Fractional-order system identification based on an improved differential evolution algorithm

With the continuous increasing of system modeling accuracy and control performance requirements, the fractional-order models are applied to describe the dynamic characteristics of the real systems more accurately over traditional integer-order models. Traditional identification algorithms for fractional-order system require stringent information on the derivatives of the objective function and initial values of the parameters, which is difficult in practical applications. The differential evolution (DE) algorithm has the advantage of simple implementation and superior performance for solving multi-dimensional complex optimization problems which is suitable for the identification of fractional-order systems. Aiming at improving the solution accuracy and convergence speed, an improved DE (IDE) algorithm for fractional-order system identification is proposed. The movement strategy of the marine predator algorithm (MPA) and the mutation strategy of randomly selecting one from the optimal individual population as the basis vector are both adopted in this proposed IDE algorithm. The parameter information of the successfully mutated individual is archived during the iteration process. The scaling factor and crossover probability factor are adaptively adjusted according to the archived information to enhance the best solution accuracy obtained in the search process. By testing 13 sets of unimodal and multimodal functions with high-performance optimization algorithms, the accuracy performance of the proposed IDE solution is verified. The IDE algorithm is applied to identify the parameters of the fractional-order system of permanent magnet synchronous motor with simulation and experiment. The identification results clearly show the effectiveness of the proposed methodology.