Abstract
Although the active disturbance rejection controller can obtain good control performance without relying on specific model information, it targets integer-order systems. Fractional-order characteristics are commonly existed in practical systems. For fractional-order systems, it is more targeted to use the order information of the fractional-order model to design the active disturbance rejection controller, so as to obtain better control performance. A fractional active disturbance rejection controller composed of FOESO and FOPID (IDE-FOPID-FOESO) is proposed in this paper. The fractional-order extended state observer (FOESO) is designed based on the order information and the nonlinear state error feedback is replaced by the fractional-order PID controller (FOPID) whose parameters are obtained by the improved differential evolution algorithm (IDE). For IDE algorithm, the basis vector is randomly selected from the optimal individual population in the mutation strategy, and the scaling factor and cross-probability factor are adaptively adjusted according to the information of the successfully mutated individual in the search process to improve the exploration and mining capabilities of the algorithm. The simulation results show that the IDE algorithm can obtain the better parameters of FOPID faster compared with traditional DE algorithm and the IDE-FOPID-FOESO controller can be better applied to fractional-order systems with better control performance.
A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel
