Design of Non-overshooting Fractional-Order PD and PID Controllers for Special Case of Fractional-Order Plants

This study focuses on shaping the transient response of special case of fractional-order systems by using fractional-order PD (FOPD) and fractional-order PID (FOPID) controllers. For a plant with a fractional-order pole, a FOPID controller is designed in which the orders of its derivative and integral terms are considered equal to the commensurate order of the plant while for an integrating plant with a fractional-order pole, a FOPD controller is designed. The region of controller parameters is extracted to obtain a closed-loop system with a monotonically decreasing magnitude–frequency response. This leads to a non-overshooting or low-overshoot step response. The gain crossover frequency and phase isodamping conditions are employed to select appropriate controller parameters among the mentioned region. The numerical examples are provided to show the efficiency of the proposed FOPD and FOPID controllers.