Fractional-order time-delay systems boast better dynamic performance than integer-order ones in optimally controlling industrial design objects. However, in lack of commendable methodologies, designing proper controllers for these systems confronts a plurality of challenges. This study puts forth an innovative design approach that merges frequency-domain analysis with time-domain optimization concepts, so that fractional-order Tilt-Integral-Derivative (TID) controllers can be acquired. To pursue a stable control system loop, the tilted and integral gains of fractional-order TID controllers are identified as per frequency-domain specifications, including gain crossover frequency and phase margin. In light of these specifications (e.g., the integral of time-weighted absolute error (ITAE)), the differential gain and fractional-order operator λ of the controller are determined, which accomplishes a desirable dynamic performance in the time domain. This article expounds on the procedure of how to develop the proposed fractional-order TID controller and furnishes illustrative examples for the research steps. As manifested by the simulation results, the proposed controller dramatically upgrades the control performance of the system in contrast to conventional PID, FOPI, and FOPID controllers. Moreover, it outperforms PID and fuzzy PID in terms of responding to the demand variations in step signals.
Zhang et al. (Sat,) studied this question.