Fractional-order PID controller design for time-delay systems based on modified Bode’s ideal transfer function

This paper proposes a design method for a robust fractional-order PID (FOPID) controller for time-delay systems. A new Bode's ideal transfer function is introduced to tolerance the time-delay in loop. Robust stability is analyzed for the Bode's model in terms of gain and phase margins to help the parameter tuning. To simplify FOPID design from solving nonlinear equations, five unknown parameters are reduced to one in the Bode shaping by data fitting between a parametric model and the real plant. Then, the problem is simply solved by one-dimensional searching. Furthermore, the proposed FOPID controller design is extended to multi-input and multi-output (MIMO) systems by using disturbance observer (DOB). Finally, simulation results are presented to show the effectiveness of the proposed method.