Stability Analysis And Parameter Design Of DC-DC Converter Based On Fractional Order PI~? Control

There are higher requirements for the performance of DC-DC converter systems,due to the wide application in high-precision fields such as industrial instruments,military,aerospace and so on.When the control method of the DC-DC converter is not reasonable,if it is subject to external interference(such as load parameter changes and DC input voltage fluctuations),it may cause the converter's output performance index to deteriorate.Compared with the integer order PID controller,the fractional order PI~?D~?controller greatly improves the dimension of parameter tuning,thus providing the possibility of obtaining better control performance.However,the complexity of the fractional order calculation greatly increases the difficulty of the theoretical analysis of the fractional order control system.In addition,the control parameter design method based on complex frequency domain indicators requires complex nonlinear equations to be solved,resulting in difficulties in engineering applications.In this paper,based on the fractional order PI~?control,the stability boundary trajectory theory is used to derive the analytical expression of the boundary of the stable region of the DC-DC converter system in the K_p-K_i plane.Then,the parameter design method of PI~?controller based on the expected closed-loop response and the parameter design method of optimal PI~?controller based on constraint of parameter stability field.Firstly,the closed-loop characteristic equation of the DC-DC converter based on PI~?control is derived.Then,the method of constructing real and complex root stable boundary is given,which is based on the theory of stable boundary trajectory,that is,using the mathematical relationship between the real root and complex root in the closed-loop characteristic root and the critical stable state of the system.Based on the above theory,the analytical expressions that can accurately describe these stable boundaries are derived.Then,taking Buck and Boost converters as examples,all the stable regions of K_p and K_i in the PI~?controller are obtained,and the accuracy of the obtained stable boundary is verified by simulation and experiment.According to the above analysis,the change rules of all stable regions on the K_p-K_i plane of the Buck converter and Boost converter system when?changes are obtained.Then,based on the theory of Taylor series expansion,a PI~?control parameter tuning method based on expected response is proposed.Taking the unit negative feedback system of Bode's ideal function as the desired closed loop system,which has the characteristic of Gain robustness.The parameter tuning steps and formulas of PI~?controller and PI controller are derived respectively.Finally,taking the Buck converter as an example,the effectiveness of the proposed parameter design method and the correctness of the derivation results are verified by simulation.From the simulation results,the parameters obtained by the proposed method make the system obtain the desired gain robust.Finally,combining the intelligent algorithm and the parameter stability domain solution method,the controller's parameter optimization range is constrained in the parameter stability domain,and the optimal PI~?controller parameters and PI control that satisfy the absolute error integral(ITAE index)in the stable region are obtained.Parameter.The performance of the closed-loop system of Buck converter under optimized order PI~?control and PI control is analyzed from the frequency domain.Further,a simulation and experiment platform were built to verify that the designed fractional-order PI~?controller made the Buck converter system better robustness.