A super-spiral sliding mode control method combined with backflow power optimization

Abstract

The application relates to a super-helix sliding mode control method combined with reflux power optimization, which comprises the following steps: S1, analyzing the transmission power, the mathematical model of reflux power and the ZVS characteristics of a DAB converter in two modes under extended phase shift modulation, and establishing a reduced-order model of the DAB converter based on the mathematical model of transmission power. The application has the beneficial effect that compared with PI and traditional sliding mode control strategies, the super-helix sliding mode control strategy proposed in the application can significantly improve the dynamic performance of the converter when the load is switched, the input voltage is suddenly changed and the reference voltage is changed, can effectively suppress the chattering phenomenon in the traditional sliding mode, improves the stability of the system, and compared with single phase shift modulation, the reflux power optimization algorithm under the extended phase shift modulation can well reduce the reflux power generated by the DAB converter, and can guarantee the ZVS characteristics of the switching device.

Description

Technical Field

[0001] This invention relates to the field of reflux power optimization technology, and in particular to a superspiral sliding mode control method that combines reflux power optimization. Background Technology

[0002] To achieve the strategic goal of "carbon peaking and carbon neutrality," we should accelerate the construction of a new power system. Vigorously developing new energy power represented by wind and solar power and promoting the grid connection and consumption of a high proportion of renewable energy will become the top priority for my country in building a new power system.

[0003] Compared to AC microgrids, DC microgrids do not require phase and frequency tracking of voltage, resulting in improved controllability and reliability, making them more suitable for the integration of distributed power sources and loads. Dual Active Bridge (DAB) converters are widely used in DC microgrids due to their advantages such as high power density, electrical isolation, bidirectional energy flow, and ease of soft switching.

[0004] As a key component of DC microgrid structures, DAB converters require excellent steady-state characteristics and dynamic response. Regarding steady-state performance, while DAB converters under traditional single-phase-shift modulation offer advantages such as simple control and ease of implementation, they also suffer from problems like high return power, low converter transmission efficiency, and high current stress. In existing technologies, some researchers have increased control degrees of freedom by introducing an inner phase shift (D1) into the H-bridge on the primary side of the converter, thus reducing return power and improving system efficiency to some extent. Other researchers have further optimized return power as the objective function and solved for the optimal phase shift, but this only analyzed one operating mode, and the obtained optimal phase shift is not the globally optimal solution. The literature "Optimization Control Strategy for Dual Active Bridge DC-DC Converters with Extended Phase Shift Control" divides the DAB converter under EPS modulation into two operating modes and proposes an optimization scheme to achieve minimum current stress across the entire power range. The literature "Optimization Selection and Analysis of Phase Shift Angle for Dual Active Bridges Based on Extended Phase Shift Control" re-establishes the transmission power model of the DAB converter under EPS control using a new phase shift angle, simplifying the analysis of transmission power and the selection of the phase shift angle. The literature "Global Current Stress Analysis and Optimization Control Strategy of Dual-Phase-Shift Control for Dual-Active Full-Bridge Converters" and "Segmented Optimization Control of Minimum Return Power for Bidirectional Full-Bridge DC-DC Converters Based on Dual-Phase-Shift Control" employs dual-phase-shift (DPS) modulation. By introducing the same inner shift ratio D1 on the secondary-side H-bridge as the primary-side H-bridge, it increases control freedom. Simultaneously, it segments the transmitted power, optimizing current stress or return power within different power segments, thus improving converter efficiency across the entire power range. However, the identical inner shift ratio on both sides of the full-bridge limits control flexibility. The literature "Normalization of Phase Shift Control and Minimum Return Power Control for Full-Bridge Isolated DC / DC Converters" proposes a triple-phase-shift (TPS) modulation method. By introducing intermediate variables, it provides a return power optimization scheme, significantly reducing system return power and improving system efficiency under rated output power. However, this scheme only analyzes specific voltage matching conditions and lacks general applicability. The aforementioned literature mainly focuses on the steady-state performance of the converter, but does not analyze the dynamic characteristics of the converter under various disturbances.

[0005] Because DC microgrids are connected to a large number of new energy devices and random loads, problems such as distributed power fluctuations, frequent load switching, and uncertain disturbances can cause DC bus voltage fluctuations, thus affecting the stable operation of the DC microgrid. Therefore, DAB converters require excellent dynamic response performance. To improve the dynamic performance of DAB converters, the paper "Load Current Feedforward Control Method for Bidirectional Full-Bridge DC-DC Converters" proposes a load current feedforward control method, which can achieve a fast dynamic response when the load changes abruptly. However, this control method is not effective when facing other types of disturbances such as sudden changes in input voltage. The paper "Virtual Power Control Method for Bidirectional Active Bridge DC-DC Converters Based on Input Voltage Feedforward" combines virtual power control with input voltage feedforward. This method can effectively suppress output voltage ripple when the input voltage changes. The paper "Hyperlocal Model Control Strategy for Dual Active Full-Bridge Converters" proposes a hyperlocal model control strategy, which improves the control effect by introducing a sliding mode observer to accurately estimate the unknowns in the hyperlocal model. All of the above control strategies use SPS modulation and only optimize dynamic performance, without addressing steady-state performance optimization. To simultaneously optimize the steady-state and dynamic performance of the converter, the paper "A Model-Feedforward-Based Current Stress Optimization Method for Dual Active Bridge DC-DC Converters" proposes a model-feedforward-based current stress optimization method under DPS modulation. However, this method requires certain circuit parameters to participate in the calculation, making the algorithm susceptible to parameter influences. The paper "Triple Phase-Shift Optimization Control of Dual Active Bridge DC-DC Converters Combining Current Stress Optimization and Virtual Voltage Compensation" adopts a TPS modulation strategy and proposes a hybrid control scheme combining current stress optimization and virtual voltage compensation, but it has three degrees of freedom, making control implementation relatively complex. Since DAB converters are nonlinear systems, traditional linear control strategies do not provide ideal control results. Sliding Mode Control (SMC) is a typical nonlinear control method that does not rely on a precise mathematical model of the controlled object and has strong robustness to load fluctuations and parameter perturbations, making it very suitable for controlling nonlinear systems like DAB converters. However, traditional sliding mode control methods suffer from chattering problems. Although some researchers have proposed a dual-integral sliding mode control strategy, this method has a fast transient response to load changes and reference voltage changes. Although the paper uses the arctangent function instead of the sign function as the high-frequency switching term to suppress chattering, the control input signal is still a discontinuous function, and this method comes at the cost of some robustness. It also has certain limitations in practical applications.

[0006] In summary, in order to suppress chattering in sliding mode control, have strong robustness to perturbations, and optimize steady-state performance, this application proposes a super-spiral sliding mode control method for DAB converters that combines extended phase-shift modulation with return power optimization using the super-spiral algorithm in second-order sliding mode. Summary of the Invention

[0007] In view of the above-mentioned problems existing in the prior art, the main objective of the present invention is to provide a super-spiral sliding mode control method that combines return power optimization.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows: A superspiral sliding mode control method incorporating return power optimization includes the following steps: S1. Analyze the mathematical models of transmission power and return power of the DAB converter under extended phase-shift modulation and the ZVS characteristics, and establish a reduced-order model of the DAB converter based on the transmission power mathematical model. S2. Using return power as the objective function and transmission power and soft-switching characteristics as constraints, the optimal shift ratio combination is found using the Karush-Kuhn-Tucker conditional method. S3. Design the equivalent part of the superspiral sliding mode control using the DAB converter reduced-order model and use the superspiral algorithm as the switching part. S4. Conduct experimental verification and accurately measure the specific value of the reduction in return current power when the voltage is changed.

[0009] Among them, S11, DAB extended phase-shift modulation analysis and mathematical modeling are performed; S111. Based on the relationship between D1 and D2, the power transfer model of the DAB converter under EPS modulation is divided into two types, namely: Pattern 1: 0≤D2≤D1≤1; Pattern 2: 0≤D1≤D2≤1; Inductor current i under mode one condition L It exhibits half-cycle positive and negative symmetry, and the inductor current values ​​at each moment within the half-switching cycle are: ; The voltage conversion ratio is defined as k=U in / nU o ; Since the average transmission power and return power of the DAB converter exhibit half-cycle positive and negative symmetry in both modes, the average transmission power P and return power Q are calculated as follows: ; The maximum transmission power under single-phase-shift control is used as the reference value, that is: ; By combining the equations, the per-unit values ​​of the DAB converter's transmission power and return power under Mode 1 conditions are obtained as follows: ; To reduce switching losses and improve transmission efficiency of the converter, the ZVS condition of the switching transistors must be met while reducing return power. The ZVS condition in mode one is as follows: ; Combining equation (1), we get: ; In the S112, DAB converter reduced-order model, under extended phase-shift modulation mode, the power transferred from the primary side to the secondary side of the converter is: ; When the transformer turns ratio n, inductance L, and switching frequency fs are determined, the magnitude and direction of the DAB power flow can be adjusted by adjusting the shift ratio (D1, D2). Secondary output capacitor C out The dynamic energy equation is expressed as: ; in P C The actual power stored in the output capacitor is equal to the converter's transmitted power minus the output power, i.e.: ; Substituting equations (7) and (9) into the equation and simplifying, we obtain the dynamic equation for the output voltage as follows: ; Equation (10) can be expressed in the form of system equations as follows: ; in, , , .

[0010] Furthermore, the present invention also includes: S21. Control system design; S22. Return power optimization: When the transmission power P is constant, there are multiple different combinations of (D1, D2), and different combinations of (D1, D2) correspond to different return power values. Therefore, there must exist a pair of (D1, D2) values ​​that minimizes the return power of the converter. The Karush-Kuhn-Tucker (KKT) conditional method is a method for finding the extrema of a multivariate function whose variables are restricted by one or more constraints. Its form is: ; Using return power as the objective function, transmission power as the equality constraint, and ZVS characteristics as the inequality constraint, the Lagrangian polynomial is established as follows: ; Where λ and μ are the Lagrange multiplier and relaxation variable, respectively, and P* is the given transmission power; The Lagrange polynomial under Mode 1 is: ; The local optimal solution for mode 1 is: ; Based on the constraints of Mode 1: 0≤D2≤D1≤1, the transmission power range at this time is: ; Applying the above method to solve under Mode 2 conditions yields a local optimum for Mode 2: ; Based on the above analysis, the expressions for the optimal shift ratio combinations (D1, D2) within different power ranges are shown in the table below. ; The table shows that the optimization scheme covers the entire power range of 0 ≤ P* ≤ 1; The S22 and STSMC controller design utilizes the reduced-order model of the DAB converter to design the equivalent part of the super-spiral sliding mode control, adopts the super-spiral algorithm in the second-order sliding mode as the switching part, and works together with the inner shift ratio D1 to generate the outer shift ratio D2 to adjust the transmission power of the converter, thereby adjusting the output voltage of the converter. The controller is designed using the dynamic equation of the output voltage in the formula. Systematic error is defined as: ; Among them U ref This is the reference value for the output voltage; The sliding variable s is designed as follows: ; An integral term is introduced into the sliding variable s to eliminate the steady-state error of the output voltage; Let the sliding variable s = 0 and solve the differential equation to obtain the expression for the systematic error e: ; In the formula c o Let e ​​be the initial value of the output voltage error in steady state. From the error expression, we know that as time t→∞, the error e→0 must be guaranteed, i.e., the output voltage Uo→U ref Then the value of K must be greater than zero, and the convergence speed depends on the value of the controller gain K; Differentiating with respect to the sliding variable s, we get: ; Within one sampling period, the reference voltage U refIt can be regarded as a constant value, and its reciprocal with respect to time is zero. Therefore, substituting equation (11) into equation (21) yields: ; In equivalent sliding mode control, the controller input u consists of two parts: ; Where u eq To substitute the system state trajectory into the equivalent part of the model over the sliding variables, u sw To ensure that the system state does not deviate from the switching control section of the sliding variable; Let s′=0 in the formula, and use u eq The equivalent input u of the model is obtained by substituting u in the equation. eq for: ; Switching control term u in first-order sliding mode sw Usually: ; Since the switching control term is a symbolic function and directly acts on the control input u eq In this process, the control signal becomes discontinuous, which leads to chattering. Chattering not only affects the accuracy of control and increases energy consumption, but also easily excites high-frequency unmodeled dynamics in the system, damaging the system's performance and even causing the system to oscillate or become unstable. The superspiral control law consists of two parts, expressed as: ; The first part u1 is a continuous function of the sliding variable, which plays a role in the arrival phase of the sliding mode control process. The second part u2 is the integral of the sign function of the sliding variable over time, which plays a role in the sliding phase. It can be seen that when the parameters α>0 and η>0, the state of the system can converge to the origin in a finite time, at which point s=s′=0. Substituting equations (24) and (26) into (23), we obtain the control input u of the DAB converter under EPS modulation as follows: ; From the equation, we can see that the relationship between the control input u and the inward shift ratio D1 and the outward shift ratio D2 is as follows: ; The inner shift ratio D1 generated by the aforementioned return power optimization algorithm can be used to inversely solve for the outer shift ratio D2, which is used to adjust the output voltage of the DAB converter. Its expression is as follows: ; Substituting equation (27) into equation (22), we obtain the expression for the first derivative of the sliding variable s: ; To verify the stability of the designed super-helical sliding mode controller, stability analysis was performed on the system shown in the equation using Lyapunov functions. For ease of analysis, the equation was rewritten in the following form: ; Where c1=nU in α / 4Lf s C out c2=nU in η / 4Lf s C out ; Introducing a new state vector: ; but ; The derivative of z is: ; Define the Lyapunov function as: ; Where p is a symmetric positive definite matrix, and its α and η are positive numbers, defined as follows: ; Therefore, the Lyapunov function V(z) ≥ 0; Differentiating V(z) with respect to: ; Where matrix Q is: ; Therefore, if Q is a positive definite matrix, i.e. p(Q)>0, then the function V′(z)<0. According to Lyapunov's second law, the expression is asymptotically stable in this case. set up ; Then matrix Q can be simplified to a diagonal matrix: ; At this point, the eigenvalues ​​of matrix Q are: ; To guarantee that matrix Q is positive definite, we only need p1(Q) > 0, at which point we have: ; Let c1=nU in α / 4Lf s C out c2=nU in η / 4Lfs C out Substituting into equations (39) and (42) and simplifying, we obtain the following constraint condition for the positive definiteness of matrix Q: ; This condition serves as a constraint for selecting controller parameters.

[0011] Furthermore, the present invention also includes: S31. Experimental Results and Analysis: A low-power experimental platform for the DAB converter was built, and its dynamic performance was compared with that of EPS-modulated PI control (Expanded Phase Shift-PI Control, EPS-PI) and EPS-modulated sliding mode control (Expanded Phase Shift-Sliding Mode Control, EPS-SMC) under load switching, sudden input voltage change, and reference voltage change conditions. The steady-state characteristics were also compared with those of traditional SPS modulation. S32. Observe the experimental waveforms of the primary side AC voltage Uab, secondary side AC voltage Ucd, inductor current iL, and calculated primary side instantaneous transmission power Pt under the control of SPS and EPS-STSMC, based on the different input voltage, output voltage, and load resistance.

[0012] Furthermore, the present invention also includes: S4. Draw conclusions based on the data; S41. Taking the DAB converter as the research object, this paper derives the converter transmission power and return power model under EPS modulation, applies the KKT algorithm to optimize the return power, and combines the super-spiral sliding mode control strategy to improve the dynamic performance of the converter. The results are compared with PI and traditional sliding mode control schemes, and the results are presented in theoretical analysis and experimental results.

[0013] Furthermore, the present invention also includes: In the DAB extended phase-shift modulation analysis in step S111, the DAB converter, under extended phase-shift modulation, includes the driving sequences of each switching transistor, the primary and secondary voltage waveforms, and the inductor current waveforms. T s For half a switching cycle of the switching transistor, D1 is the inward shift ratio of the primary-side H-bridge, D2 is the outward shift ratio between the primary-side H-bridge and the secondary-side H-bridge, and Uab and Ucd are the bridge arm voltages of the primary-side and secondary-side H-bridges, respectively.

[0014] Furthermore, the present invention also includes: In the general form of the method for finding the extrema of a multivariate function whose variables are restricted by one or more constraints in step S22, F(X) is the objective function, gu(X) is the equality constraint that needs to be satisfied, and hv(X) is the inequality constraint that needs to be satisfied.

[0015] Furthermore, the present invention also includes: In step S22, the super-helical sliding mode control incorporates the high-frequency switching term ηsgn(s) from the traditional sliding mode control into the integral operation. This means that the discontinuous high-frequency switching term no longer directly affects the control input u, making the control signal continuous and thus suppressing chattering. At the same time, the super-helical algorithm only needs to know the information of the sliding variable s and does not need to know any information about the first derivative of the sliding variable, which simplifies the design of the control system.

[0016] Furthermore, the present invention also includes: the superspiral algorithm in step S22 is a second-order sliding mode algorithm, which is suitable for systems with a relative order of 1; as can be seen from the formula, the relative order of the system is 1, and the superspiral algorithm can eliminate discontinuous terms in traditional SMC control by using the switching control part.

[0017] Compared with the prior art, the advantages and positive effects of the present invention are as follows: This invention derives the transmission power and return power models of the converter under EPS modulation, applies the KKT algorithm to optimize the return power, and combines a super-spiral sliding mode control strategy to improve the dynamic performance of the converter. Compared with PI and traditional sliding mode control schemes, it has the following advantages: 1. Compared with PI and traditional sliding mode control strategies, the proposed super-spiral sliding mode control strategy can significantly improve the dynamic performance of the converter when the load is switched, the input voltage changes abruptly, and the reference voltage changes. At the same time, it can effectively suppress chattering in traditional sliding mode and improve the stability of the system. 2. Compared with single phase-shift modulation, the extended phase-shift modulation return power optimization algorithm proposed in this paper can effectively reduce the return power generated by the DAB converter, while ensuring the ZVS characteristics of the switching devices. Attached Figure Description

[0018] Figure 1 This invention provides a DC microgrid system structure diagram that incorporates a super-helical sliding mode control method with optimized return power. Figure 2 This invention provides a dual active bridge DC-DC converter topology diagram that incorporates a super-spiral sliding mode control method with optimized return power. Figure 3 The present invention provides a waveform diagram of a DAB converter under extended phase-shift modulation in mode 1, which combines a super-helical sliding mode control method with return power optimization. Figure 4 The present invention provides a waveform diagram of a DAB converter in mode 2 under extended phase-shift modulation, which combines a super-spiral sliding mode control method with return power optimization. Figure 5This invention provides an overall control block diagram of a DAB converter that incorporates a super-spiral sliding mode control method with optimized return power. Figure 6 EPS-PI control diagram (a) is provided for the present invention, which combines a super-spiral sliding mode control method with return power optimization. Figure 7 EPS-SMC control diagram (a) is provided for the present invention, which combines a super-spiral sliding mode control method with return power optimization. Figure 8 EPS-STSMC control diagram (a) is provided for the present invention, which combines a super spiral sliding mode control method with return power optimization. Figure 9 EPS-PI control diagram (b) is provided for the present invention, which combines a super-spiral sliding mode control method with return power optimization. Figure 10 EPS-SMC control diagram (b) is provided for the present invention, which combines a super-spiral sliding mode control method with return power optimization. Figure 11 EPS-STSMC control diagram (b) is provided for the present invention, which combines a super spiral sliding mode control method with return power optimization. Figure 12 The present invention provides an EPS-PI control diagram (c) that combines a super-spiral sliding mode control method with return power optimization. Figure 13 The present invention provides an EPS-SMC control diagram (c) that combines a super-spiral sliding mode control method with return power optimization. Figure 14 The present invention provides an EPS-STSMC control diagram (c) that combines a super-spiral sliding mode control method with return power optimization. Figure 15 The present invention provides an EPS-PI control diagram (d) that combines a super-spiral sliding mode control method with return power optimization. Figure 16 The present invention provides an EPS-SMC control diagram (d) that combines a super-spiral sliding mode control method with return power optimization. Figure 17 The present invention provides an EPS-STSMC control diagram (d) that combines a super-spiral sliding mode control method with return power optimization. Figure 18 The present invention provides an EPS-PI control diagram (e) for a super-spiral sliding mode control method that combines return power optimization. Figure 19 The present invention provides an EPS-SMC control diagram (e) that combines a super-spiral sliding mode control method with return power optimization. Figure 20 The present invention provides an EPS-STSMC control diagram (e) that combines a super-spiral sliding mode control method with return power optimization. Figure 21 The present invention provides a D2 waveform diagram generated under the EPS-SMC and EPS-STSMC control strategies of a super spiral sliding mode control method that combines return power optimization. Figure 22 The SPS control diagram (a) for the present invention provides a super-spiral sliding mode control method that combines return power optimization; Figure 23 The present invention provides an EPS-STSMC control diagram (f) that combines a super-spiral sliding mode control method with return power optimization. Figure 24 SPS control diagram (b) is provided for the present invention, which combines a super-spiral sliding mode control method with return power optimization. Figure 28 is an EPS-STSMC control diagram (g) of the super spiral sliding mode control method combined with return power optimization provided by the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0020] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Example

[0021] A superspiral sliding mode control method incorporating return power optimization includes the following steps: S1. Analyze the mathematical models of transmission power and return power of the DAB converter under extended phase-shift modulation and the ZVS characteristics, and establish a reduced-order model of the DAB converter based on the transmission power mathematical model. S2. Using return power as the objective function and transmission power and soft-switching characteristics as constraints, the optimal shift ratio combination is found using the Karush-Kuhn-Tucker conditional method. S3. Design the equivalent part of the superspiral sliding mode control using the DAB converter reduced-order model and use the superspiral algorithm as the switching part. S4. Conduct experimental verification and accurately measure the specific value of the reduction in return current power when the voltage is changed.

[0022] Among them, S11, DAB extended phase-shift modulation analysis and mathematical modeling are performed; S111. Based on the relationship between D1 and D2, the power transfer model of the DAB converter under EPS modulation can be divided into two types, namely: Pattern 1: 0≤D2≤D1≤1; Pattern 2: 0≤D1≤D2≤1; Combination Figure 3 and Figure 4 The following analysis uses Mode 1 as an example. The principle of the analysis process under Mode 2 is similar to that under Mode 1. Under the condition of Mode 1, the inductor current i L It exhibits half-cycle positive and negative symmetry, and the inductor current values ​​at each moment within the half-switching cycle are: ; The voltage conversion ratio is defined as k=U in / nU o： Since the average transmission power and return power of the DAB converter exhibit half-cycle positive and negative symmetry in both modes, the average transmission power P and return power Q can be calculated as follows: ; The maximum transmission power under single-phase-shift control is used as the reference value, that is: ; By combining the two equations, the per-unit values ​​of the DAB converter's transmission power and return power under Mode 1 conditions can be obtained as follows: ; To reduce the switching losses of the converter and improve transmission efficiency, the ZVS condition of the switching transistors must be satisfied while reducing the return power. The ZVS condition in mode one is as follows: ; Combining equation (1), we can obtain: ; In the S112, DAB converter reduced-order model, under extended phase-shift modulation mode, the power transferred from the primary side to the secondary side of the converter can be obtained from the equation as follows: ; When the transformer turns ratio n, inductance L, and switching frequency fs are determined, the magnitude and direction of the DAB power flow can be adjusted by adjusting the shift ratio (D1, D2). The dynamic energy equation for the secondary output capacitor Cout can be expressed as: ; in P C The actual power stored in the output capacitor is equal to the converter's transmitted power minus the output power, i.e.: ; Substituting the equations and rearranging them, we obtain the dynamic equation for the output voltage as follows: ; The equation can be expressed in the form of a system equation as follows: ; in, , , .

[0023] Among them, S21, control system design; S22. Return power optimization: When the transmission power P is constant, there are multiple different combinations of (D1, D2), and different combinations of (D1, D2) correspond to different return power values. Therefore, there must exist a pair of (D1, D2) values ​​that minimizes the return power of the converter. The Karush-Kuhn-Tucker (KKT) conditional method is a method for finding the extrema of a multivariate function whose variables are restricted by one or more constraints. Its general form is: ; Using return power as the objective function, transmission power as the equality constraint, and ZVS characteristics as the inequality constraint, the Lagrangian polynomial is established as follows: ; Where λ and μ are the Lagrange multiplier and relaxation variable, respectively, and P* is the given transmission power; The Lagrange polynomial under Mode 1 is: ; The local optimal solution for mode 1 is: ; Based on the constraint of Mode 1: 0≤D2≤D1≤1, the transmission power range at this time can be calculated as follows: ; Applying the above method to solve under Mode 2 conditions yields a local optimum for Mode 2: ; Based on the above analysis, the expressions for the optimal shift ratio combination (D1, D2) in different power ranges are shown in Table 1. As can be seen from the table, the optimized scheme covers the entire power range of 0≤P*≤1.

[0024] S22, STSMC Controller Design: This section uses the reduced-order model of the DAB converter to design the equivalent part of the super-spiral sliding mode control, adopts the super-spiral algorithm in the second-order sliding mode as the switching part, and works together with the inner shift ratio D1 to generate the outer shift ratio D2 to adjust the transmission power of the converter, thereby adjusting the output voltage of the converter. The controller is designed using the dynamic equation of the output voltage in the formula. Systematic error is defined as: ; Among them U ref This is the reference value for the output voltage; The sliding variable s is designed as follows: ; Introducing an integral term into the sliding variable s can eliminate the steady-state error of the output voltage; Setting the sliding variable s=0 and solving the differential equation yields the expression for the systematic error e: ; In the formula c o Let e ​​be the initial value of the output voltage error in steady state. From the error expression, we know that as time t→∞, the error e→0 must be guaranteed, i.e., the output voltage Uo→U ref Then the value of K must be greater than zero, and the convergence speed depends on the value of the controller gain K; Differentiating with respect to the sliding variable s, we get: ; Because the reference voltage U is within a sampling period ref It can be considered a constant, and its reciprocal with respect to time is zero. Therefore, substituting the formula into the equation yields... ; The control method used in this paper is essentially equivalent sliding mode control. The controller input u consists of two parts: ; Where u eq To substitute the system state trajectory into the equivalent part of the model over the sliding variables, u sw To ensure that the system state does not deviate from the switching control section of the sliding variable; Let s′=0 in the formula, and use u eqThe equivalent input u of the model is obtained by substituting u in the equation. eq for: ; In first-order sliding mode, the switching control term usw is typically: ; Since the switching control term is a symbolic function and directly acts on the control input u eq In this process, the control signal becomes discontinuous, which leads to chattering. Chattering not only affects the accuracy of control and increases energy consumption, but also easily excites high-frequency unmodeled dynamics in the system, damaging the system's performance and even causing the system to oscillate or become unstable. The superspiral control law consists of two parts, which can be expressed as: ; The first part u1 is a continuous function of the sliding variable, which plays a role in the arrival phase of the sliding mode control process. The second part u2 is the integral of the sign function of the sliding variable over time, which plays a role in the sliding phase. It can be seen that when the parameters α>0 and η>0, the state of the system can converge to the origin in a finite time, at which point s=s′=0. Substituting the equations into the given equations, we can obtain the control input u of the DAB converter under EPS modulation as follows: ; From the equation, we can see that the relationship between the control input u and the inward shift ratio D1 and the outward shift ratio D2 is as follows: ; The inner shift ratio D1 generated by the return power optimization algorithm described above can be used to inversely solve for the outer shift ratio D2, which is used to adjust the output voltage of the DAB converter. Its expression is as follows: ; Substituting the equation into the expression, we obtain the first derivative expression for the sliding variable s as follows: ; To verify the stability of the designed super-helical sliding mode controller, stability analysis was performed on the system shown in the equation using Lyapunov functions. For ease of analysis, the equation was rewritten in the following form: ; Where c1=nU in α / 4Lf s C out c2=nU in η / 4Lf s C out ; Introducing a new state vector: ; but ; The derivative of z is: ; In this paper, the Lyapunov function is defined as: ; Where p is a symmetric positive definite matrix, and its α and η are positive numbers, defined as follows: ; Therefore, the Lyapunov function V(z) ≥ 0; Differentiating V(z) with respect to it, we get: ; Where matrix Q is: ; Therefore, if Q is a positive definite matrix, i.e. p(Q)>0, then the function V′(z)<0. According to Lyapunov's second law, the expression is asymptotically stable in this case. set up ; Then matrix Q can be simplified to a diagonal matrix: ; At this point, the eigenvalues ​​of matrix Q are: ; To guarantee that matrix Q is positive definite, we only need p1(Q) > 0, at which point we have: ; Let c1=nU in α / 4Lf s C out c2=nU in η / 4Lf s C out Substituting into the equation and simplifying, we obtain the constraint condition for the positive definiteness of matrix Q as follows: ; This condition serves as a constraint for selecting controller parameters.

[0025] S31, Experimental Results and Analysis: A low-power experimental platform for the DAB converter was built, and its dynamic performance was compared with that of EPS-modulated PI control (Expanded Phase Shift-PI Control, EPS-PI) and EPS-modulated sliding mode control (Expanded Phase Shift-Sliding Mode Control, EPS-SMC) under load switching, input voltage change, and reference voltage change conditions. It was also compared with the steady-state characteristics under traditional SPS modulation. The control parameters are shown in the table below when different control strategies are adopted.

[0026] S32. Observe the primary side AC voltage U under SPS and EPS-STSMC control based on the different input voltage, output voltage, and load resistance. ab AC voltage U on the secondary side cd Inductor current i L And the calculated instantaneous transmission power P on the primary side t Experimental waveform.

[0027] S4, drawing conclusions based on data; S41. Taking the DAB converter as the research object, this paper derives the converter transmission power and return power model under EPS modulation, applies the KKT algorithm to optimize the return power, and combines the super-spiral sliding mode control strategy to improve the dynamic performance of the converter. The results are compared with PI and traditional sliding mode control schemes, and the results are presented in theoretical analysis and experimental results.

[0028] In step S111, during the DAB extended phase-shift modulation analysis, the DAB converter, under extended phase-shift modulation, includes various switching transistor drive sequences, primary and secondary voltage waveforms, and inductor current waveforms. T s For half a switching cycle of the switching transistor, D1 is the inward shift of the primary-side H-bridge, D2 is the outward shift between the primary-side H-bridge and the secondary-side H-bridge, and U... ab U cd These are the bridge arm voltages of the H-bridge on the primary and secondary sides, respectively.

[0029] In the general form of the method for finding the extrema of a multivariate function whose variables are restricted by one or more constraints in step S22, F(X) is the objective function, g u (X) represents the equality constraints that need to be satisfied, h v (X) represents the inequality constraints that need to be satisfied.

[0030] In step S22, the super-helical sliding mode control incorporates the high-frequency switching term ηsgn(s) from the traditional sliding mode control into the integral operation. This means that the discontinuous high-frequency switching term no longer directly affects the control input u, making the control signal continuous and thus suppressing chattering. At the same time, the super-helical algorithm only needs to know the information of the sliding variable s and does not need to know any information about the first derivative of the sliding variable, which simplifies the design of the control system.

[0031] In step S22, the superspiral algorithm is a second-order sliding mode algorithm, which is suitable for systems with a relative order of 1. As can be seen from the formula, the relative order of the system is 1. The superspiral algorithm can eliminate discontinuities in traditional SMC control by using the switching control part.

[0032] When the input voltage U in =350V, Output voltage U o The experimental waveforms of the DAB converter's output voltage, load current, and inductor current under three different control schemes are shown below when the voltage is 120V and the load resistance changes from 10Ω to 20Ω. Figure 6 , Figure 7 and Figure 8 As shown, when the load is switched from full load to half load, the dynamic adjustment time of the output voltage under EPS-PI control is 25ms, accompanied by an overshoot of 14.5V. The dynamic adjustment time of the output voltage under EPS-SMC control is 20ms, and the overshoot is 5V. The dynamic adjustment time of the output voltage under EPS-STSMC control is only 4ms, and the overshoot is 1.5V. Compared with the first two control schemes, the adjustment time under the EPS-STSMC scheme is reduced by 84% and 80%, respectively, and the overshoot is reduced by 89.6% and 70%, respectively. When the input voltage U in =350V, Output voltage U o The experimental waveforms of the DAB converter's output voltage, load current, and inductor current under three different control schemes are shown below when the voltage is 120V and the load resistance changes from 20Ω to 10Ω. Figure 9 , Figure 10 and Figure 11 As shown, when the load changes from half load to full load, the dynamic adjustment time of the output voltage under EPS-PI control is 24ms, accompanied by a voltage drop of 12.8V. Under EPS-SMC control, the dynamic adjustment time of the output voltage is 20ms and the voltage drop is 5.5V. Under EPS-STSMC control, the dynamic adjustment time of the output voltage is 4ms and the voltage drop is 1.6V. Compared with the first two control schemes, the adjustment time under the EPS-STSMC scheme is reduced by 83.3% and 80% respectively, and the voltage drop is reduced by 87.5% and 70.9% respectively. The experimental results show that the EPS-STSMC scheme has stronger robustness and better dynamic performance than the first two control schemes under load switching conditions. When the output voltage U o =120V, load resistance R=10Ω, input voltage U in The experimental waveforms of the DAB converter's input voltage, output voltage, and inductor current under three different control schemes when the voltage changes from 350V to 300V are shown below. Figure 12 , Figure 13 and Figure 14 As shown: As can be seen from the figure, when the input voltage decreases, the output voltage regulation time of the EPS-PI scheme is 25ms and the voltage drop is 2V, while the output voltage regulation time and voltage drop of the EPS-SMC scheme are both greater than those of the EPS-PI scheme, at 30ms and 11V respectively. The regulation time of the EPS-SMC scheme is 0ms and the voltage fluctuation is 0V. When the output voltage U o =120V, load resistance R=10Ω, input voltage U in The experimental waveforms of the DAB converter's input voltage, output voltage, and inductor current under three different control schemes when the voltage changes from 300V to 350V are shown below. Figure 15 , Figure 16 and Figure 17 As shown: The experimental waveforms show that when the input voltage increases, the output voltage regulation times of the EPS-PI, EPS-SMC, and EPS-STSMC schemes are 25ms, 34ms, and 0ms, respectively, and the overshoots are 2V, 9V, and 0V, respectively. When the input voltage changes abruptly, the control scheme proposed in this paper has the best dynamic performance, followed by the PI control scheme, and the SMC control scheme is the worst. When the input voltage U in =350V, load resistance R=10Ω, reference voltage U ref The experimental waveforms of the DAB converter's output voltage, load current, and inductor current under three different control schemes when transitioning from 120V to 140V and from 140V to 100V are shown below. Figure 18 , Figure 19 and Figure 20 As shown: When the reference voltage U ref When changing from 120V to 140V, the voltage regulation times under the three control strategies EPS-PI, EPS-SMC, and EPS-STSMC are 30ms, 30ms, and 4ms, respectively, with overshoots of 4V, 3V, and 0.5V. When the reference voltage U... refWhen the output voltage regulation time is from 140V to 100V, it is 32ms, 28ms and 6ms respectively, and the voltage fluctuation is 8V, 4.5V and 1V. Under the condition of sudden change of reference voltage, all three control strategies can achieve zero steady-state error tracking within a limited time. However, the output voltage regulation time is shorter and the voltage fluctuation is smaller under EPS-STSMC control. When the input voltage U in =350V, Output voltage U o When the voltage is 120V, the load resistance R=10Ω, and the system is in steady state, the difference between the D2 waveforms generated by the EPS-SMC and EPS-STSMC control strategies is as follows: Figure 21 As shown: In the figure, the waveform represents the outward shift generated under the traditional sliding mode control scheme, while the black waveform represents the outward shift generated under the super-spiral sliding mode control scheme. Compared with the traditional sliding mode control method, the outward shift generated under the super-spiral sliding mode control scheme has smaller fluctuations compared to D2, indicating that the STSMC algorithm can effectively suppress chattering and verifying the correctness of the theory. When the input voltage U in =350V, Output voltage U o With a voltage of 120V, a load resistance of R=10Ω, and the system in steady state, the experimental waveforms of the primary-side AC voltage Uab, the secondary-side AC voltage Ucd, the inductor current iL, and the calculated primary-side instantaneous power transfer Pt under SPS and EPS-STSMC control are as follows: Figure 22 and Figure 23 As shown; The return power is calculated by integrating according to equation (2) within half a switching cycle. Figure 22 , 23 , Figure 24 and Figure 25 The shaded area represents the return current power generated by the DAB converter during a half-switching cycle. When k=1.94, the return current power during the half-cycle under SPS modulation is approximately 0.136W, while under EPS modulation it is only 0.02W, a reduction of 85.3% compared to SPS modulation. Furthermore, both primary and secondary switching devices achieve zero-voltage switching (ZVS). When k=1.67, the return current power during the half-cycle under SPS modulation is approximately 0.097W, while under EPS modulation it is 0.0093W. Under EPS modulation, both switching devices achieve ZVS, verifying the correctness and effectiveness of the return current power optimization strategy. Simultaneously, as the voltage conversion ratio k decreases, the return current power also decreases accordingly. Therefore, this method derives the transmission power and return power models of the converter under EPS modulation, applies the KKT algorithm to optimize the return power, and combines a super-spiral sliding mode control strategy to improve the dynamic performance of the converter. Compared with PI and traditional sliding mode control schemes, it has the following advantages: 1. Compared with PI and traditional sliding mode control strategies, the proposed super-spiral sliding mode control strategy can significantly improve the dynamic performance of the converter when the load is switched, the input voltage changes abruptly, and the reference voltage changes. At the same time, it can effectively suppress chattering in traditional sliding mode and improve the stability of the system. 2. Compared with single phase-shift modulation, the extended phase-shift modulation return power optimization algorithm proposed in this paper can effectively reduce the return power generated by the DAB converter, while ensuring the ZVS characteristics of the switching devices.

[0033] Finally, it should be noted that the above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A superspiral sliding mode control method combining reflux power optimization, characterized in that: Includes the following steps: S1. Analyze the mathematical models of transmission power and return power of the DAB converter under extended phase-shift modulation and the ZVS characteristics, and establish a reduced-order model of the DAB converter based on the transmission power mathematical model. S2. Using return power as the objective function and transmission power and soft-switching characteristics as constraints, the optimal shift ratio combination is found using the KKT condition method. S3. Design the equivalent part of the superspiral sliding mode control using the DAB converter reduced-order model and use the superspiral algorithm as the switching part. S4. Conduct experimental verification and accurately measure the specific value by which the return power can be reduced when the voltage is changed. S11. Perform DAB extended phase-shift modulation analysis and mathematical modeling; S111. Based on the relationship between D1 and D2, the power transfer model of the DAB converter under EPS modulation is divided into two types, namely: Pattern 1: 0≤D2≤D1≤1; Pattern 2: 0≤D1≤D2≤1; Inductor current i under mode one condition L It exhibits half-cycle positive and negative symmetry, and the inductor current values ​​at each moment within the half-switching cycle are: ； The voltage conversion ratio is defined as k=U in / nU o ; Since the average transmission power and return power of the DAB converter exhibit half-cycle positive and negative symmetry in both modes, the average transmission power P and return power Q are calculated as follows: ； The maximum transmission power under single-phase-shift control is used as the reference value, that is: ； By combining the equations, the per-unit values ​​of the DAB converter's transmission power and return power under Mode 1 conditions are obtained as follows: ； To reduce switching losses and improve transmission efficiency of the converter, the ZVS condition of the switching transistors must be met while reducing return power. The ZVS condition in mode one is as follows: ； Combining the formulas, we get: ； S112, DAB converter reduced-order model, under extended phase-shift modulation mode, according to equation (2), the power transmitted from the primary side to the secondary side of the converter is: ； When the transformer turns ratio n, inductance L, and switching frequency fs are determined, the magnitude and direction of the DAB power flow are adjusted by adjusting the shift ratio (D1, D2). Secondary output capacitor C out The dynamic energy equation is expressed as: ； Where P C The actual power stored in the output capacitor is equal to the converter's transmitted power minus the output power, i.e.: ； Substituting equations (7) and (9) into (8) and rearranging, we obtain the dynamic equation for the output voltage as follows: ； Equation (10) can be expressed in the form of system equations as follows: ； in, , , ; S21. Control system design; S22. Return power optimization: When the transmission power P is constant, there are multiple different combinations of (D1, D2), and different combinations of (D1, D2) correspond to different return power values. Therefore, there must exist a pair of (D1, D2) values ​​that minimizes the return power of the converter. The Karush-Kuhn-Tucker (KKT) conditional method is a method for finding the extrema of a multivariate function whose variables are restricted by one or more constraints. Its form is: ； Using return power as the objective function, transmission power as the equality constraint, and ZVS characteristics as the inequality constraint, the Lagrangian polynomial is established as follows: ； Where λ and μ are the Lagrange multiplier and relaxation variable, respectively, and P* is the given transmission power; The Lagrange polynomial under Mode 1 is: ； The local optimal solution for mode 1 is: ； Based on the constraints of Mode 1: 0≤D2≤D1≤1, the transmission power range at this time is: ； Applying the above method to solve under Mode 2 conditions yields a local optimum for Mode 2: ； Based on the above analysis, the expressions for the optimal shift ratio combinations (D1, D2) within different power ranges are shown in the table below. ； The table shows that the optimization scheme covers the entire power range of 0 ≤ P* ≤ 1; The S22 and STSMC controller design utilizes the reduced-order model of the DAB converter to design the equivalent part of the super-spiral sliding mode control, adopts the super-spiral algorithm in the second-order sliding mode as the switching part, and works together with the inner shift ratio D1 to generate the outer shift ratio D2 to adjust the transmission power of the converter, thereby adjusting the output voltage of the converter. The controller is designed using the dynamic equation of the output voltage in the formula. Systematic error is defined as: ； Among them U ref This is the reference value for the output voltage. The sliding variable s is designed as follows: ； An integral term is introduced into the sliding variable s to eliminate the steady-state error of the output voltage; Let the sliding variable s = 0 and solve the differential equation to obtain the expression for the systematic error e: ； In the formula c o Let e ​​be the initial value of the output voltage error in steady state. From the error expression, we know that as time t→∞, the error e→0 must be guaranteed, i.e., the output voltage Uo→U ref Then the value of K must be greater than zero, and the convergence speed depends on the value of the controller gain K; Differentiating with respect to the sliding variable s, we get: ； Within one sampling period, the reference voltage U ref It can be regarded as a constant value, and its reciprocal with respect to time is zero. Therefore, substituting equation (11) into equation (21) yields: ； In equivalent sliding mode control, the controller input u consists of two parts: ； Where u eq To substitute the system state trajectory into the equivalent part of the model over the sliding variables, u sw To ensure that the system state does not deviate from the switching control section of the sliding variable; Let s′=0 in the formula, and use u eq The equivalent input u of the model is obtained by substituting u in the equation. eq for: ； Switching control term u in first-order sliding mode sw Usually: ； Since the switching control term is a symbolic function and directly acts on the control input u eq In this process, the control signal becomes discontinuous, which leads to chattering. Chattering not only affects the accuracy of control and increases energy consumption, but also easily excites high-frequency unmodeled dynamics in the system, damaging the system's performance and even causing the system to oscillate or become unstable. The superspiral control law consists of two parts, expressed as: ； The first part u1 is a continuous function of the sliding variable, which plays a role in the arrival phase of the sliding mode control process. The second part u2 is the integral of the sign function of the sliding variable over time, which plays a role in the sliding phase. It can be seen that when the parameters α>0 and η>0, the state of the system can converge to the origin in a finite time, at which point s=s′=0. Substituting equations (24) and (26) into (23), we can obtain the control input u of the DAB converter under EPS modulation as follows: ； From the equation, we can see that the relationship between the control input u and the inward shift ratio D1 and the outward shift ratio D2 is as follows: ； The inner shift ratio D1 generated by the aforementioned return power optimization algorithm can be used to inversely solve for the outer shift ratio D2, which is used to adjust the output voltage of the DAB converter. Its expression is as follows: ； Substituting equation (27) into equation (22), we obtain the expression for the first derivative of the sliding variable s: ； To verify the stability of the designed super-helical sliding mode controller, stability analysis was performed on the system shown in the equation using Lyapunov functions. For ease of analysis, the equation was rewritten in the following form: ； Where c1=nU in α / 4Lf s C out c2=nU in η / 4Lf s C out ; Introducing a new state vector: ； but ； The derivative of z is: ； Define the Lyapunov function as: ； Where p is a symmetric positive definite matrix, and its α and η are positive numbers, defined as follows: ； Therefore, the Lyapunov function V(z) ≥ 0; Differentiating V(z) with respect to: ； Where matrix Q is: ； Therefore, if Q is a positive definite matrix, i.e. p(Q)>0, then the function V′(z)<0. According to Lyapunov's second law, equation (30) is asymptotically stable at this time. set up ； Then matrix Q can be simplified to a diagonal matrix: ； At this point, the eigenvalues ​​of matrix Q are: ； To guarantee that matrix Q is positive definite, we only need p1(Q) > 0, at which point we have: ； Let c1=nU in α / 4Lf s C out c2=nU in η / 4Lf s C out Substituting into equations (39) and (42) and simplifying, we obtain the following constraint condition for the positive definiteness of matrix Q: ； This condition serves as a constraint for selecting controller parameters.

2. The superspiral sliding mode control method combined with reflux power optimization according to claim 1, characterized in that: In the DAB extended phase-shift modulation analysis in step S111, T s For half a switching cycle of the switching transistor, D1 is the inward shift of the primary-side H-bridge, D2 is the outward shift between the primary-side H-bridge and the secondary-side H-bridge, and U... ab U cd These are the bridge arm voltages of the H-bridge on the primary and secondary sides, respectively.

3. The superspiral sliding mode control method combined with reflux power optimization according to claim 1, characterized in that: In the general form of the method for finding the extrema of a multivariate function whose variables are restricted by one or more constraints in step S22, F(X) is the objective function, g u (X) represents the equality constraints that need to be satisfied, h v (X) represents the inequality constraints that need to be satisfied.

4. The superspiral sliding mode control method combined with reflux power optimization according to claim 1, characterized in that: In step S22, the super-spiral sliding mode control incorporates the high-frequency switching term ηsgn(s) from the traditional sliding mode control into the integral operation. This means that the discontinuous high-frequency switching term no longer directly affects the control input u, making the control signal continuous and thus suppressing chattering.

5. The superspiral sliding mode control method combined with reflux power optimization according to claim 1, characterized in that: The super spiral algorithm in step S22 is a second-order sliding mode algorithm, which is suitable for systems with a relative order of 1. As can be seen from equation (22), the relative order of the system is 1. The super spiral algorithm can eliminate the discontinuities in the traditional SMC control by switching the control part.

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