Design of PIλ-PDμ controller for high-order systems based on model order reduction using BB-BC and time moment matching

Abstract

In this paper, a practical fractional proportional–integral and proportional–derivative (PIλ-PDμ) controller tuning method and a model reduction method are proposed for high-order systems with or without time delay. First, the Big Bang–Big Crunch (BB-BC) algorithm and the time moment matching method are used to reduce the order of the high-order system function, and the approximate low-order system function is obtained. Second, the parameter region of fractional-order PIλ-PDμ controller is obtained according to the D partition method, and the improved weighted geometric center (WGC) method is introduced to select the special points in the stable region as the control parameters. Then, the fractional-order PIλ controller is discretized by Muir method, and the fractional-order PDμ controller is discretized by continued fraction expansion (CFE). Finally, the BB-BC algorithm is used to optimize the control parameters, and the parameters with better control performance are obtained. The simulation results show that the fractional PIλ-PDμ parameter setting method based on BB-BC algorithm can improve the control performance of the system, and the model reduction scheme based on the combination of moment matching method and BB-BC algorithm is effective in both time domain and frequency domain analysis.