Optimal robust fractional order PI^λD controller synthesis for first order plus time delay systems

In this paper, a practical and systematic tuning procedure combining both frequency-domain (FD) and time-domain (TD) specifications is proposed to obtain an optimal robust fractional order (FO) PI^λD (FOPI^λD) controller for the first order plus time delay (FOPTD) processes. The FD specifications (i.e. phase margin (PM), gain crossover frequency (ω_gc) and flat phase constrain (FPC)) guarantee the systemic stability and robustness to plant gain variations. Meanwhile, the TD specification (i.e. the smallest J_ITAE) achieves optimal dynamic performance. Furthermore, the entire feasible regions of two frequency-domain specifications ω_gc and PM have been obtained with a synthesis scheme and visualized in three-dimensional plots which can be used as prior knowledge before the controller design. The comparisons of feasible region with FOPI and integer order PID (IOPID) controllers clearly present the superiority of proposed FOPI^λD controller. Simulation illustration for delay dominant systems, lag dominant systems and high order system with one zero, using the proposed optimal robust FOPI^λD controller is presented to demonstrate the significant performance improvement over FOPI controller, three-parameter FOPID controller, Ziegler-Nichols FOPID controller, fractional filter-FOPID controller and SIMC-PI controller.