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Fuzzy logic based PID controllers have been studied in this paper,considering several combinations of hybrid controllers by grouping theproportional, integral and derivative actions with fuzzy inferencing indifferent forms. Fractional order (FO) rate of error signal and FO integral ofcontrol signal have been used in the design of a family of decomposed hybrid FOfuzzy PID controllers. The input and output scaling factors (SF) along with theintegro-differential operators are tuned with real coded genetic algorithm (GA)to produce optimum closed loop performance by simultaneous consideration of thecontrol loop error index and the control signal. Three different classes offractional order oscillatory processes with various levels of relativedominance between time constant and time delay have been used to test thecomparative merits of the proposed family of hybrid fractional order fuzzy PIDcontrollers. Performance comparison of the different FO fuzzy PID controllerstructures has been done in terms of optimal set-point tracking, loaddisturbance rejection and minimal variation of manipulated variable or smalleractuator requirement etc. In addition, multi-objective Non-dominated SortingGenetic Algorithm (NSGA-II) has been used to study the Pareto optimaltrade-offs between the set point tracking and control signal, and the set pointtracking and load disturbance performance for each of the controller structureto handle the three different types of processes.

Performance Comparison of Optimal Fractional Order Hybrid Fuzzy PID Controllers for Handling Oscillatory Fractional Order Processes with Dead Time