Self-regulatory Fractional Fuzzy Control for Dynamic Systems: An Analytical Approach

This paper presents an analytical design of a fractional order fuzzy proportional integral plus derivative (FOFPI + D) controller. Artificial intelligence is incorporated into the controller with the help of a formula-based fuzzy logic system. The designed scheme combines fractional order fuzzy PI (FOFPI) and fractional order fuzzy D (FOFD) controller, derived from fundamental FOPID control law. The proposed scheme enjoys the linear structure of the FOPID controllers with non-linear gains that provide self-tuning control capability. The sufficient condition for stability of the closed-loop system is also established using the graphical approach. Performance of the proposed FOFPI + D, its integer order variant (FPI + D), and conventional controllers is examined for control of a highly non-linear and uncertain two-link robotic manipulator system. The optimum parameters of controllers are found by minimising aggregated control variation and error objective through non-dominated sorting genetic algorithm-II (NSGA-II). The comparison for trajectory tracking shows that FOFPI + D has the minimum integral absolute error (IAE) compared to other controllers. Further, rigorous performance investigations are performed to verify the robustness of designed controllers against parametric uncertainties, the varying boundary conditions of reference trajectory and disturbance rejection. It is concluded from the results that the proposed FOFPI + D controller exhibits superior performance.