Dynamic Analysis and Fuzzy Fixed-Time Optimal Synchronization Control of Unidirectionally Coupled FO Permanent Magnet Synchronous Generator System

This article focuses on dynamic analysis and the fuzzy fixed-time optimal synchronization control problem of unidirectionally coupled fractional-order (FO) permanent magnet synchronous generator (PMSG) system. The synchronization model between FO master and slave PMSGs with capacitive and resistive couplings is built. The dynamic analysis fully reveals its abundant dynamical behaviors including chaotic oscillations and gives stability/instability boundaries with the designed numerical method. In controller design, the hierarchical type-2 fuzzy neural network (HT2FNN) with a transformation is designed to approximate unknown functions, the fixed-time command filter matched up with the compensating signal is proposed to achieve precise estimate and fast convergence, and a fixed-time preconfigured performance function integrated with a smooth and invertible function is built to realize fixed-time convergence and performance constraint. Then a fuzzy fixed-time optimal synchronization control scheme fusing with the HT2FNN, filter, performance function and optimal control is developed under the FO backstepping theory. The stability analysis proves that all signals of the closed-loop system are bounded along with the cost function being minimized. Finally, numerical simulation results verify the feasibility and advantages of our scheme.