Robust fractional order PID controller synthesis for the first order plus integral system

The fractional order PID (FOPID) controller has been found to have the potential to provide more flexibility in the design options than the integer order PID (IOPID) controller. However, in the FOPID controller design practice, investigations are still required in selecting the achievable design specifications and controller parameters. In order to obtain a practical tuning method for the FOPID controller, taking the first order plus integral systems as the plants, the complete achievable regions of the design specifications are collected and analyzed. In addition, the selectable integral and derivative orders of the FOPID controller are also collected and modeled. With the prior knowledge obtained, a synthesis method for the FOPID controller is proposed to make the control system achieve the desired flat-phase characteristic. To verify the effectiveness of the proposed method, the synthesis method is applied to design the FOPID controller for the permanent magnet synchronous motor (PMSM) speed servo system. Simulation and experimental results show that system with the FOPID controller can achieve satisfying tracking performance and disturbance rejection performance.