Optimal Fractional Order Proportional Integral Controller for Varying Time-Delay Systems

In many industrial processes, the first order plus time delay (FOPDT) is still being widely used. FOPDT systems are also called “KLT systems (gain, delay, and time constant).” Considering uncertainties in the time delay, this paper attempts to answer this research question: “Will a fractional order controller help and do better?” In this paper, we first focus on fractional order proportional and integral controller (FOPI) for varying time-delay systems. Based on our previously proposed FOPI controller tuning rules using fractional Ms constrained integral gain optimization (F-MIGO), we tried to simultaneously maximize the jitter margin and ITAE performance (minimize ITAE performance index) for a set of hundred KLT systems having different time-constants and time-delay values. We observed that the optimization results in enlarged jitter margin of all systems at expense of a slight decrease in ITAE performance of delay dominated systems. Further, the F-MIGO optimization based tuning rules were summarized by approximation of optimized gain parameters and fractional orders α of the FOPI controller. Simulation results are presented to verify the proposed new tuning rules for best jitter margin and ITAE performance.