Fractional-Order PI Control Method for Fractional-Order Dual Active Bridge Converter

Abstract

The present invention relates to a fractional-order PI control method for a fractional-order dual-active bridge converter, specifically, according to the system parameters of the fractional-order dual-active bridge converter, the fractional-order transfer function from control to output of the fractional-order dual-active bridge converter is calculated; according to the fractional-order transfer function, the open-loop transfer function of the fractional-order dual-active bridge converter control system is determined; according to the open-loop transfer function, the minimum objective function of the parameters to be optimized of the fractional-order PI controller is designed; according to the minimum objective function, the control parameters of the fractional-order PI controller are optimized using a genetic algorithm. The present invention guides the parameter design of the optimal fractional-order PI controller of the fractional-order dual-active bridge converter based on the fractional-order model of the dual-active bridge converter and the expected effect, so as to obtain the optimal performance of the system, so that the system has a faster response speed, a smaller overshoot, a stronger anti-disturbance ability, and better control quality.

Description

Technical Field

[0001] The invention relates to a control method of a dual active bridge converter, in particular to a fractional order PI control method of a fractional order dual active bridge converter. Background Art

[0002] The dual active bridge converter is widely used in various occasions such as electric vehicles, smart grids and energy storage systems due to its symmetrical structure, zero voltage switching capability and flexible control mode. At present, the optimization control of the dual active bridge converter is mainly in the two aspects of modulation mode and control mode. In terms of modulation mode, the mainstream methods include single phase shift modulation (SPS), double phase shift modulation (DPS) and triple phase shift modulation (TPS). By optimizing the modulation mode, the reactive power of the dual active bridge converter can be suppressed and the peak current can be reduced. In terms of closed-loop control, traditional PID control is mostly used. This control method has a simple structure, is easy to design, and does not require high accuracy of the system model. The existing dual active bridge converter based on integer order model adopts PID control.

[0003] In actual engineering applications, the PID controller's parameter adaptability is insufficient, and it is unable to accurately control the fractional-order dual active bridge converter, and it is unable to guarantee the stable operation of the system under various working conditions. In industrial applications, due to the lack of operator experience, there will be many situations where the control loop tuning effect is poor. In addition, various control methods based on integer-order models, especially when the inductor and capacitor orders are relatively low, the designed integer-order PID parameters have problems such as poor dynamic response, too long time to reach steady state, and even output voltage instability, which cannot solve the nonlinearity, parameter and structural uncertainty of the fractional-order controlled object. Therefore, the control method based on the integer-order model cannot be applied to the fractional-order model of the dual active bridge converter. Summary of the invention

[0004] The purpose of the present invention is to provide a fractional-order PI control method for a fractional-order dual active bridge converter to solve the problem that the control method based on integer-order model is not applicable to the fractional-order model.

[0005] Purpose of the present invention is achieved in that:

[0006] A fractional-order PI control method for a fractional-order dual active bridge converter comprises the following steps:

[0007] S1. According to the system parameters of the fractional-order dual active bridge converter, the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter is calculated. vd (s);

[0008] S2, the fractional order transfer function G obtained in step S1 vd (s), determine the open-loop transfer function G of the fractional-order dual active bridge converter control system o (s);

[0009] S3, according to the open-loop transfer function G of the fractional-order dual active bridge converter control system o (s), design the minimum objective function ITAE of the parameters to be optimized for the fractional-order PI controller;

[0010] S4, according to the minimum objective function ITAE of the controller parameters designed in step S3, the control parameter K of the fractional-order PI controller is optimized by using a genetic algorithm p ,K i , the value of λ.

[0011] Furthermore, the specific calculation method of step S1 of the present invention is:

[0012] S1-1 Determine the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter vd (s) is:

[0013]

[0014] Where s is the complex frequency in the Laplace transform, is the AC small signal complex function of the capacitor voltage, d(s) is the complex function of the shift phase d; and Δ(s) are respectively complex functions after Laplace transformation, and their calculation formula is:

[0015]

[0016]

[0017] Where R is the load impedance, C o is the output capacitor, α is the inductor order, β is the capacitor order, A 11 , A 12 、E 11 All are correlation coefficients; the calculation formulas of each correlation coefficient are expressed as follows:

[0018]

[0019]

[0020]

[0021] Among them, V i is the input voltage, V o is the output voltage, T is half cycle, L sis the inductance, D is the DC component of the shift ratio d, and n is the high-frequency transformer ratio.

[0022] S1-2 Substitute the system parameters into formula (1) to calculate the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter: vd (s).

[0023] Furthermore, the specific method of step S2 of the present invention is:

[0024] S2-1 Determine the transfer function G of the fractional-order PI controller of the dual active bridge converter c (s) is:

[0025]

[0026] Among them, K p is the proportionality coefficient, K i is the integration coefficient, and λ(0<λ<2) is the order of the integrator.

[0027] S2-2 Determine the open-loop transfer function G of the fractional-order dual active bridge converter control system o (s) is:

[0028] G o (s) = G vd (s)·G c (s) (8)

[0029] Furthermore, the specific method of step S3 of the present invention is:

[0030] S3-1 uses a genetic algorithm to globally optimize the parameters of the fractional-order PI controller. The optimization criterion of the minimum objective function ITAE of the genetic algorithm optimization parameters is:

[0031]

[0032] Wherein, t is the working time of the fractional-order dual active bridge converter, and e(t) is the system error of the fractional-order dual active bridge converter. S3-2 Determine the parameter optimization objective function J of the fractional-order PI controller as:

[0033]

[0034] Among them, ω1 and ω2 are control coefficients, and u(t) is the output of the fractional-order PI controller.

[0035] S3-3 uses a penalty function to avoid excessive overshoot of the fractional-order PI controller, and takes the overshoot as an item of the objective function. The parameter optimization objective function J1 of the fractional-order PI controller is:

[0036]

[0037] Among them, ω3 is the control coefficient and σ(t) is the system overshoot function.

[0038] The system error e(t), the output u(t) of the fractional-order PI controller and the system overshoot function σ(t) are calculated as follows:

[0039] e(t)=v ref (t)-v o (t) (12)

[0040]

[0041] σ(t)=v o (t)-v o (t-1) (14)

[0042] in, represents fractional integral, with the lower limit of the integral being 0 and the upper limit being t; v ref (t) is v ref (s) in time domain, v ref (s) System output voltage reference transfer function; v o (t) is v o (s) in time domain, v o (s) Output voltage transfer function.

[0043] S3-4 Optimizing the fractional-order PI controller parameter K using genetic algorithm p ,K i ,λ, when the minimum objective function ITAE of the genetic algorithm optimization parameters reaches the minimum value, the system obtains comprehensive control performance.

[0044] Furthermore, the specific method of step S4 of the present invention is:

[0045] S4-1 generates the initial population P(0); sets the parameter encoding method and the maximum evolutionary number G, and randomly generates M individuals according to the approximate range of each parameter. The individuals represent the initial values ​​of the parameters of the fractional-order PI controller;

[0046] S4-2 calculates the system error e(t) of the fractional-order dual active bridge converter control system under the step action and the output u(t) of the fractional-order PI controller according to the initial parameter values, selects formula (10) or formula (11) according to the overshoot value, and calculates the fitness function value Q of each individual;

[0047] S4-3 determines whether the algorithm termination condition is met according to the individual fitness function value Q; if the termination condition is met, exit, and the individual is used as the parameter of the fractional-order PI controller; if the termination condition is not met, execute S4-4;

[0048] S4-4 uses genetic algorithm to perform mutation, crossover and selection operations on population P(t) to generate the next generation population P(t+1);

[0049] S4-5 Repeat steps S4-3 and S4-4 until the parameters converge or reach the desired index. The output at this time is the optimized fractional-order PI controller parameter K p ,K i , the value of λ.

[0050] The present invention guides the parameter design of the fractional-order PI controller of the fractional-order dual active bridge converter based on the fractional-order model and expected effect of the dual active bridge converter, uses the DP method to determine the stability domain of the converter, and uses the ITAE criterion as the minimum objective function of the genetic algorithm optimization parameters according to the global optimization characteristics of the genetic algorithm to obtain the performance of the system. By adopting the control method of the fractional-order PI, the system can have a faster response speed, a smaller overshoot, a stronger anti-disturbance ability, and better control quality under the actual working environment or application requirements.

[0051] In the single phase shift control mode, the present invention controls the fractional order transfer function G to the output according to the fractional order model of the dual active bridge converter. vd (s). This is used to guide the design of the fractional-order controller of the dual active bridge converter; based on the obtained transfer function, the control system flow chart of the fractional-order PI controller is designed, the DP method is used to determine the stability region of the converter, the global optimization characteristics of the genetic algorithm are used, and the ITAE criterion is used as the minimum objective function of the genetic algorithm optimization parameters to obtain the control parameter K of the fractional-order PI controller. p ,K i ,λ, so that the system can obtain performance. By adopting the fractional-order PI controller designed for the fractional-order dual active bridge converter in the present invention, the system can achieve better control effect under various working environments or application requirements compared with the traditional PID controller. The overshoot is smaller, the rise time and response time are shorter, the anti-disturbance ability is stronger, and the control quality is better. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a topology of a fractional-order dual active bridge converter.

[0053] Figure 2 It is the structural block diagram of the feedback control system of the fractional-order dual active bridge converter.

[0054] Figure 3 It is a schematic diagram of genetic algorithm optimization of fractional-order PI controller.

[0055] Figure 4 It is a simulation model of fractional-order PI controller.

[0056] Figure 5 It is the system step response under traditional PID control and fractional-order PI control.

[0057] Figure 6 is the dynamic response of the system when the load is disturbed.

[0058] Figure 7 is the system transient response to input voltage disturbance. DETAILED DESCRIPTION

[0059] like Figure 1 As shown in the figure, the topology of the fractional-order dual active bridge converter includes a primary full bridge, a secondary full bridge, a transformer, a fractional-order inductor and a fractional-order capacitor. The system parameters of the fractional-order dual active bridge converter mainly include: the input voltage V i , output voltage V o , half cycle T, inductance L s , operating frequency f s , inductor order α, output capacitor C o , capacitor order β, input current I i , output current I o , shift ratio d, load impedance R and high-frequency transformer ratio n, etc.

[0060] The fractional-order PI control method of the dual active bridge converter fractional-order model of the present invention comprises the following steps:

[0061] Step S1: According to the system parameters of the fractional-order dual active bridge converter, the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter is calculated. vd (s), the specific method is:

[0062] S1-1 Determine the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter vd (s) is:

[0063]

[0064] Where s is the complex frequency in the Laplace transform, is the AC small signal complex function of the capacitor voltage, d(s) is the complex function of the shift phase d; and Δ(s) are respectively complex functions after Laplace transformation, and their calculation formula is:

[0065]

[0066]

[0067] Where R is the load impedance, C o is the output capacitor, α is the inductor order, β is the capacitor order, A 11 , A 12 、E 11 All are correlation coefficients; the calculation formulas of each correlation coefficient are expressed as follows:

[0068]

[0069]

[0070]

[0071] Among them, V i is the input voltage, V o is the output voltage, T is half cycle, L s is the inductance, D is the DC component of the shift ratio d, and n is the high-frequency transformer ratio.

[0072] S1-2 Substituting the system parameters into formula (1), the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter can be calculated. vd (s).

[0073] Step S2: Based on the fractional order transfer function G obtained in step S1 vd (s), with the goal of small steady-state output error, fast dynamic response and small overshoot of the dual active bridge converter, the fractional-order PI controller is designed, that is, the open-loop transfer function G of the fractional-order dual active bridge converter control system is determined. o (s), the specific method is:

[0074] In order to improve the output voltage V o accuracy and increase the output voltage V o Stability, a fractional-order PI feedback control method is designed to improve the steady-state accuracy and dynamic performance of the dual active bridge converter. Figure 2 As shown in the figure, the structure of the fractional-order PI control system of the fractional-order dual active bridge converter is: the system output voltage reference transfer function v ref (s) and output voltage transfer function v o (s) is compared to obtain the system error transfer function e(s), and the fractional-order PI controller transfer function G c (s) to obtain the control quantity u(s), and the fractional-order transfer function G from control to output acting on the fractional-order dual active bridge converter is vd(s) Finally, the output voltage v of the fractional-order dual active bridge converter is controlled o (s) Maintain stable output.

[0075] Among them, G c (s) is the transfer function of the fractional-order PI controller of the dual active bridge converter, G vd (s) is the fractional-order transfer function from control to output of the dual active bridge converter, v ref (s) is the reference output voltage transfer function, e(s) is the error signal transfer function, d(s) is the phase shift transfer function, V o (s) is the transfer function of the output voltage.

[0076] The design process of the control link is as follows: The actual output voltage V o (s) and the reference output voltage v ref (s) is compared to get the error signal e(s), which is then passed through the fractional-order PI controller G c (s) to obtain the control quantity d(s), and finally control the actual output voltage V of the dual active bridge converter o (s) Remain stable.

[0077] in:

[0078]

[0079] Among them, K p is the proportionality coefficient, K i is the integral coefficient, and λ(0<λ<2) is the order of the integrator. Figure 2 It can be seen that applying the fractional-order PI controller G c (s), the open-loop transfer function G of the fractional-order dual active bridge converter control system is o (s) is:

[0080] G o (s) = G vd (s)·G c (s) (8)

[0081] Step S3: According to the open-loop transfer function G of the fractional-order dual active bridge converter control system o (s), design the minimum objective function ITAE of the fractional-order PI controller to be optimized, such as Figure 3 As shown, the specific method is:

[0082] S3-1 by G o From the open-loop transfer function expression (8) of (s), it can be seen that the performance of the fractional-order dual active bridge converter control system is related to the parameter K of the fractional-order PI controller. p ,K i,λ is related to the size. Considering the nonlinearity and complexity of the fractional-order PI controller and the fractional-order dual active bridge converter, a genetic algorithm is used to globally optimize the parameters of the fractional-order PI controller. At the same time, the minimum objective function ITAE of the genetic algorithm optimization parameters is multiplied by the absolute value of the error:

[0083]

[0084] Wherein, t is the working time of the fractional-order dual active bridge converter, and e(t) is the system error of the fractional-order dual active bridge converter.

[0085] S3-2 considers preventing the controller output control quantity u(t) from being too large, and the corresponding parameter optimization objective function J of the fractional-order PI controller is:

[0086]

[0087] Among them, ω1 and ω2 are control coefficients, and u(t) is the output of the fractional-order PI controller.

[0088] In order to avoid excessive overshoot, S3-3 adopts a penalty function, that is, once the overshoot exceeds a certain limit, the overshoot is used as an item of the objective function. The corresponding controller parameter optimization objective function J1 is:

[0089]

[0090] Among them, ω3 is the control coefficient and σ(t) is the system overshoot function.

[0091] The calculation method of the system error e(t), the output u(t) of the fractional-order PI controller and the system overshoot function σ(t) is:

[0092] e(t)=v ref (t)-v o (t) (12)

[0093]

[0094] σ(t)=v o (t)-v o (t-1) (14)

[0095] in, represents fractional integral, with the lower limit of the integral being 0 and the upper limit being t; v ref (t) is v ref (s) in time domain, v ref (s) System output voltage reference transfer function; v o (t) is v o (s) in time domain, vo (s) Output voltage transfer function.

[0096] S3-4 Optimizing fractional-order PI using genetic algorithm λ Controller parameter K p ,K i ,λ, when the minimum objective function ITAE of the genetic algorithm optimization parameters reaches the minimum value, the system obtains comprehensive control performance.

[0097] Step S4: According to the minimum objective function ITAE of the controller parameters designed in step S3, the control parameter K of the fractional-order PI controller is optimized using a genetic algorithm p ,K i ,λ value, such as Figure 5 As shown, the specific method is:

[0098] S4-1 generates the initial population P(0). Set the parameter encoding method and the maximum evolutionary generation G, and randomly generate M individuals according to the approximate range of each parameter. The individuals represent the initial values ​​of the parameters of the fractional-order PI controller.

[0099] S4-2 calculates the system error e(t) and the fractional-order PI controller output u(t) of the fractional-order dual active bridge converter control system under step action according to the individual initial values, and selects formula (10) or formula (11) according to the size of the overshoot to calculate the fitness function value Q of each individual.

[0100] S4-3 determines whether the algorithm termination condition is met according to the individual fitness function value Q. If the termination condition is met, exit, at this time, the individual is the parameter, and the system comprehensively controls the performance; if the termination condition is not met, go to S4-4.

[0101] The S4-4 genetic algorithm performs mutation, crossover, and selection operations on the population P(t) to generate the next generation population P(t+1).

[0102] S4-5 repeats S4-3 and S4-4 until the parameters converge or reach the desired index, then output K p ,K i , the value of λ.

[0103] In order to verify the fractional-order PI control method proposed by the present invention for the fractional-order dual active bridge converter, a simulation model is built through the MATLAB / Simulink simulation platform, experimental verification is carried out, and a comparative experiment is carried out with the traditional PID controller. The design parameters of the dual active bridge converter are shown in Table 1.

[0104] Table 1: Dual active bridge converter simulation parameters

[0105]

[0106] The inductor model is CS270075, the order of which is α=0.91. The capacitor model is A700V156M01 6ATE040, the order of which is β=0.83, ω1=0.1, ω2=0.001, ω3=10.

[0107] exist Figure 4 Under the simulation model of the fractional-order PI controller shown in FIG. 1 and the simulation parameters of the dual active bridge converter shown in Table 1, the parameter K of the fractional-order PI controller designed for the fractional-order dual active bridge converter proposed in the present invention is p =0.003016,K i =19.92,λ=0.821. To compare the control effect of the fractional-order PI controller for the fractional-order dual active bridge converter proposed in the present invention with the existing traditional PID, under the same optimization simulation conditions, the traditional PID parameters are: K p =0.00666,K i =5.2326. The ITAE performance index value under the fractional-order PI control of the present invention is 0.00575, and the ITAE performance index value under the integer-order PI control is 0.02453. Since the ITAE index is a comprehensive index that takes into account the dynamic performance and steady-state performance of the control system, and the smaller the index is, the better the performance of the system such as response speed and steady-state accuracy is. It can be seen that compared with the traditional PID control, the ITAE value of the system under fractional-order PI control is better.

[0108] Depend on Figure 6 The control system state response of the fractional-order dual active bridge converter of the fractional-order PI controller and the traditional PID control is shown. It can be seen that the rise time and adjustment time of the system using the fractional-order PI controller are significantly smaller than the traditional PID control, the overshoot is within 5%, and the steady-state error is within 0.3%. For the traditional PID control, although the system has no overshoot, the system dynamic response is relatively slow, there is oscillation, and the system steady-state error is large. The fractional-order PI control effect is better than the traditional PID control due to the fact that the fractional-order PID controller has an additional fractional-order calculus parameter λ that can be precisely adjusted.

[0109] Depend on Figure 5 The step response of the system shown shows that the load is reduced in 0.02s when the system is in a stable state.

[0110] from Figure 7The transient response of the system to the input voltage disturbance shown in the figure shows that, in the startup phase, the fractional-order PI control enters the steady state faster than the traditional PID control. When external disturbances occur, the dual active bridge converter under the fractional-order PI control has stronger robustness. At the moment of load mutation, the output voltage of the fractional-order control system quickly recovers stability after several extremely small amplitude oscillations, that is, the dynamic drop and recovery time of the system are relatively small, and the system has strong anti-load disturbance capability.

[0111] The steady-state process of the fractional-order dual active bridge converter control system under fractional-order PI control is shown in Figure 2. A step disturbance (disturbance voltage v i =1800V), the system dynamic response process is as follows Figure 7 As shown. Figure 7 It can be seen that when the input voltage fluctuates, the system dynamic drop is very small and the output voltage v o Maintaining the set voltage at 750V, the system has a good suppression effect on input voltage disturbances.

[0112] According to the aforementioned parameter design principle of the fractional-order dual active bridge converter feedback control system, when the reference voltage v ref =750V, the system outputs 750V stably. Under this condition, the given voltage (v ref =800V), the corresponding expected output voltage is v o =800V, the transient response of the system is as follows Figure 7 As shown. Figure 7 It can be seen that the error between the output voltage and the expected output voltage of the fractional-order control system is within 0.3% when the voltage is stable during a given voltage mutation process. Secondly, the system output has a certain overshoot (within 5%) at the moment of mutation, the adjustment time is relatively small, and the system has good fast following performance.

[0113] From the above analysis and simulation, it can be seen that among the control parameters optimized by ITAE, the fractional-order dual active bridge converter has a faster response speed under fractional-order PI control and is more robust against load and input voltage disturbances.

Claims

1. A fractional-order PI control method for a fractional-order dual active bridge converter, characterized in that: The following steps are involved: S1. According to the system parameters of the fractional-order dual active bridge converter, the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter is calculated. vd (s); S2, the fractional order transfer function G obtained in step S1 vd (s), determine the open-loop transfer function G of the fractional-order dual active bridge converter control system o (s); S3, according to the open-loop transfer function G of the fractional-order dual active bridge converter control system o (s), design the minimum objective function ITAE of the parameters to be optimized for the fractional-order PI controller; S4, according to the minimum objective function ITAE of the controller parameters designed in step S3, the control parameter K of the fractional-order PI controller is optimized by using a genetic algorithm p ,K i , the value of λ; The specific calculation method of step S1 is: S1-1 Determine the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter vd (s) is: Where s is the complex frequency in the Laplace transform, is the small AC signal complex function of the capacitor voltage, d(s) is the complex function of the shift phase d; and △(s) are respectively complex functions after Laplace transformation, and their calculation formula is: Where R is the load impedance, C o is the output capacitor, α is the inductor order, β is the capacitor order, A 11 , A 12 、E 11 All are correlation coefficients; the calculation formulas of each correlation coefficient are expressed as follows: Among them, V i is the input voltage, V o is the output voltage, T is half cycle, L s is the inductance, D is the DC component of the shift ratio d, and n is the high-frequency transformer ratio; S1-2 Substitute the system parameters into formula (1) to calculate the fractional-order transfer function G from control to output of the fractional-order dual active bridge converter: vd (s); The specific method of step S2 is: S2-1 Determine the transfer function G of the fractional-order PI controller of the dual active bridge converter c (s) is: Among them, K p is the proportionality coefficient, K i is the integration coefficient, λ is the order of the integrator, 0<λ<2; S2-2 Determine the open-loop transfer function G of the fractional-order dual active bridge converter control system o (s) is: G o (s)=G vd (s)·G c (s) (8)。 2. The fractional-order PI control method of the fractional-order dual active bridge converter according to claim 1, characterized in that: The specific method of step S3 is: S3-1 uses a genetic algorithm to globally optimize the parameters of the fractional-order PI controller. The optimization criterion of the minimum objective function ITAE of the genetic algorithm optimization parameters is: Wherein, t is the working time of the fractional-order dual active bridge converter, and e(t) is the system error of the dual active bridge converter; S3-2 determines the parameter optimization objective function J of the fractional-order PI controller as: Among them, ω1 and ω2 are control coefficients, and u(t) is the output of the fractional-order PI controller; S3-3 uses a penalty function to avoid excessive overshoot of the fractional-order PI controller, and takes the overshoot as an item of the objective function. The parameter optimization objective function J1 of the fractional-order PI controller is: Among them, ω3 is the control coefficient, σ(t) is the system overshoot function; The calculation method of the system error e(t), the output u(t) of the fractional-order PI controller and the system overshoot function σ(t) is: e(t)=v ref (t)-v o (t) (12) σ(t)=v o (t)-v o (t-1) (14) in, represents fractional integral, with the lower limit of the integral being 0 and the upper limit being t; v ref (t) is v ref (s) in time domain, v ref (s) System output voltage reference transfer function; v o (t) is v o (s) in time domain, v o (s) Output voltage transfer function; S3-4 Optimize the fractional-order PI controller parameter K using genetic algorithm p ,K i ,λ, when the minimum objective function ITAE of the genetic algorithm optimization parameters reaches the minimum value, the system obtains comprehensive control performance.

3. The fractional-order PI control method of the fractional-order dual active bridge converter according to claim 2, characterized in that: Step S4 The specific method is: S4-1 generates the initial population P(0); sets the parameter encoding method and the maximum evolutionary number G, and randomly generates M individuals according to the approximate range of each parameter. The individuals represent the initial values ​​of the parameters of the fractional-order PI controller; S4-2 calculates the system error e(t) of the fractional-order dual active bridge converter control system under the step action and the output u(t) of the fractional-order PI controller according to the initial parameter values, selects formula (10) or formula (11) according to the overshoot amount, and calculates the fitness function Q of each individual; S4-3 determines whether the algorithm termination condition is met according to the individual fitness function value Q; If the termination condition is met, the system exits, and the individual is used as the parameter of the fractional-order PI controller. If the termination condition is not met, execute S4-4; S4-4 uses genetic algorithm to perform mutation, crossover and selection operations on population P(t) to generate the next generation population P(t+1); S4-5 Repeat steps S4-3 and S4-4 until the parameters converge or reach the desired index. The output at this time is the optimized fractional-order PI controller parameter K p ,K i , the value of λ.

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