CN106372348A - Vector fitting model order reduction method based on error control in linear system - Google Patents

Abstract

The invention discloses a vector fitting model order reduction method based on error control in a linear system. Specific to the conventional vector fitting, the order of a constructed pole-residue model is always very high under a wide frequency band, particularly in a highly-dynamic linear system with a resonance point. An error control function is introduced, data including important features of the linear system are selected in a continuous iteration way, and certain slightly-varied data representing details are neglected, so that the order of the constructed model is effectively reduced under the condition of sacrificing certain modeling accuracy. A low-order pole-residue macro model is obtained under the condition that the modeling accuracy requirement is met. The pole-residue macro model is further transformed into a state space model, passive processing is performed, and the constructed pole-residue macro model is output lastly. By adopting the vector fitting model order reduction method, the balance between model accuracy and complexity is realized, and the simulation efficiency of electromagnetically-compatible electromagnetic emission is increased.

Description

Error control-based vector fitting model order reduction method in linear system

Technical Field

The invention relates to an error control-based vector fitting model order reduction method in a linear system, belongs to the technical field of electromagnetic compatibility, and lays a foundation for realizing electromagnetic compatibility quantitative design simulation.

Background

With the development of electronic systems towards high frequency, high speed, miniaturization, multi-functionalization and integration, the problem of electromagnetic compatibility is more and more prominent in the design process of electronic systems, and has become one of the key problems restricting the development of electronic systems.

The accurate and effective electromagnetic emission model is the key for performing electromagnetic compatibility prediction simulation and quantitative design of an electronic system. The current popular modeling method based on vector fitting can quickly establish a broadband equivalent model according to the measurement or simulation data of network parameters of a linear system, such as S parameters. However, the model established for the broadband linear system according to the traditional vector fitting is often higher in order and low in simulation efficiency. The problem of electromagnetic compatibility of electronic systems is mostly caused by the out-of-band characteristics of circuits or components, so that it is urgently needed to establish a broadband electromagnetic compatibility model with the out-of-band characteristics of interference circuits or components. Therefore, it is necessary to establish a low-order model with a certain accuracy to improve the simulation efficiency of electromagnetic compatible electromagnetic emission.

Disclosure of Invention

The purpose of the invention is: the method overcomes the defects of the prior art, provides a vector fitting model order reduction method based on error control in a linear system, further obtains a low-order high-precision model, realizes the balance of model precision and complexity, and improves the simulation efficiency of electromagnetic compatibility electromagnetic emission.

The invention relates to a vector fitting model order reduction method based on error control in a linear system. Data containing important transmission characteristics of a linear system is selected by introducing an error control function and adopting a continuous iteration mode, and the order of the established model is effectively reduced under the condition of sacrificing small modeling precision by neglecting micro-variation data at certain representative details. The method comprises the following concrete steps:

the method comprises the following steps: obtaining network parameters

Simulating the modeling object by full-wave simulation software such as HFSS, CST or Microwave Office to obtain the S (scattering) parameter value of the port network parameter at different frequency points in the wide frequency bands_i＝j2πf_i。

Step two: establishing a low-order pole-residue macro model

The specific modeling flow diagram is shown in fig. 1. In the figure, σ represents the root mean square error, and the error control function is defined as:

$\mathrm{\δ}\left(s_i\right)=\frac{\left|\right|H_{Raw}\left(s_i\right)|-|H_{Fit}\left(s_i\right)\left|\right|}{\left|H_{Raw}\left(s_i\right)\right|}$

wherein H_Raw(s_i) Representing simulated scattering parameter data, H_Fit(s_i) Represents a vector fit established macro model, i ═ 1, 2.. k.; sigma₀For the pre-set root-mean-square error,₀the function threshold is controlled for a preset error.

The modeling part comprises two iterative loops, wherein the first iterative loop is a vector fitting algorithm modeling iterative loop, and the other iterative loop is a modeling array selection iterative loop. The modeling array is from H_Raw(s_i) Data representing important transfer characteristics of the modeled object is selected.

1) Iterative loop of vector fitting algorithm modeling

The first step is as follows: and uniformly selecting several pairs of data from the S scattering parameters acquired in the step one in the whole wide frequency band as an initial modeling array.

The second step is that: modeling using a conventional vector fitting algorithm

Obtaining frequency domain scattering parameters of linear system by simulation or measurement

Suppose the pole-residue macro model to be built is H_Fit(s) the mathematical expression of which is:

$H_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{r_m}{s-p_m}+d---\left(1\right)$

where s ═ j ω represents a complex frequency variable, ω is an angular frequency, and r_m，p_mRespectively the mth residue and the pole of the macro model to be identified, and d is a constant term value. The objective of the vector fit is to require the pole p in equation (1)_mThe residue r_mAnd the value of d.

Identification of poles:

setting an initial poleWhile introducing a scale factor sigma(s).

$\mathrm{\σ}\left(s\right)={\mathrm{\Σ}}_{m=1}^N\frac{{\tilde{r}}_m}{s-{\stackrel{\‾}{p}}_m}+1---\left(2\right)$

Wherein,the mth residue value representing the scale factor σ(s).

Multiplying σ(s) by H_Fit(s) obtaining a new pole-residue macro model

${\mathrm{\Σ}}_{m=1}^N\frac{{\hat{r}}_m}{s-{\stackrel{\‾}{p}}_m}+\hat{d}=H_{Fit}\left(s\right)({\mathrm{\Σ}}_{m=1}^N\frac{{\tilde{r}}_m}{s-{\stackrel{\‾}{p}}_m}+1)---\left(3\right)$

Wherein,the ith residue value representing the new pole-residue macro model,constant term values representing the new pole-residue macro model. By shifting, further:

${\mathrm{\Σ}}_{m=1}^N\frac{{\hat{r}}_m}{s-{\stackrel{\‾}{p}}_m}+\hat{d}-H_{Fit}\left(s\right){\mathrm{\Σ}}_{m=1}^N\frac{{\tilde{r}}_m}{s-{\stackrel{\‾}{p}}_m}=H_{Fit}\left(s\right)---\left(4\right)$

in the formula (4), theRegarded as unknown quantity, at discrete frequency points s_i＝jω_iWhere i is 1,2,. K and K > 2(N +1), and with H_Raw(s_i) Approximate substitution of (A) for H_Fit(s_i) Finally, the following system of linear equations can be obtained.

AX＝b (5)

The matrix a and the vector X, b in the system of linear equations are defined as follows:

$A=\left[\begin{array}{ccccccc}\frac{1}{{\mathrm{j\ω}}_1-{\stackrel{\‾}{p}}_1}& \mathrm{...}& \frac{1}{{\mathrm{j\ω}}_1-{\stackrel{\‾}{p}}_N}& 1& \frac{-H_{Raw}\left({\mathrm{j\ω}}_1\right)}{{\mathrm{j\ω}}_1-{\stackrel{\‾}{p}}_1}& \mathrm{...}& \frac{-H_{Raw}\left({\mathrm{j\ω}}_1\right)}{{\mathrm{j\ω}}_1-{\stackrel{\‾}{p}}_N}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{..}\\ \frac{1}{{\mathrm{j\ω}}_K-{\stackrel{\‾}{p}}_1}& \mathrm{...}& \frac{1}{{\mathrm{j\ω}}_K-{\stackrel{\‾}{p}}_N}& 1& \frac{-H_{Raw}\left({\mathrm{j\ω}}_K\right)}{{\mathrm{j\ω}}_K-{\stackrel{\‾}{p}}_1}& \mathrm{...}& \frac{-H_{Raw}\left({\mathrm{j\ω}}_K\right)}{{\mathrm{j\ω}}_K-{\stackrel{\‾}{p}}_N}\end{array}\right]---\left(6\right)$

$X={({\hat{r}}_1,{\hat{r}}_2,...{\hat{r}}_N,\hat{d},{\tilde{r}}_1,{\tilde{r}}_2,...{\tilde{r}}_N)}^T---\left(7\right)$

b＝(H_Raw(jω₁),...,H_Raw(jω_K))^T(8)

equation (5) is an overdetermined linear system of equations that can be solved for the unknown variable X by the minimum mean square error criterion. The new pole value can be passedCalculated, where A is the value containing the initial poleB is a unit column vector,to compriseThe row vector of (2). Stopping the iteration when the scale factor sigma(s) is close to 1 through a plurality of iterations, and outputting a final pole value p_m(m＝1,…,N)。

Residue and constant term identification

When the pole identification is completed, p is obtained_m(m is 1, …, N), the residue r in this case_m(m ═ 1, …, N) and the constant term d can be identified by equation (9).

A'x'＝b' (9)

Wherein:

$A^{\′}=\[\begin{array}{cccc}\frac{1}{{\mathrm{j\ω}}_1-p_1}& \mathrm{...}& \frac{1}{{\mathrm{j\ω}}_1-p_N}& 1\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ \frac{1}{{\mathrm{j\ω}}_K-p_1}& \mathrm{...}& \frac{1}{{\mathrm{j\ω}}_K-p_N}& 1\end{array}\]$

x'＝[r₁,r₂,…,r_N,d]^T

b'＝[H_Raw(jω₁),…,H_Raw(jω_K)]^T

at this point, a pole-residue macro model is obtained.

The third step: calculating the root mean square error sigma between the model built by vector fitting and the modeling array, if sigma is less than or equal to sigma₀And outputting the vector fitting model. Otherwise, increasing the order, and repeating the second step until the sigma is less than or equal to the sigma₀。

2) Selecting a modeling array iteration loop

The first step is as follows: after the vector fitting model is obtained, the error function(s) is calculated_i)；

$\mathrm{\δ}\left(s_i\right)=\frac{\left|\right|H_{Raw}\left(s_i\right)|-|H_{Fit}\left(s_i\right)\left|\right|}{\left|H_{Raw}\left(s_i\right)\right|}$

Wherein H_Raw(s_i) Representing simulated scattering parameter data, H_Fit(s_i) Represents the macro model created by vector fitting, i ═ 1, 2.

The second step is that: if max ((s)_i))≤₀Outputting a pole-residue model of the broadband, and entering 3) passivity judgment and strength. If max ((s)_i))＞₀And adding new data to the modeling array, and re-entering 1) a vector fitting algorithm modeling iteration loop. Wherein the new data added is selected in(s)_i) The maximum.

Through multiple iterative cycles, preset modeling precision sigma₀And₀all satisfied, the output pole-residue macro model is:

$H_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{r_m}{s-a_m}+d$

where s ═ j ω. Omega is the angular frequency, a_mFor the pole-residue macro model H_FitM-th extreme value of(s), r_mFor the pole-residue macro model H_Fit(s) m-th residue value, d is a constant term value, and N represents a pole-residue macro model H_FitThe order of(s).

3) And (4) passivity judgment and enhancement.

And (3) converting the obtained pole-residue macro model into a state space model:

wherein x is a state variable, u is an input vector, y is an output vector,expressing the derivation of x, A, B, C, and D are matrices of state equation coefficients.

Constructing an passivity judgment matrix J ═ (A-B (D-I) from the coefficient matrix of the state equation^-1C)(A-B(D+I)^-1C) (ii) a Calculating the eigenvalues λ of the matrix J_iIf λ_iIf the real number is negative, the state space model does not meet passivity; otherwise, the state space model satisfies passivity.

When the state space model does not satisfy passivity, the residue r is checked_mAnd d, carrying out disturbance treatment on the constant term to enhance the passivity of the constant term.

${\mathrm{\ΔH}}_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{{\mathrm{\Δr}}_m}{s-a_m}+\mathrm{\Δ}d\≅0$

Wherein, Δ r_mLeave a number of macro-models for poles H_Fit(s) mth residue r_mThe value of the perturbation, Δ d, is left as a poleNumber macro model H_Fit(s) the perturbation value of the constant term d, N representing the order of the macro model.

Make the eigenvalue lambda of the passivity decision matrix J_iThere are no negative real numbers. After multiple iterative corrections, the model can be ensured to meet the passivity requirement. Finally outputting a high-precision low-order pole-residue macro model H_Fit。

The invention has the advantages and positive effects that:

when a linear circuit system is too large and complex, and a specific circuit and any parameter of the system are not mastered, and when an electromagnetic compatibility problem occurs, if broadband modeling analysis is carried out, the complexity of a model established by adopting a traditional vector fitting algorithm is very high. The method provided by the invention can establish a high-precision low-order equivalent model and improve the simulation efficiency.

When the simulation data are modeled, the low-order broadband model of the original linear system can be established only by less simulation data, the accuracy is high, and the internal structure and specific parameters of a circuit are not required to be known.

Compared with other model order reduction methods, the method has higher modeling precision under the same order, especially for the minimum value point. The method is more suitable for linear system modeling with a large number of resonance points.

Drawings

FIG. 1 is a flow chart of an error control-based vector fitting model order reduction method in the present invention;

FIG. 2 is a three-dimensional model diagram of a validation example microstrip filter;

FIG. 3 is a schematic diagram of a verification example filter circuit;

FIG. 4 is a schematic diagram of a validation example filter size;

FIG. 5 is a graph comparing a model built by conventional vector fitting with measured data;

FIG. 6 is a graph comparing a model built by a classical balanced truncation model reduction method with test data;

FIG. 7 is a graph comparing the model created by the present invention with test data.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples.

The vector fitting model order reduction method based on error control provided by the invention firstly obtains linear system port network parameters such as scattering (S) parameters under a certain bandwidth through simulation. Data containing important characteristics of a linear system are selected by introducing an error control function in a continuous iteration mode, and the order of the established model is effectively reduced under the condition of sacrificing certain modeling precision by neglecting micro-variation data representing details. And under the condition of meeting the requirement of modeling precision, obtaining a low-order pole-residue macro model. And then further converting the pole-residue macro model into a state space model, then carrying out passivity treatment, and finally outputting the built pole-residue macro model.

The simulation software of the port scattering parameters of the linear system comprises the following steps: microwave Office simulation software from AWR corporation. Obtaining scattering parameters of linear port by simulations_i＝j2πf_i，f_iRepresenting a frequency point. And then, modeling is carried out by adopting Matlab software according to a flow chart 1, and finally a low-order pole-residue macro model is obtained.

The following description takes a 0-8 GHz microstrip low-pass filter as a modeling object:

fig. 2 is a three-dimensional model diagram of a micro-strip filter of an adopted verification example, and it can be seen from the diagram that the micro-strip filter has a symmetrical structure. Fig. 4 is a schematic diagram of specific dimensions of a microstrip filter of an example of verification used, and specific dimensions are shown in table 1, where L represents the length of a microstrip line, and W represents the width of the microstrip line.

Table 1 verification example microstrip filter dimension value table (unit mm)

LA	LB	LC	LD	LE	LF
						2.540	1.776	2.032	1.118	1.981	2.743
WA	WB	WC	WD	WE	WF
						0.3810	0.254	0.1397	0.1778	0.3556	0.2540

And simulating the 0-8 GHz low-pass filter by using AWR company Microwave Office software to obtain 2-10 GHz S11 parameters, wherein FIG. 3 shows a simulation model of the adopted micro-strip filter in the Microwave Office simulation software. The invention relates to a vector fitting model order reduction method based on error control, which comprises the following steps of one to four.

The method comprises the following steps: network parameter acquisition

Port scattering parameter simulation is carried out on the low-pass filter of the modeling object through Microwave Office simulation software of AWR company, and S11 parameter data of 2-10 GHz frequency band are obtainedWherein s is_iFrequency point, H, corresponding to simulation data_Raw(s_i) And the S12 parameter of scattering under the corresponding frequency point is shown, and K represents the number of the frequency points.

Step two: and establishing a low-order macro model.

Separately setting the root mean square error sigma₀And error control function threshold₀，σ₀1.000dB and₀＝3dB。

the modeling part comprises two iteration loops, wherein the first iteration loop is a vector fitting algorithm modeling iteration loop, and the other iteration loop is selected for modeling data.

1) Iterative loop of vector fitting algorithm modeling

The first step is as follows: at the whole 2-10 GHzS-parameters obtained from step one in wide frequency bandUniformly selecting four data as an initial modeling array.

The second step is that: modeling by adopting traditional vector fitting algorithm

For a specific process, please refer to the description about the conventional vector fitting modeling in the specific implementation steps.

The third step: calculating the root mean square error sigma between the model built by vector fitting and the modeling array, if sigma is less than or equal to sigma₀Then proceed to 2). Otherwise, increasing the order, and repeating the second step until the sigma is less than or equal to the sigma₀。

2) Model data selection iterative loop

The first step is as follows: the root mean square error between the model established by the vector fitting algorithm and the modeling array satisfies the condition that sigma is less than or equal to sigma₀Then, an error function is calculated

$\mathrm{\δ}\left(s_i\right)=\frac{\left|\right|H_{Raw}\left(s_i\right)|-|H_{Fit}\left(s_i\right)\left|\right|}{\left|H_{Raw}\left(s_i\right)\right|}$

Wherein H_Raw(s_i) Representing simulated scattering parameter data, H_Fit(s_i) Represents the macro model created by vector fitting, i ═ 1, 2.

The second step is that: determining whether or not max (max) is satisfied_i)≤₀. If yes, outputting a pole-residue macro model of the broadband, and performing passive reinforcement. And if not, adding new data to the modeling array, and re-entering 1) the vector fitting algorithm modeling iterative loop. Wherein the new data added is selected in_iThe maximum.

The final output pole-residue macro model is:

$H_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{r_m}{s-a_m}+d$

where s ═ j ω denotes a complex frequency variable. Omega is the angular frequency, a_mFor the pole-residue macro model H_FitM-th extreme value of(s), r_mFor the pole-residue macro model H_Fit(s) m-th residue value, d is a constant term value, and N represents a pole-residue macro model H_FitThe order of(s).

Step three: and (4) passivity judgment and enhancement.

And (3) converting the obtained pole-residue macro model into a state space model:

wherein x is a state variable, u is an input vector, y is an output vector,expressing the derivation of x, A, B, C, and D are matrices of state equation coefficients.

Constructing an passivity judgment matrix J ═ (A-B (D-I) from the coefficient matrix of the state equation^-1C)(A-B(D+I)^-1C) (ii) a Calculating the eigenvalues λ of the matrix J_iIf λ_iIf the real number is negative, the state space model does not meet passivity; otherwise, the state space model satisfies passivity.

When the state space model does not satisfy passivity, the residue r is checked_mAnd the constant term d is subjected to perturbation treatment to ensure the passivity of the mixture.

${\mathrm{\ΔH}}_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{{\mathrm{\Δr}}_m}{s-a_m}+\mathrm{\Δ}d\≅0$

Make the eigenvalue lambda of the passivity decision matrix J_iThere are no negative real numbers. After multiple iterative corrections, the model can be ensured to meet the passivity requirement. Finally outputting a low-order pole-residue macro model H_FitAs shown in fig. 6. It can be seen from fig. 6 that the resulting 14 th order pole residue macro model has an error of 0.1336dB at the resonance point of 4.5 GHz.

In order to embody the advantages of the present invention, the microstrip filter S11 in the example was modeled using a conventional vector fitting algorithm, and the model is shown in fig. 5 when it is of order 45. It can be seen from fig. 5 that the 45 th order pole residue macro model has an error of 5.195dB at the resonance point of 4.5 GHz. The 45 th order pole residue macro model created by the traditional vector fitting algorithm is then model reduced using the classical equilibrium truncated model reduction method, again to 14 th order for comparison, but with 16.590dB error at the resonance point, as shown in fig. 7. Compared with the traditional vector fitting modeling method and the balanced truncation model order reduction method, the pole-residue macro model established at the minimum value point has higher modeling precision, realizes the balance of model precision and complexity, and greatly improves the simulation efficiency of electromagnetic compatibility electromagnetic emission.

The above examples are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.

Claims (5)

1. An error control-based vector fitting model order reduction method in a linear system is characterized by comprising the following steps:

the method comprises the following steps: acquiring linear system port network parameters under a set bandwidth through simulation;

step two: uniformly selecting a plurality of pairs of data from the network parameters obtained in the step one in the whole set bandwidth as initial modeling arrays;

step three: modeling the modeling array by adopting a vector fitting algorithm;

step four: vector adopted for calculationThe root mean square error sigma between the model established by the quantity fitting algorithm and the modeling array is calculated, and if the root mean square error sigma is less than or equal to the sigma₀Then the vector fitting model, σ, is output₀The error is a preset root mean square error; otherwise, increasing the order, and repeating the third step until sigma is less than or equal to sigma₀；

Step five: after the vector fitting model is obtained, the error function(s) is calculated_i)；

Step six: if max ((s)_i))≤₀Outputting a pole-residue model of the wide frequency band, entering the passivity judgment and enhancement in the sixth step,₀is a preset value; if max ((s)_i))＞₀If so, adding new data to the modeling array, and re-entering the step three iteration loop; through an iterative loop, a predetermined value σ₀And₀all satisfied, the output pole-residue macro model is:

$H_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{r_m}{s-a_m}+d$

wherein, s ═ j ω represents a complex frequency variable; omega is the angular frequency, a_mLeave a number of macro-models for poles H_Fit(s) mth extreme value, r_mLeave a number of macro-models for poles H_Fit(s) mth residue value, d is the pole residue macro model H_FitConstant term value of(s), N represents the pole residue macro model H_Fit(s) order;

step six: passivity judgment and enhancement are carried out, and model fullness is finally ensured after multiple iterative correctionsThe passivity requirement is satisfied; finally outputting a high-precision low-order pole-residue macro model H_Fit：

${\mathrm{\ΔH}}_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{{\mathrm{\Δr}}_m}{s-a_m}+\mathrm{\Δ}d\≅0$

Wherein, Δ r_mLeave a number of macro-models for poles H_Fit(s) mth residue r_mThe perturbation value of (1) is a pole residue macro model H_Fit(s) the perturbation value of the constant term d.

2. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: in the first step, full-wave simulation software HFSS, CST or Microwave Office is adopted to simulate.

3. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: in said step five, the error function(s)_i) The calculation formula of (a) is as follows:

$\mathrm{\δ}\left(s_i\right)=\frac{\left|\right|H_{Raw}\left(s_i\right)|-|H_{Fit}\left(s_i\right)\left|\right|}{\left|H_{Raw}\left(s_i\right)\right|}$

wherein H_Raw(s_i) Data representing the simulation-derived parameters of the linear system port network, H_Fit(s_i) Represents the macro model created by vector fitting, i ═ 1, 2.

4. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: in said step five, the new data added is selected in(s)_i) The maximum.

5. The method for reducing the order of the vector fitting model based on the error control in the linear system according to claim 1, wherein: the sixth step is specifically realized as follows:

and (3) converting the obtained pole-residue macro model into a state space model:

wherein x is a state variable, u is an input vector, y is an output vector,expressing the derivation of x, A, B, C, and D as a matrix of state equation coefficients;

constructing an passivity judgment matrix J ═ (A-B (D-I) from the coefficient matrix of the state equation^-1C)(A-B(D+I)^-1C) (ii) a Calculating the eigenvalues λ of the matrix J_iIf λ_iIf the real number is negative, the state space model does not meet passivity; otherwise, the state space model satisfies passivity;

when the state space model does not satisfy passivity, the residue r is checked_mThe constant term d is subjected to disturbance treatment to enhance the passivity of the constant term d;

${\mathrm{\ΔH}}_{Fit}\left(s\right)=\underset{m=1}{\overset{N}{\Σ}}\frac{{\mathrm{\Δr}}_m}{s-a_m}+\mathrm{\Δ}d\≅0$

make the eigenvalue lambda of the passivity decision matrix J_iThere are no negative real numbers; after multiple iterative corrections, the model is finally guaranteed to meet the passivity requirement; finally outputting a high-precision low-order pole-residue macro model H_Fit。