Direct synthesis approach to design fractional PID controller for SISO and MIMO systems based on Smith predictor structure applied for time-delay non integer-order models

Our work on this paper aims on developing the strategies of fractional order controller (FOC) design based on use time-domain specifications (Percentage of overshoot (PO) and Settling time (ts)) to control non integer-order models with plus time delay (NIOPTD or fractional order models). Considering a fractional Smith predictor structure, a efficient and simple analytical strategy to tuning a FOC for fractional models is suggested. The design strategy is based on desired time-domain specifications (PO and ts). To achieve these requirements, many tuning analytical formulas are derived using on Bode’s ideal closed-loop transfer function. The resulting new controller can be decomposed into fractional order PID controller cascaded with a fractional order filter. The parameters of the FOPID controller are directly obtained by using the parameters of the fractional order models and the fractional-order filter parameters are easily obtained Using formulas of time-domain specifications (PO and ts). After a successful implementation of the proposed fractional controller on single-input-single-output (SISO) process, it is implemented on the complex system (multi-input multi-output (MIMO) system). Where the simulation results show that the suggested strategy of fractional Smith predictor improves the closed-loop control system compared to other controllers.