Optimal and robust PI λ D μ tuning strategy for fractional order time delay processes satisfying robust gain margin, phase margin, and gain crossover frequency constraints

The paper develops an optimal and robust fractional order PID (ORFOPID) controller tuning strategy applicable to fractional order time delay (FOTD) processes, based on pre-designated gain margin (GM), phase margin (PM), and gain crossover frequency (GCF) constraints. This strategy is applicable to general FOTD systems without requiring model reduction or time delay approximation. The GM and PM tester (GPMT) method is exploited to impose preassigned safety margin constraints on the considered FOTD systems. The stability equation method validates the stability condition and constructs GM-related, PM-related, and GCFrelated boundaries. These boundaries are then used to graphically determine the feasible stable area (FSA) and the GPM specifications-oriented region (GPMSOR), encompassing all feasible RFOPID controllers. The λ and μ of the FOPID controller are adjusted to expand the FSA and GPMSOR, thereby providing a broader selection of RFOPID controllers. Searching within the GPMSOR identifies the ORFOPID controller that minimizes the IAE or ISE. Knowing the search range reduces the time to find the ORFOPID controller. This controller robustly stabilizes the considered FOTD processes, satisfying the prescribed constraints and improves the tracking and disturbance rejection responses. The design strategy is detailed in a design flowchart. Simulation studies validate the effectiveness of the proposed strategy.