfer matrix into a preset right-fraction matrix form to obtain a right-fraction matrix;
and determining a polynomial transfer matrix according to the right fractional matrix.
3. The method of claim 1, wherein the extracting polynomial transfer vectors of the polynomial transfer matrix comprises:
extracting each column vector in the polynomial transfer matrix to obtain a plurality of column vectors;
determining the polynomial transfer vector from the plurality of column vectors.
4. The state space model calculation method of a multivariate fractional order system according to claim 1, wherein the directed graph is composed of a finite set of nodes and an edge set, and constructing the directed graph satisfying a preset condition according to the polynomial transfer vector comprises:
constructing the directed graph in which the finite set of nodes and the edge set satisfy a preset condition according to the polynomial transfer vector.
5. The method for calculating the state space model of the multivariate fractional order system according to any one of claims 1 to 4, wherein the determining the first model parameters corresponding to the polynomial transfer vectors according to the directed graph, the preset construction vectors, the polynomial transfer vectors, the preset first relations and the preset corresponding relations comprises:
corresponding to the preset construction vector according to the directed graph to determine a first vector matrix and a second vector matrix;
according to the polynomial transfer vector, representing the polynomial transfer vector by a preset first relational expression to determine a third directional model coefficient and a fourth directional model coefficient;
determining a first directed model coefficient and a second directed model coefficient according to the first vector matrix, the second vector matrix and a preset corresponding relation;
and determining a first model parameter corresponding to the polynomial transfer vector according to the first directed model coefficient, the second directed model coefficient, the third directed model coefficient and the fourth directed model coefficient.
6. The method of claim 5, wherein the determining the second model parameter corresponding to the polynomial transfer matrix according to the first model parameter and the polynomial transfer matrix comprises:
obtaining column vectors of the polynomial transfer matrix to obtain a plurality of polynomial column vectors;
calculating the first model parameters of the polynomial column vectors to obtain first model parameters;
and obtaining the second model parameters corresponding to the polynomial transfer matrix according to the plurality of first model parameters.
7. The method for calculating the state space model of the multivariate fractional order system according to any one of claims 1 to 4, wherein the determining the state space model corresponding to the rational transfer matrix according to the second model parameter, a preset algorithm and a preset model relation comprises:
substituting a first polynomial model coefficient, a second polynomial model coefficient, a third polynomial model coefficient and a fourth polynomial model coefficient in the second model parameter into the preset algorithm to obtain a first model coefficient, a second model coefficient, a third model coefficient and a fourth model coefficient;
and substituting the first model coefficient, the second model coefficient, the third model coefficient and the fourth model coefficient into the preset model relational expression to obtain the state space model corresponding to the rational transfer matrix.
8. A state space model computation system for a multivariate fractional order system, comprising:
the acquisition module is used for acquiring a rational transfer matrix of the multivariate fractional order system and constructing a polynomial transfer matrix according to the rational transfer matrix;
an extraction module for extracting polynomial transfer vectors of the polynomial transfer matrix;
the construction module is used for constructing a directed graph meeting a preset condition according to the polynomial transfer vector;
the first parameter calculation module is used for determining a first model parameter corresponding to the polynomial transfer vector according to the directed graph, a preset construction vector, a preset first relational expression and a preset corresponding relation;
the second parameter calculation module is used for determining second model parameters corresponding to the polynomial transfer matrix according to the first model parameters and the polynomial transfer matrix;
and the state space model construction module is used for determining the state space model corresponding to the rational transfer matrix according to the second model parameter, a preset algorithm and a preset model relational expression.
9. An electronic control apparatus, characterized by comprising:
at least one processor, and,
a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform a method of state space model computation for a multivariate fractional order system as claimed in any one of claims 1 to 7.
10. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the state space model calculation method of the multivariate fractional order system according to any one of claims 1 to 7.
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