Fractional order proportional derivative control for first order plus time delay plants: achieving phase and gain specifications simultaneously

The aim of the method in this paper is to achieve desired gain and phase specifications for robustness and performance of first order plus time delay plants. The previously proposed method "frequency frame", implemented for tuning fractional order proportional integral controllers, is applied on such plants controlled with a fractional order proportional derivative controller. Four specifications of gain and phase are considered in the Bode plot inspired from an ideal system. The frame is drawn enclosing the magnitude and phase curves limited by gain and phase crossover frequencies. Then, the size of the frame is tuned to provide loop-shaping of the curves to meet desired properties. The iso-damping property is achieved by shaping the phase curve. Similarly, numerous studies in the literature work on robustness achievement by loop shaping the phase curve of the Bode plot. However, the "frequency frame" approach is a new perspective in controller tuning. Two examples are illustratively given to prove the proposed method. Plants in the examples are also considered to be due to load disturbances. Simulation results and effects of the method are clearly explained.