Routh order reduction modeling method for CLLLC resonant DC-DC converter

Abstract

In order to solve the problem that a controller is complex in design due to the fact that the order of a small signal model of a CLLLC resonant converter built through an extended description function method is too high, the invention provides a Routh order reduction modeling method for the CLLLC resonant type DC-DC converter, according to the high-order polynomial decomposition principle, a transfer function is subjected to rational expansion, a characteristic equation is written in parallel, a Routh table is built, and the Routh order reduction modeling method for the CLLLC resonant type DC-DC converter is obtained. And finally, calculating parameters in the Routh table to generate a reduced-order model. According to the method, the problems of poor convergence and stability and the like of an existing order reduction method are solved, it is guaranteed that the original system is replaced by the low-order model under the condition that the dynamic stability is similar to that of the original system, and therefore the follow-up system controller design is simplified.

Description

Technical Field

[0001] The invention belongs to the technical field of power electronic converters, and in particular relates to a Routh order reduction modeling method for a CLLLC resonant DC-DC converter. Background Art

[0002] With the development of the electric vehicle industry, the development of new energy chargers has become a key step influencing the technological progress of electric vehicles. In order to realize the collection, conversion and transmission of new energy, the dual active full-bridge bidirectional DC-DC converter has become a key energy conversion device. The CLLLC resonant converter has become a research hotspot in recent years due to its natural soft switching characteristics, high transmission efficiency, high density and other advantages. Its development and maturity are of great significance to solving the energy crisis and protecting the ecological environment.

[0003] For CLLLC resonant topology, fundamental wave approximation has gradually become its main modeling method. The basic principle is to assume that the fundamental wave components of voltage and current realize the entire energy output from the input to the output of the converter, and to treat the resonant converter as a linear network. The input and output characteristics are analyzed by the sinusoidal steady-state analysis method. However, the accuracy of this model is not high, and it has a high accuracy only near the resonant frequency point. The time domain analysis method divides a switching cycle into multiple stages according to the working waveform of the converter, lists the state equations of each stage, and uses the boundary conditions between the connected modes to solve the corresponding state variables, and obtains the relationship between the variables and the corresponding change curve. The order of the equation in this method is high, there are many variables, and the calculation is too complicated. The above methods are all steady-state analysis methods, without dynamic analysis capabilities. The fundamental wave in the model established by the extended description function is obtained by superposition of sine and cosine functions of the same frequency, which is more accurate. In addition, the extended description function model represents the state quantity containing high-frequency switching frequency information with two sine and cosine components with stable amplitudes. In the subsequent modeling process, the sine and cosine parts are classified into different categories, and circuit equations are written for them respectively. The switching frequency information in the nonlinear state quantity can be separated and converted into two linear quantities, which meets the small ripple assumption in the state space averaging method and can perform good dynamic analysis of the model.

[0004] For the controller design of CLLLC resonant bidirectional DC / DC converter, it is necessary to model its small signal. However, the small signal model obtained by the extended function method is a 9th-order high-order model, which is difficult to apply to the design of the controller. Therefore, how to simplify the model by reducing the order of the model has become the core of current research. Among the existing order reduction methods, the Krylov subspace order reduction method is used to reduce the network order, but the algorithm has a high number of iterations, high computational complexity, and the convergence problem is not easy to solve. It may not always converge, or the convergence speed is very slow; and although the Pade order reduction method simplifies the computational complexity, it also has the problem of convergence. At the same time, for models with poor fitting, the stability of the order reduction cannot be guaranteed. The Routh order reduction method can well guarantee the stability of the reduced-order model and has good accuracy. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a Routh reduced-order modeling method for a CLLLC resonant DC-DC converter.

[0006] In order to achieve the above-mentioned purpose of the invention, the overall technical solution adopted by the present invention is to perform small signal modeling of the CLLLC resonant converter through the extended describing function method to generate a linear small signal model, select the topology parameters through steady-state modeling, and judge the stability of the model according to the Routh-Hurwiz criterion. Finally, according to the principle of high-order polynomial decomposition, the high-order model of the system is rationally expanded and the Routh table is calculated to generate a reduced-order model.

[0007] A Routh reduced-order modeling method for CLLLC resonant DC-DC converter, the specific steps are as follows:

[0008] Step 1, analyze the working principle of the CLLLC resonant circuit, construct the equivalent circuit of the CLLLC resonant converter, and define the state quantity, input variable and output variable;

[0009] Input voltage V in After the primary side inversion part, the input voltage of the resonant cavity is set to V AB , mode 1 is the current flowing through the primary side resonant inductor L r1 The current flowing through the excitation inductance L m The current difference between the two is transmitted to the secondary side through the transformer, and then passes through the rectifier bridge part of the secondary side to form the output side capacitor C out With load R L Power supply, in this process, L r1 With C r1Series resonance occurs, and the resonant current is sinusoidal, rising first and then falling, while the magnetizing inductance is clamped by the transformer, and its current rises linearly from the initial value;

[0010] Mode 2 is when the resonant inductor current is equal to the magnetizing inductor current, the transformer primary current is zero, and no current flows to the secondary side. At this time, the output voltage is C out Provided, the transformer will not be clamped by the magnetizing inductance, L m Will be with C r1 , L r1 When the input voltage of the resonant cavity is reversed, the magnetizing inductance will not participate in the resonance.

[0011] From the above modal analysis, it can be seen that i Lr2 You can use Lr1 with i Lm It cannot be expressed as an independent state variable. By analyzing the circuit mode, the state variable is determined to be the resonant capacitor voltage V cr1 、V cr2 With the resonant current i Lr1 , and the excitation current i Lm , output capacitor voltage V out ;

[0012] Step 2, write the nonlinear state equations of the relevant state quantities through Kirchhoff's voltage and current laws;

[0013]

[0014] Step 3, using the extended description function method for linear approximation;

[0015] Define the switching frequency as ω s , as shown in formula 2:

[0016] Formula II I Lr1s ,I Lr1c ,I Lms ,I Lmc 、V Cr1s 、V Cr1c 、V Cr2s 、V Cr2c are the amplitudes of the sine component and cosine component of the corresponding variables respectively;

[0017] By classifying the sine part and the cosine part, the switching frequency information in the nonlinear state quantity can be separated to complete the linearization.

[0018] Step 4, modeling and calculating circuit parameters by steady-state analysis method, and solving the steady-state operating point from the circuit parameters (i.e., solving the steady-state value of each state quantity when the input voltage and switching frequency are known);

[0019] Assuming that only the fundamental component of the switching frequency is used for energy transmission, the nonlinear square wave voltage signal is converted into a sine wave voltage of the fundamental frequency, thereby making the converter equivalent to a linear network. The equivalent circuit of the CLLLC resonant bidirectional DC / DC converter is obtained by the fundamental equivalent analysis method;

[0020] The steady-state DC gain of the CLLLC resonant circuit can be calculated as:

[0021] From equation 3, we can see that the voltage gain is related to the quality element Q, the excitation inductance Lm and the resonant inductance L r1 Ratio k and normalized frequency ω n By analyzing the relationship between parameters, appropriate parameters can be selected;

[0022] Arrange the obtained CLLLC resonant circuit state equation, substitute the selected circuit parameters, and solve the steady-state value of the state variable;

[0023] Step 5: When the CLLLC resonant converter is running at a stable operating point, a small signal disturbance is added, and each variable is expressed as the sum of the steady-state value and the corresponding disturbance value. After discarding the second-order quantity and the steady-state quantity, the small signal model of the CLLLC converter is obtained:

[0024] The small signal model of the bidirectional full-bridge CLLLC resonant converter is written in the form of a state-space equation:

[0025] A, B, and C are the system state matrix, input matrix, and output matrix respectively;

[0026] The transfer function of the small signal model is calculated by formula 6:

[0027] Step 6, judging the stability of the transfer function according to the Routh-Hurwiz criterion;

[0028] Calculate and generate Routh table;

[0029] in,

[0030] i,j satisfies,

[0031] c 1,1 =b n ,c 1,2 =b n-2 ,…;c 2,1 =b n-1 ,c 2,2 =b n-3 ,…;

[0032] Determine the coefficients in the Routh table. If c i+1 , 1>0, i≥1, then it is a stable model.

[0033] Step 7, based on the high-order polynomial decomposition principle, rationally expand the high-order model of the system;

[0034]

[0035] in,

[0036] Establish parameter α i , β i Routh table with type nine:

[0037] in,

[0038] Through calculation and solution, it can be determined that the reduced-order model is:

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] (1) The extended description function used in the present invention has the ability of dynamic analysis. The state variables of the resonant converter contain high-frequency switching ripple components, so they cannot meet the small ripple assumption in the traditional state space averaging method. The extended description function rule can meet the small ripple assumption in the state space averaging method and establish an accurate small signal model;

[0041] (2) The present invention adopts Routh reduction method to reduce the order of the established small signal model. It is essentially a hybrid continued fraction reduction method, which divides the denominator and the numerator into two independent parts for reduction processing. That is, the denominator of the reduced-order model is only related to the denominator of the original model and has nothing to do with the numerator of the original model. It avoids the occurrence of convergence problems and ensures the stability of the reduced-order model. At the same time, the error is very small and the accuracy is very high. Under the condition of ensuring that the dynamic characteristics and stability are similar to those of the original system, the established low-order model is used to replace the original model, which greatly simplifies the subsequent control design and has strong practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 , a circuit diagram of a CLLLC resonant converter in the present invention;

[0043] Figure 2 , the equivalent circuit diagram of the CLLLC converter mode 1 in the present invention;

[0044] Figure 3 , the equivalent circuit diagram of the CLLLC converter mode 2 in the present invention;

[0045] Figure 4 , voltage gain curves under different k values ​​in the present invention;

[0046] Figure 5 , voltage gain curves at different Q values ​​in the present invention;

[0047] Figure 6 , voltage gain curves at different Q values ​​in the present invention;

[0048] Figure 7 , the state response curves of the full-order and reduced-order transfer functions of the present invention;

[0049] Figure 8 , a curve of the difference between the reduced-order transfer function and the full-order transfer function in the present invention; DETAILED DESCRIPTION

[0050] The technical solution will be clearly and completely described below in conjunction with the preferred examples and drawings of the present invention. It should be understood that the preferred examples are only for illustrating the present invention, not for limiting the scope of protection of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0051] The present invention provides a small signal modeling and order reduction method for a CLLLC resonant converter. First, the modal analysis of the CLLLC circuit topology is performed and a nonlinear state equation is established in combination with the circuit principle. The nonlinear quantity in the above equation is converted into a coupled linear quantity by an extended description function method. At the same time, the steady-state operating point is solved by the circuit parameters, and a small signal disturbance is superimposed on the steady-state point to obtain a small signal model, and the transfer function of the switching frequency to the output voltage disturbance is finally obtained through the model. For the order reduction method of the high-order model of a given system in the frequency domain, the Routh order reduction method is used to reduce the order of the high-order model, and the Routh-Hurwiz criterion is used to expand it, and the Routh table is established to realize the denominator and the numerator into two independent parts for order reduction, and a reduced-order model is generated, which better ensures the stability of the reduced-order model. By adopting the present invention, the original high-order system can be replaced by a low-order model under the condition of ensuring that the dynamic stability is similar to that of the original system, which greatly simplifies the analysis and design of the system controller.

[0052] A small signal modeling and order reduction method for a CLLLC resonant converter, wherein the specific steps of the small signal modeling of the CLLLC resonant converter are as follows:

[0053] Step 1, CLLLC resonant converter circuit diagram as shown Figure 1 As shown, the working principle of the CLLLC resonant circuit is analyzed, the equivalent circuit of the CLLLC resonant converter is constructed, and the state quantity, input variable and output variable are defined;

[0054] Input voltage V in After the primary side inversion part, the input voltage of the resonant cavity is set to V AB , mode 1 is the current flowing through the primary side resonant inductor L r1 The current flowing through the excitation inductance L m The current difference between the two is transmitted to the secondary side through the transformer, and then passes through the rectifier bridge part of the secondary side to form the output side capacitor C out With load R L Power supply, in this process, L r1 With C r1 Series resonance occurs, and the resonant current is sinusoidal, rising first and then falling, while the magnetizing inductance is clamped by the transformer, and its current rises linearly from the initial value;

[0055] Mode 2 is when the resonant inductor current is equal to the magnetizing inductor current, the transformer primary current is zero, and no current flows to the secondary side. At this time, the output voltage is C out Provided, the transformer will not be clamped by the magnetizing inductance, L m Will be with C r1 , L r1When the input voltage of the resonant cavity is reversed, the magnetizing inductance will not participate in the resonance.

[0056] From the above modal analysis, it can be seen that i Lr2 You can use Lr1 with i Lm It cannot be expressed as an independent state variable. By analyzing the circuit mode, the state variable is determined to be the resonant capacitor voltage V cr1 、V cr2 With the resonant current i Lr1 , and the excitation current i Lm , output capacitor voltage V out ;

[0057] The equivalent circuit diagram of CLLLC converter mode 1 is as follows: Figure 2 As shown, the equivalent circuit diagram of mode 2 is as follows Figure 3 As shown;

[0058] Step 2, write the nonlinear state equations of the relevant state quantities through Kirchhoff's voltage and current laws;

[0059] The KVL and KCL equations are written for the constructed equivalent circuit using the weighted average method. Assume that the switching frequency f s The corresponding period is T s , resonant frequency f r The corresponding period is T r ;

[0060]

[0061] Decoupling the coupled equations in equation 1 yields:

[0062]

[0063] in:

[0064] Step 3, using the extended describing function method to perform linear approximation to obtain the state space equation;

[0065] Resonance voltage v Cr1 、v Cr2 and the resonant current i Lr1 And the excitation current i Lm They can all be expressed in the form of extended description functions:

[0066]

[0067] Formula 4 I Lr1s ,I Lr1c ,I Lms ,I Lmc 、VCr1s 、V Cr1c 、V Cr2s 、V Cr2c are the amplitudes of the sine component and cosine component of the corresponding variables respectively;

[0068]

[0069] So we can use the function sgn(i Lr1 -i Lm )·V out To represent v CD ;

[0070] The nonlinear term v AB 、v CD Use Fourier series expansion to express it in fundamental wave form, and put |i Lr1 -i Lm |Written in the form of average value, the nonlinear state equation in the above formula can be approximately written as a linear equation system. The linear transformation process of the nonlinear term is as follows:

[0071]

[0072]

[0073] After derivation, we get:

[0074]

[0075] Step 4: Model and calculate circuit parameters through steady-state analysis method, and solve the steady-state operating point from the circuit parameters: when the input voltage and switching frequency are known, solve the steady-state value of each state quantity;

[0076] Resonant converters generally improve transmission efficiency by operating near the resonant frequency. At this time, the current waveform of the resonant circuit is approximately a sine wave. The fundamental wave equivalent analysis method is used for analysis, that is, it is assumed that only the fundamental wave component of the switching frequency is used for energy transmission, and the nonlinear square wave voltage signal is converted into a sine wave voltage of the fundamental frequency, thereby making the converter equivalent to a linear network. The equivalent circuit diagram of the CLLLC resonant bidirectional DC / DC converter obtained by the fundamental wave equivalent analysis method is shown in the figure below. Figure 4 As shown;

[0077] To simplify the analysis, assume that the transformer ratio n is 1; u ab 、u cd are the output voltage of the primary side of the converter and the input voltage of the secondary side of the converter respectively; R eq is the equivalent load resistance;

[0078] according to Figure 2 , we can get the transfer function H(jω) of the CLLLC resonant bidirectional DC / DC converters )for:

[0079]

[0080] Expand and simplify to get:

[0081]

[0082] At resonance, the imaginary part of the converter's transfer function is zero, and after rearranging, we can get:

[0083]

[0084] definition

[0085] Quality factor Q = Z 0 / R eq Formula 13;

[0086] Characteristic impedance Z 0 =(L r1 / C r1 ) 1 / 2 Formula 14;

[0087]

[0088]

[0089] Then formula 11 can be simplified to:

[0090] Solving equation 17, we get:

[0091] Let the normalized frequency ω n =ω s / ω rl , the voltage gain of the converter is:

[0092]

[0093] When the switch operates at the resonant point, that is, the switching frequency is equal to the resonant frequency, ω s =ω r , the voltage gain expression of the converter can be simplified as:

[0094]

[0095] From Equation 19, we can see that when the switch operates at the resonant point, the voltage gain of the converter is independent of the load, and the primary side resonant inductor L r1 and the secondary side resonant inductor L r2 Equal h = 1, the primary side resonant capacitor C r1 and the secondary side resonant capacitor C r2When g = 1, the voltage gain of the converter is always 1, and the forward and reverse transmission characteristics remain completely consistent;

[0096] In order to ensure the consistency of the forward and reverse operation of the converter, h=g=1 is set. At this time, the voltage gain expression of the converter is:

[0097]

[0098] From Equation 21, we can see that at this time, the voltage gain is related to the quality element Q and the excitation inductance L m With the resonant inductor L r1 Ratio k and normalized frequency ω n related;

[0099] Now set Q = 0.2, and get the voltage gain curve characteristics of normalized frequency under different k values ​​as follows Figure 4 As shown;

[0100] Depend on Figure 5 It can be seen that when the switching frequency of the converter is equal to the resonant frequency, at this time, the impedance of the series resonance of the resonant components is 0, and the voltage gain is always 1 regardless of how the k value changes. As the k value decreases, the voltage gain peak becomes larger, which widens the output voltage range of the converter. However, the smaller the k value, the smaller the excitation inductance, which will cause the excitation current to increase, thereby increasing the conduction loss of the switch and reducing the efficiency of the converter. As the k value increases, the voltage gain peak continues to decrease, and the gain curve becomes flatter near the resonance point, which will cause the frequency modulation range to become larger. When the k value is too large, the voltage gain is always less than 1 and cannot meet the converter requirements;

[0101] Quality Factor Q and Equivalent Load R eq Inversely proportional to the load, the voltage gain decreases as the load increases. Now set k = 5, and get the voltage gain curve of the normalized frequency under different quality factors Q as follows Figure 5 As shown;

[0102] Depend on Figure 6 It can be seen that when the switching frequency is equal to the resonant frequency, the voltage gain is always 1, regardless of the Q value. When the Q value is too large, the voltage gain changes in opposite trends on both sides of the resonance point, and the voltage gain is always less than 1; when the Q value is too small, the voltage gain changes greatly with the operating frequency, and is easily affected by external interference, resulting in unstable output voltage. Therefore, it is necessary to ensure that the ideal voltage gain curve can be obtained when the converter quality factor is the highest;

[0103] According to the above analysis, the parameters of the simulation circuit are selected, and the input voltage V in =400V, resonant frequency is 500kHz, switching frequency is 470kHz, L r1 =1.9e-6H,L r2=1.6e-6H,C r1 =57.4e-9F,C r2 =82e-9F, load resistance R L =30Ω, transformer turns ratio is 4:3;

[0104] After reorganizing step 3, the state space equation of the bidirectional full-bridge CLLLC resonant converter can be obtained. The circuit equation in steady state is as follows:

[0105]

[0106] When the bidirectional full-bridge CLLLC resonant converter is working stably, the state variable I Lr1s ,I Lr1c ,I Lms ,I Lmc 、V Cr1s 、V Cr1c 、V Cr2s 、V Cr2c and V out It is also stable, and all are zero after differentiation. Therefore, by substituting the obtained parameters, the steady-state values ​​of the above state variables can be solved.

[0107] Step 5, assume that the bidirectional full-bridge CLLLC resonant converter operates at a stable operating point, add a small signal disturbance, and each variable is expressed as the sum of the steady-state value and the corresponding disturbance value. To simplify the calculation, the small signal model of the CLLLC converter is obtained by discarding the second-order quantity and the steady-state quantity:

[0108] The state equation of the small signal is shown in Equation 24:

[0109]

[0110] The small signal model of the CLLLC converter is written in matrix form:

[0111]

[0112] Among them, the input variables are: State variables: Output variables:

[0113]

[0114] Substituting the selected circuit parameters, the parameters of the A, B, and C matrices are:

[0115]

[0116] B=[-5.2164 -355.1376 -2095.1 30.7737 -3.7949 -354.9733 -0.84847.3388 0] T

[0117] C=[0 0 0 0 0 0 0 0 1]

[0118] The transfer function of the small signal model can be written as:

[0119]

[0120] Bring in:

[0121] A small signal modeling and order reduction method for a CLLLC resonant converter, wherein the specific steps of reducing the order of the small signal model of the CLLLC resonant converter are as follows:

[0122] Step 1, by observing the A matrix, the small signal model obtained is a 9th-order model, and the stability of the transfer function is determined according to the Routh-Hurwiz criterion;

[0123] Calculate and generate Routh table;

[0124] in,

[0125] i,j satisfies,

[0126] c 1,1 =b n ,c 1,2 =b n-2 ,…;c 2,1 =b n-1 ,c 2,2 =b n-3 ,…

[0127] Determine the coefficients in the Routh table. If c i+1,1 >0, i≥1 is a stable model;

[0128] Step 2, based on the principle of high-order polynomial decomposition, rationally expand the high-order model of the system;

[0129]

[0130] in,

[0131] Step 3: Establish parameter α i , β iRouth table:

[0132] α i Routh table:

[0133] β i Routh table:

[0134] Step 4, substitute formula 30:

[0135] in,

[0136] Through its calculation and solution, it can be determined that its reduced-order model is:

[0137] By using this method, the small signal high-order model of CLLLC is reduced to 2nd order, 3rd order, 4th order and 5th order respectively;

[0138] The second-order model is:

[0139] The third-order model is:

[0140] The fourth-order model is:

[0141] The fifth-order model is:

[0142] like Figure 7 As shown, the state response curves of each reduced-order transfer function can be observed. The error of each order state response curve is small and the practicability is strong.

[0143] like Figure 8 As shown, the comparison effect between the reduced-order model and the full-order model can be observed more clearly, and through comparison, it can be obtained that for the CLLLC model with this parameter, the third-order reduction effect is the best;

[0144] The present invention cites specific embodiments to illustrate the principles and implementation methods of the present invention. Professionals and technicians in this field will realize that the above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with this technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. The general principles defined in this article can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown in this article, but should conform to the widest scope consistent with the principles and novel features disclosed in this article. All equivalent changes or modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims

1. A Routh reduced-order modeling method for a CLLLC resonant DC-DC converter, characterized by: The following steps are involved: (1) Small signal modeling of the CLLLC resonant circuit is performed by using the extended description function method to generate a small signal model; (2) Design parameters of the CLLLC resonant converter and bring them into the model; (3) Determine the stability of the model based on the Routh-Hurwiz criterion; (4) Based on the principle of high-order polynomial decomposition, the high-order model of the system is rationally expanded; (5) Establish a Routh table and generate a reduced-order model.

2. The small signal modeling method of the CLLLC resonant circuit according to claim 1, characterized in that: The CLLLC resonant circuit is subjected to small signal modeling by an extended function method to generate a linear small signal model, the steps of which include: (1) Analyze the working mode of the circuit, construct the equivalent circuit of CLLLC, define five state variables (such as capacitor voltage and inductor current in the resonant cavity), determine the input variable as the switching frequency disturbance and the output variable as the output voltage disturbance; (2) Write the state equations and output equations of the constructed equivalent circuit according to Kirchhoff's voltage and current laws; (3) Use the extended describing function method to linearize and approximate it, and obtain the state space equation; (4) Modeling and calculating circuit parameters through steady-state analysis method, and solving the steady-state operating point from the circuit parameters: when the input voltage and switching frequency are known, the steady-state value of each state quantity is solved; (5) The small signal disturbance and the separation disturbance are superimposed on the steady-state point and linearized. The final state space equation is the small signal model based on the steady-state operating point.

3. The small signal modeling method of the CLLLC resonant circuit as claimed in claim 2, characterized in that: The steps of performing harmonic approximation on the state variables and extending the description of the input variable switching frequency disturbance and the output variable include: (1) converting the fundamental voltage of the input variable into a frequency modulated signal to decompose the determined state variable into a sine signal and a cosine signal superimposed on each other; (2) deriving the decomposed state variables respectively; (3) The equations are linearized according to the extended describing function method to obtain an approximate system of linear equations.

4. The parameter design of the CLLLC resonant circuit as claimed in claim 2, characterized in that: The following steps are involved: (1) Use fundamental wave analysis method to conduct steady-state modeling of CLLLC resonant converter; (2) List the steady-state DC gain of the CLLLC resonant converter; (3) Focusing on the high-frequency transformer ratio n, the quality factor Q of the resonant network, and the excitation inductance L m And the ratio k of excitation inductance to resonant inductance is used for parameter selection.

5. The stability of the transfer function established by the Routh-Hurwiz criterion as claimed in claim 1, characterized in that: By observing the parameters in the established Routh table, the following steps are included: (1) Write the characteristic equation based on the transfer function of the system; (2) Calculate and generate Routh table; in, i,j satisfies, (3) Determine the coefficients in the Routh table. If c i+1，1 >0, i≥1, then it is a stable model.

6. The small signal model reduction method of the CLLLC resonant circuit according to claim 1, characterized in that The denominator and the numerator are divided into two independent parts for order reduction, that is, the denominator of the reduced-order model is only related to the denominator of the original model and has nothing to do with the numerator of the original model, including the following steps: (1) According to the required high-order model of the system and the principle of high-order polynomial decomposition, the transfer function is rationally expanded; (2) Establish Routh table through analysis and calculation; (3) Substitute the parameters in the Routh table into formula 1, in, Through its computational solution, its reduced-order model can be determined.

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