A Hybrid Fuzzy Fractional Order PID Sliding-Mode Controller design using PSO algorithm for interconnected Nonlinear Systems

The aim of this paper is to develop a hybrid fuzzy fractional order sliding mode controller (FFOSMC) for a class of interconnected nonlinear systems. Firstly a PI^{alpha}D^{alpha} sliding surface is proposed, on which the control law is designed. Mathematical proof for the stability condition and convergence of the system is presented, taking into account the theory of the fractional order calculus. In order to reduce the chattering phenomenon in sliding mode control (SMC), a Takagi-Sugeno fuzzy logic controller is used to replace the discontinuity in the signum function, and to ensure optimal performance in the closed loop system, the PSO algorithm is used. Finally the e?ectiveness of the proposed approach of FFOSMC-based PSO algorithm compared with the FFOSMC using PD^{alpha} sliding surface and FSMC using the conventional PID sliding surface is demonstrated by simulation results for a coupled double pendulum system.

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