CN110095982B - Automatic identification method for load characteristics, state space model and control method for power supply - Google Patents

Automatic identification method for load characteristics, state space model and control method for power supply Download PDF

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CN110095982B
CN110095982B CN201910321220.7A CN201910321220A CN110095982B CN 110095982 B CN110095982 B CN 110095982B CN 201910321220 A CN201910321220 A CN 201910321220A CN 110095982 B CN110095982 B CN 110095982B
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疏坤
章明
韩超
龙锋利
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Jiangsu Cascc Intelligent Industrial Equipment Co ltd
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Abstract

The invention relates to the identification field, in particular to an automatic identification method of load characteristics, a state space model and a control method of a power supply, wherein the automatic identification method of embedded load characteristics comprises the following steps: taking a unit module with load characteristics as an identified object; output y by recognition of a recognized object ID Identify input u ID Constructing a self-adaptive state space model; the adaptive state space model is adapted to adjust the recognition input to the recognized object according to its variation. The method realizes the automatic construction of the self-adaptive state space model according to the input and output characteristics of the identified object.

Description

Automatic identification method for load characteristics, state space model and control method for power supply
Technical Field
The invention relates to the field of identification, in particular to an automatic identification method for load characteristics, a state space model and a control method for a power supply.
Background
At present, in many fields, input and output characteristics of an external controlled object are automatically identified according to different sampling period settings, and a state space model of the external controlled object is automatically output, so as to fulfill detection requirements of the controlled object in different industries.
Based on the above technical problems, a new automatic identification method for load characteristics, a state space model and a control method for power supply are needed to be designed.
Disclosure of Invention
The invention aims to provide an automatic identification method of load characteristics, a state space model and a control method of a power supply.
In order to solve the above technical problems, the present invention provides an automatic identification method for embedded load characteristics, including:
taking a unit module with load characteristics as an identified object;
output y by recognition of a recognized object ID Identify input u ID Constructing a self-adaptive state space model;
the adaptive state space model is adapted to adjust the recognition input to the recognized object according to its variation.
Further, the automatic identification method for the embedded load characteristics further comprises the following steps:
will recognize input u ID And an identification output y corresponding thereto ID A pair of I/O data pairs recorded as the adaptive state space model; and
by recognizing input u ID And an identification output y ID The method for constructing the adaptive state space model comprises the following steps:
calculating the order I of the estimated adaptive state space model according to the number s of I/O data pairs, constructing a matrix column number j used in constructing a Hankel matrix, and constructing a Hankel matrix by using the value of the matrix column number N used in constructing the Hankel matrix, wherein
Figure BDA0002034762530000021
Setting the adaptive state space model to have m-dimensional input and l-dimensional output, and corresponding identification input
Figure BDA0002034762530000022
Set the identification output->
Figure BDA0002034762530000023
Wherein k is E [0, s-1]]S is greater than 5 times m×i, m being the dimension of the input signal; l is the dimension of the output signal; k is a discrete time variable;
Figure BDA0002034762530000024
is the real number domain.
Further, a recognition input u is constructed from the values of i, j and N ID And an identification output y ID Hankel matrix of (a), i.e.)
Figure BDA0002034762530000025
Figure BDA0002034762530000026
Figure BDA0002034762530000027
Figure BDA0002034762530000028
In the Hankel matrix described above, U 0,i,N Is an input Hankel matrix before the i-th moment; u (U) i,j,N Inputting Hankel matrixes from the ith moment to the jth moment; y is Y 0,i,N An output Hankel matrix before the ith moment; y is Y i,j,N Is the output Hankel matrix from the i-th moment to the j-th moment.
Further, U is 0,i,N 、U i,j,N 、Y 0,i,N And Y i,j,N LQ decomposition is performed, orthogonal projection is performed to obtain an adaptive state space model extended observability matrix Γ j I.e.
Figure BDA0002034762530000031
In the method, in the process of the invention,
Figure BDA0002034762530000032
Figure BDA0002034762530000033
wherein the method comprises the steps of
L 11 ～L 44 Reflecting U 0,i,N Is spread into space, U i,j,N The row vectors are spatially spread to Y 0,i,N Is spread into space, Y i,j,N Is stretched into a projection component of space.
Further, for L 42 And L 43 Singular value decomposition of matrices, i.e.
Figure BDA0002034762530000034
Wherein U is [ L ] 42 L 43 ]A matrix is subjected to singular value decomposition to obtain a left-hand matrix;
v is [ L ] 42 L 43 ]Right-square matrix obtained by singular value decomposition of matrix;
sigma is a eigenvalue matrix of the adaptive state space model;
t is the transpose;
Σ 1 a non-zero characteristic value of a self-adaptive state space model of the identified object;
Σ 2 is a zero matrix;
U 1 ,U 2 is based on sigma 1 The number of U is divided into blocks, U 1 Is equal to Σ 1 Line number of U 2 Is equal to Σ 2 The number of rows of (3); and
V 1 T ,
Figure BDA0002034762530000035
is based on sigma 1 Number of pairs V T Partitioning, V 1 T Is equal to Σ 1 Column number of->
Figure BDA0002034762530000036
Is equal to Σ 2 Is a column number of columns.
Further, take U 1 The left n column vectors are denoted as U n ，U n The upper l (j-1) row of (C) is denoted as U p The lower l (j-1) column is denoted as U q Then the state space model matrix is self-adapted
Figure BDA0002034762530000041
C is U n Upper row of (2); n is the actual order obtained by i.
Further, the overdetermined equation is solved by a least square method to obtain an adaptive state space model matrix A, B, C, D and an initial state x 0 And constructing an adaptive state space model of the identified object, namely
The overdetermined equation is:
Figure BDA0002034762530000042
wherein: y is Y 0,s,1 To y ID Is written in the form of a single column vector; Γ -shaped structure s Expanding a considerable matrix for a system of identified objects; phi, ψ, Ω, xi are intermediate variables;
Figure BDA0002034762530000043
Y 0,s,1 column and column rows for all the identification output data;
Figure BDA0002034762530000044
Figure BDA0002034762530000045
Figure BDA0002034762530000046
is Kronecker product;
Figure BDA0002034762530000047
I l is an l-dimensional identity matrix;
Figure BDA0002034762530000048
vec () is the column of matrix columns in brackets; τ is the subscript used in the accumulation operation;
the adaptive state space model is:
x k+1 ＝Ax k +Bu k
y k ＝Cx k +Du k ；
wherein x is k+1 Forecasting the state variable of the identified object at the next moment of the current k moment; x is x k To be identified as a pairState variable estimation values like time k; u (u) k An input signal at the moment k of the identified object; y is k Forecast the output signal of the identified object at the moment k.
Further, the automatic identification method for the embedded load characteristics further comprises the following steps: verifying whether the adaptive state-space model is accurate, i.e
The recognized object receives the verification recognition input u test After which verification identification output y is generated test And utilizes the adaptive state space model to identify the input u according to the verification test Obtaining output signal forecast y pre When y is tset And y pre And when the self-adaptive state space model is the same, the self-adaptive state space model is judged to be accurate.
In yet another aspect, the present invention further provides an adaptive state space model for automatic identification of load characteristics, comprising:
x k+1 ＝Ax k +Bu k
y k ＝Cx k +Du k ；
wherein x is k+1 Forecasting the state variable of the identified object at the next moment of the current k moment; x is x k A state variable estimated value at the moment k of the identified object; u (u) k An input signal at the moment k of the identified object; y is k Forecasting an output signal of the identified object at the moment k; A. b, C, D is an adaptive state space model matrix.
Further, the overdetermined equation is solved by a least square method to obtain an adaptive state space model matrix A, B, C, D and an initial state x 0 And constructing an adaptive state space model of the identified object, namely
The overdetermined equation is:
Figure BDA0002034762530000051
wherein: y is Y 0,s,1 To y ID Is written in the form of a single column vector; Γ -shaped structure s Expanding a considerable matrix for a system of identified objects; phi, ψ, Ω, xi are intermediate variables;
Figure BDA0002034762530000061
Y 0,s,1 column and column rows for all the identification output data;
Figure BDA0002034762530000062
Figure BDA0002034762530000063
Figure BDA0002034762530000064
is Kronecker product; />
Figure BDA0002034762530000065
I l Is an l-dimensional identity matrix;
Figure BDA0002034762530000066
vec () is the column of matrix columns in brackets; τ is the subscript used in the accumulation operation;
the adaptive state space model matrix
Figure BDA0002034762530000067
C is U n Upper row of (2);
the U is n To take U 1 N column vectors to the left of (a); u (U) n The upper l (j-1) row of (C) is denoted as U p The lower l (j-1) column is denoted as U q N is the actual order obtained by i; u (U) 1 Is equal to Σ 1 The number of rows of (3); sigma and method for producing the same 1 The characteristic value of the self-adaptive state space model of the identified object; sigma and method for producing the same 2 Is a zero matrix; i is the order of the estimated adaptive state space model.
In a third aspect, the present invention also provides a control method of a switch-mode digital power supply, including:
a power supply power main loop and a digital control board card for controlling the output voltage of the power supply power main loop;
the digital control board card is suitable for adjusting and stabilizing the output voltage according to the load characteristic change through the embedded load characteristic automatic identification method.
The method has the beneficial effects that the unit module with the load characteristic is used as an identified object; output y by recognition of a recognized object ID Identify input u ID Constructing a self-adaptive state space model; the self-adaptive state space model is suitable for adjusting the identification input of the identified object according to the change of the identified object so as to automatically construct the self-adaptive state space model according to the input and output characteristics of the identified object.
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The invention will be further described with reference to the drawings and examples.
FIG. 1 is a flow chart of an embedded load characteristic automatic identification method according to the present invention;
FIG. 2 (a) is a discrete plot of the prediction error of the resistive load adaptive state space model according to the present invention;
fig. 2 (b) is a dispersion diagram of prediction errors of the resistive load adaptive state space model according to the present invention.
Detailed Description
The invention will now be described in further detail with reference to the accompanying drawings. The drawings are simplified schematic representations which merely illustrate the basic structure of the invention and therefore show only the structures which are relevant to the invention.
Example 1
Fig. 1 is a flowchart of an embedded load characteristic automatic identification method according to the present invention.
As shown in fig. 1, the present embodiment provides an automatic identification method for embedded load characteristics, including: taking a unit module with load characteristics as an identified object (the identified object can be, but is not limited to, a transmitter, a filtering unit and a load); output y by recognition of a recognized object ID Identify input u ID Constructing an adaptive state space modelA shape; the self-adaptive state space model is suitable for adjusting the identification input of the identified object according to the change of the identified object, and the self-adaptive state space model is automatically built according to the input and output characteristics of the identified object.
In this embodiment, a pseudo random sequence generator (PRNG) is implemented on an FPGA chip to generate a series of pseudo random sequences of configurable amplitude, length and update period, which are used as the identification input u of the identified object ID The identified object is in u ID Under the action of the control unit, a series of responses are generated, and the responses are converted into digital signals which can be processed by a field sensor and an ADC (the processor control unit can take an FPGA as a control core and an integrated SOPC soft core processor), namely an identification output y ID The method comprises the steps of carrying out a first treatment on the surface of the During the identification process, the control unit issues a synchronous write signal under which the memory (which may be but is not limited to using FIFO) synchronously stores u ID And y ID Forming input/output (I/O) data pairs in a one-to-one correspondence and waiting for read signals of an on-chip bus; the introduction of PRNG can realize strong randomness signal with long repetition period, and the data update period (DUC), amplitude and length can be specified by the identification command parameters; the signal has the characteristics of large bandwidth, wide frequency spectrum and adjustable strength, and can achieve better identification effect compared with a method for identifying by using system noise; u (u) ID When updating is finished according to the preset data length, the moment is the end moment of the identification process; the on-chip processor (i.e. the SOPC soft core processor) reads the I/O data pair in the memory under the instruction of the off-chip processor (the off-chip processor may be but not limited to a PC or the like) or automatically through the on-chip bus, and stores the I/O data pair in the memory, and if the on-board FPGA off-chip RAM with a larger capacity exists, the on-board processor may also be configured to use the RAM as the memory of the on-chip processor; after the data enter the memory, the SOPC soft core processor is suitable for reading the I/O data pair and constructing a self-adaptive state space model of the identified object according to the I/O data pair.
In this embodiment, the method for automatically identifying embedded load characteristics further includes: will recognize input u ID And an identification output y corresponding thereto ID A pair of I/O data pairs recorded as the adaptive state space model; by recognizing input u ID And an identification output y ID The method for constructing the adaptive state space model comprises the following steps: calculating a pre-estimated adaptive state space model order I (which is determined by the load characteristics and recognition requirements of the recognized object and is greater than the number of main modes of the recognized object) based on the number s (recognition command parameters) of I/O data pairs, which can be, but is not limited to, a value designated as a slightly greater order of 10, the number j of matrix columns used in constructing the Hankel matrix, and the number N of matrix columns used in constructing the Hankel matrix, as a parameter of the recognition command, to construct the Hankel matrix, wherein
Figure BDA0002034762530000081
Setting the adaptive state space model to have m-dimensional input and l-dimensional output, and corresponding identification input
Figure BDA0002034762530000091
Set the identification output->
Figure BDA0002034762530000092
Wherein k is E [0, s-1]]S is greater than 5 times m×i, m being the dimension of the input signal; l is the dimension of the output signal; k is a discrete time variable;
Figure BDA0002034762530000093
is the real number domain.
In the present embodiment, the recognition input u is constructed from the values of i, j and N ID And an identification output y ID Hankel matrix of (a), i.e.)
Figure BDA0002034762530000094
Figure BDA0002034762530000095
Figure BDA0002034762530000096
Figure BDA0002034762530000097
In the Hankel matrix described above, U 0,i,N For inputting Hankel matrix (to u) before the ith moment (i.e. initial moment to the ith moment) ID Is obtained by arranging values of (a); u (U) i,j,N For inputting Hankel matrix from the ith to the jth time (u will be ID Is obtained by arranging values of (a); y is Y 0,i,N For outputting the Hankel matrix (to be y) before the ith moment (i.e. the initial moment to the ith moment) ID Is obtained by arranging values of (a); y is Y i,j,N For outputting Hankel matrices (to be y) ID Is obtained by arranging values of (a); the value of j > i, j is equal to the value of the matrix column number j, and the value of i is equal to the value of the estimated adaptive state space model order i.
In the present embodiment, U is 0,i,N 、U i,j,N 、Y 0,i,N And Y i,j,N LQ decomposition is performed, orthogonal projection is performed to obtain an adaptive state space model extended observability matrix Γ j I.e.
Figure BDA0002034762530000101
In the method, in the process of the invention,
Figure BDA0002034762530000102
Figure BDA0002034762530000103
wherein the method comprises the steps of
L 11 ～L 44 Reflecting U 0,i,N Is spread into space, U i,j,N The row vectors are spatially spread to Y 0,i,N Is spread into space, Y i,j,N Is stretched into a projection component of the space; q (Q) 1 ～Q 4 To U 0,i,N 、U i,j,N 、Y 0,i,N And Y i,j,N The Q matrix obtained by LQ decomposition is obtained by partitioning.
In the present embodiment, for L 42 And L 43 Singular value decomposition of matrices, i.e.
Figure BDA0002034762530000104
Wherein U is [ L ] 42 L 43 ]A matrix is subjected to singular value decomposition to obtain a left-hand matrix; v is [ L ] 42 L 43 ]Right-square matrix obtained by singular value decomposition of matrix; sigma is a eigenvalue matrix of the adaptive state space model; t is the transpose; sigma and method for producing the same 1 A non-zero characteristic value of a self-adaptive state space model of the identified object; sigma and method for producing the same 2 Is a zero matrix; u (U) 1 ,U 2 Is based on sigma 1 The number of U is divided into blocks, U 1 Is equal to Σ 1 Line number of U 2 Is equal to Σ 2 The number of rows of (3); v (V) 1 T ,
Figure BDA0002034762530000105
Is based on sigma 1 Number of pairs V T Partitioning, V 1 T Is equal to Σ 1 Column number of->
Figure BDA0002034762530000106
Is equal to Σ 2 Is a column number of columns.
In the present embodiment, U is taken 1 The left n column vectors are denoted as U n ，U n The upper l (j-1) row of (C) is denoted as U p The lower l (j-1) column is denoted as U q Then the state space model matrix is self-adapted
Figure BDA0002034762530000107
C is U n Upper row of (2); n is the actual order obtained by i, i.e. the value of i is automatically reduced in the calculation to the actual order n that the identified object represents at the current sampling frequency.
In the present embodiment, by least squareSolving the overdetermined equation to obtain the adaptive state space model matrix A, B, C, D and the initial state x 0 And constructing an adaptive state space model of the identified object, namely
The overdetermined equation is:
Figure BDA0002034762530000111
wherein: y is Y 0,s,1 To y ID Is written in the form of a single column vector; Γ -shaped structure s Expanding a considerable matrix for a system of identified objects; phi, ψ, Ω, xi are intermediate variables;
Figure BDA0002034762530000112
Y 0,s,1 column and column rows for all the identification output data;
Figure BDA0002034762530000113
Figure BDA0002034762530000114
Figure BDA0002034762530000115
is Kronecker product;
Figure BDA0002034762530000116
I l is an l-dimensional identity matrix;
Figure BDA0002034762530000117
vec () is the column of matrix columns in brackets; τ is the subscript used in the accumulation operation;
the adaptive state space model is:
x k+1 ＝Ax k +Bu k
y k ＝Cx k +Du k ；
wherein x is k+1 Forecasting the state variable of the identified object at the next moment of the current k moment; x is x k A state variable estimated value at the moment k of the identified object; u (u) k An input signal at the moment k of the identified object; y is k Forecast the output signal of the identified object at the moment k.
In this embodiment, the method for automatically identifying embedded load characteristics further includes: verifying whether the adaptive state-space model is accurate, i.e
The recognized object receives the verification recognition input u test After which verification identification output y is generated test And utilizes the adaptive state space model to identify the input u according to the verification test Obtaining output signal forecast y pre When y is tset And y pre When the self-adaptive state space model is the same, the self-adaptive state space model is judged to be accurate; to ensure the accuracy of the verification of the adaptive state space model, u ID And u is equal to test There should be a large uncorrelation, and the adaptive state space model should be determined by the method of u ID U is significantly different test Calculating output data conforming to the I/O data pair; the accuracy of the adaptive state space model can be verified under the most stringent conditions by using random numbers as test inputs.
In this embodiment, the embedded load characteristic automatic identification method may be, but is not limited to, programmed in a soft-core processor (i.e., SOPC soft-core processor) through c++.
Example 2
On the basis of embodiment 1, this embodiment also provides an adaptive state space model for automatic identification of load characteristics, including:
x k+1 ＝Ax k +Bu k
y k ＝Cx k +Du k ；
wherein x is k+1 Forecasting the state variable of the identified object at the next moment of the current k moment; x is x k A state variable estimated value at the moment k of the identified object; u (u) k For the input of the identified object at time kEntering a signal; y is k Forecasting an output signal of the identified object at the moment k; A. b, C, D is an adaptive state space model matrix.
In the present embodiment, the overdetermined equation is solved by the least square method to obtain the adaptive state space model matrices A, B, C, D and the initial state x 0 And constructing an adaptive state space model of the identified object, namely
The overdetermined equation is:
Figure BDA0002034762530000121
wherein: y is Y 0,s,1 To y ID Is written in the form of a single column vector; Γ -shaped structure s Expanding a considerable matrix for a system of identified objects; phi, ψ, Ω, xi are intermediate variables;
Figure BDA0002034762530000131
Y 0,s,1 column and column rows for all the identification output data;
Figure BDA0002034762530000132
Figure BDA0002034762530000133
Figure BDA0002034762530000134
is Kronecker product;
Figure BDA0002034762530000135
I l is an l-dimensional identity matrix;
Figure BDA0002034762530000136
vec () is the column of matrix columns in brackets; τ is used in the accumulation operationIs a subscript of (2);
the adaptive state space model matrix
Figure BDA0002034762530000137
C is U n Upper row of (2);
the U is n To take U 1 N column vectors to the left of (a); u (U) n The upper l (j-1) row of (C) is denoted as U p The lower l (j-1) column is denoted as U q N is the actual order obtained by i; u (U) 1 Is equal to Σ 1 The number of rows of (3); sigma and method for producing the same 1 The characteristic value of the self-adaptive state space model of the identified object; sigma and method for producing the same 2 Is a zero matrix; i is the order of the estimated adaptive state space model.
Example 3
The present embodiment further provides a control method of a switch-mode digital power supply based on embodiment 1 and embodiment 2, including: a power supply power main loop and a digital control board card for controlling the output voltage of the power supply power main loop; the digital control board card is suitable for adjusting and stabilizing the output voltage according to the load characteristic change by the embedded automatic load characteristic identification method described in the embodiment 1 and the embodiment 2.
In this embodiment, the digital control board card includes a motherboard integrating an FPGA chip, a digital I/O board, an add board, and a power board; the main board of the FPGA chip can be but is not limited to a main control chip of a CycloniI EP2C70 FPGA, so that SOPC soft-core processor, peripheral interfaces, avalon MM bus and SSDC user-defined IP are realized, and common peripherals such as a 2MB SSRAM, an EPCS64 (64 Mb) serial configuration device, a 16MB Flash memory for nonvolatile storage, an RJ45 network interface and an RS232 local communication interface, and a Santa Cruz standard expansion card interface are built on the main board; a digital quantity input/output diode, an optical coupler and a level conversion device are built on the digital quantity I/O board and are responsible for mainly controlling actions and collecting fault signals of a power supply; the ADDA board comprises an ADC, a DAC and a matched conditioning circuit and is responsible for sampling the level signal of the sensor; the power panel mainly comprises a small-sized switching power supply and is responsible for providing a 24V regulated power supply.
In order to verify the working condition of the self-adaptive state space model under the actual switch-type digital power supply and load conditions, the switch-type digital power supply is respectively connected with four loads with different characteristics, and the self-adaptive state space model test steps are as follows:
generating an identification input u using a PRNG ID Converted as a control input into a PWM signal, the load is excited, and the output current sample is taken as an identification output y ID The embedded load characteristic automatic identification method utilizes u ID And y ID Constructing a self-adaptive state space model;
generating verification recognition input u again using PRNG test And also excite the load to obtain the verification identification output y test ；
Using an adaptive state space model and u test Calculating to obtain output signal forecast y pre And with y test The comparison is performed to check the accuracy of the adaptive state space model.
To ensure the accuracy of the verification of the adaptive state space model, u ID And u is equal to test There should be a large uncorrelation, and the adaptive state space model should be determined by the method of u ID U is significantly different test Calculating output data conforming to the I/O data pair; the accuracy of the adaptive state space model can be verified under the most stringent conditions by using random numbers as test inputs.
Fig. 2 (a) is a dispersion diagram of the prediction error of the resistive load adaptive state space model according to the present invention.
Fig. 2 (b) is a dispersion diagram of prediction errors of the resistive load adaptive state space model according to the present invention.
As shown in fig. 2 (a) and 2 (b), using test results obtained by a resistive load of 0.07 Ω and a resistive load of 0.23 Ω/4.5mH, respectively, the output signal forecast y under the resistive load condition was normalized to a given range of ±0.1 and ±0.05, respectively pre And verify the identification output y test Data covariance was 1.54×10 -4 (the value is mainly affected by the error of the initial state), and the magnet load is 3.47×10 -6 The I/O characteristic of the visible model is better matched with the actual controlled object.
In summary, the present invention uses the unit module with load characteristic as the identified object; output y by recognition of a recognized object ID Identify input u ID Constructing a self-adaptive state space model; the self-adaptive state space model is suitable for adjusting the identification input of the identified object according to the change of the identified object so as to automatically construct the self-adaptive state space model according to the input and output characteristics of the identified object.
With the above-described preferred embodiments according to the present invention as an illustration, the above-described descriptions can be used by persons skilled in the relevant art to make various changes and modifications without departing from the scope of the technical idea of the present invention. The technical scope of the present invention is not limited to the description, but must be determined according to the scope of claims.

Claims (3)

1. An automatic identification method for embedded load characteristics is used for a control method of a switch type digital power supply, and is characterized in that,
the control method of the switch-mode digital power supply comprises the following steps:
a power supply power main loop and a digital control board card for controlling the output voltage of the power supply power main loop;
the digital control board card is suitable for regulating and stabilizing the output voltage according to the load characteristic change through an embedded load characteristic automatic identification method; and
the automatic identification method for the embedded load characteristics comprises the following steps:
taking a unit module with load characteristics as an identified object;
output y by recognition of a recognized object ID Identify input u ID Constructing a self-adaptive state space model;
the self-adaptive state space model is suitable for adjusting the identification input of the identified object according to the change of the identified object;
the automatic identification method for the embedded load characteristics further comprises the following steps:
will recognize input u ID And an identification output y corresponding thereto ID A pair of I/O data pairs recorded as the adaptive state space model; and
by recognizing input u ID And an identification output y ID The method for constructing the adaptive state space model comprises the following steps:
calculating the order I of the estimated adaptive state space model according to the number s of I/O data pairs, constructing a matrix column number j used in constructing a Hankel matrix, and constructing a Hankel matrix by using the value of the matrix column number N used in constructing the Hankel matrix, wherein
Figure FDA0004175598650000011
Setting the adaptive state space model to have m-dimensional input and l-dimensional output, and corresponding identification input u ID (k)∈R m Set the identification output y ID (k)∈R l ；
Wherein k is [0, s-1], s is more than 5 times of m multiplied by i, and m is the dimension of the input signal; l is the dimension of the output signal; k is a discrete time variable; r is the real number domain;
constructing a recognition input u from the values of i, j and N ID And an identification output y ID Hankel matrix of (a), i.e.)
Figure FDA0004175598650000021
Figure FDA0004175598650000022
Figure FDA0004175598650000023
Figure FDA0004175598650000024
In the Hankel matrix described above, U 0，i，N Is an input Hankel matrix before the i-th moment; u (U) i，j，N Inputting Hankel matrixes from the ith moment to the jth moment; y is Y 0，i，N An output Hankel matrix before the ith moment; y is Y i，j，N Output Hankel matrix from the ith time to the jth time;
u is set to 0，i，N 、U i，j，N 、Y 0，i，N And Y i，j，N LQ decomposition is performed, orthogonal projection is performed to obtain an adaptive state space model extended observability matrix Γ j I.e.
Figure FDA0004175598650000025
Wherein L is 11 ∈R mj×mj ，L 21 ∈R mi×mj ，L 31 ∈R li×mj ，L 41 ∈R lj×mj ，L 22 ∈R mi×mi ，L 32 ∈R li×mi ，L 42 ∈R lj ×mi ，L 33 ∈R li×li ，L 43 ∈R lj×li ，L 44 ∈R lj×lj The method comprises the steps of carrying out a first treatment on the surface of the Wherein the method comprises the steps of
L 11 ～L 44 Reflecting U 0，i,N Is spread into space, U i，j，N The row vectors are spatially spread to Y 0,i,N Is spread into space, Y i，j，N Is stretched into a projection component of the space;
for L 42 And L 43 Singular value decomposition of matrices, i.e.
Figure FDA0004175598650000031
Wherein U is [ L ] 42 L 43 ]A matrix is subjected to singular value decomposition to obtain a left-hand matrix;
v is [ L ] 42 L 43 ]Right moment obtained by matrix through singular value decomposition of matrixAn array;
sigma is a characteristic value matrix of the self-adaptive state space model;
t is the transpose;
∑ 1 a non-zero characteristic value of a self-adaptive state space model of the identified object;
∑ 2 is a zero matrix;
U 1 ，U 2 is based on sigma 1 The number of U is divided into blocks, U 1 Is equal to sigma 1 Line number of U 2 Is equal to sigma 2 The number of rows of (3); and
V 1 T ，
Figure FDA0004175598650000032
is based on sigma 1 Number of pairs V T Partitioning, V 1 T The number of rows equal to sigma 1 Column number of->
Figure FDA0004175598650000033
The number of rows equal to sigma 2 The number of columns of (a);
u taking 1 The left n column vectors are denoted as U n ，U n The upper l (j-1) row of (C) is denoted as U p The lower l (j-1) column is denoted as U q Then the state space model matrix is self-adapted
Figure FDA0004175598650000034
C is U n Upper row of (2); n is the actual order obtained by i;
solving the overdetermined equation by a least square method to obtain an adaptive state space model matrix A, B, C, D and an initial state x 0 And constructing an adaptive state space model of the identified object, namely
The overdetermined equation is:
Figure FDA0004175598650000035
wherein: y is Y 0，s，1 To y ID Is written in the form of a single column vector; Γ -shaped structure s Expanding a considerable matrix for a system of identified objects; phi, ψ, Ω, xi are intermediate variables;
Figure FDA0004175598650000041
Y 0，s，1 column and column rows for all the identification output data;
Figure FDA0004175598650000042
Figure FDA0004175598650000043
Figure FDA0004175598650000044
is Kronecker product;
Figure FDA0004175598650000045
I l is an l-dimensional identity matrix;
Ω＝vec(B)∈R mn ，Ξ＝vec(D)∈R ls vec () is the column of matrix columns in brackets; τ is the subscript used in the accumulation operation;
the adaptive state space model is:
x k+1 ＝Ax k +Bu k
y k ＝Cx k +Du k ；
wherein x is k+1 Forecasting the state variable of the identified object at the next moment of the current k moment; x is x k A state variable estimated value at the moment k of the identified object; u (u) k An input signal at the moment k of the identified object; y is k Forecast the output signal of the identified object at the moment k.
2. The method for automatically identifying embedded load characteristics according to claim 1, wherein,
the automatic identification method for the embedded load characteristics further comprises the following steps: verifying whether the adaptive state-space model is accurate, i.e
The recognized object receives the verification recognition input u test After which verification identification output y is generated test And utilizes the adaptive state space model to identify the input u according to the verification test Obtaining output signal forecast y pre When y is test And y pre And when the self-adaptive state space model is the same, the self-adaptive state space model is judged to be accurate.
3. An adaptive state space model for use in the automatic load characteristic identification method of claim 1, comprising:
x k+1 ＝Ax k +Bu k
y k ＝Cx k +Du k ；
wherein x is k+1 Forecasting the state variable of the identified object at the next moment of the current k moment; x is x k A state variable estimated value at the moment k of the identified object; u (u) k An input signal at the moment k of the identified object; y is k Forecasting an output signal of the identified object at the moment k; A. b, C, D is an adaptive state space model matrix.
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