A new approach to optimal design of digital fractional-order PI-λ D-μcontroller

Fractional-order (PID mu)-D-lambda controller has been under intensive investigations for better control performance in recent years. To facilitate the implementation of digital controller, the (PID mu)-D-lambda controller is usually firstly optimally designed in continuous domain, and then discretized to obtain a digital (PID mu)-D-lambda controller. However, the aforementioned methodology may lead to performance deterioration and other undesirable results. To tackle the issues identified above, a new approach is proposed to directly design the optimal digital (PID mu)-D-lambda controller, which is formulated to be a controller optimization problem with six tunable parameters by using the parameterized Al-Alaoui operator for discretization. To optimize the digital (PID mu)-D-lambda controller, an improved PSO-SADV algorithm with switching adaptive delayed velocities has been developed to deal with some frequently encountered obstacle phenomena in the optimization problem, and the superiorities of the PSO-SADV are verified by several comparative simulation experiments. Finally, the PSO-SADV is employed to handle the parameter optimization issue of the digital (PID mu)-D-lambda controller based on the ITSE index of step response. Several illustrative simulation experiments are carried out upon some typical controlled objects for the comparison with the (PID mu)-D-lambda controller and its discretizations, and the effectiveness and superiority of the new approach can be confirmed by the simulation results. (C) 2019 Elsevier B.V. All rights reserved.