Synchronization of Chaotic Gyros with Uncertainty and External Disturbance by Fuzzy PI Sliding Mode Control

In this paper, an approach for synchronization chaotic gyros proposed using fuzzy sliding mode control. The proposed method will be investigated in the presence of trigonometric function uncertainty and trigonometric function external disturbance in the dynamic equations of the gyroscope. Proportional-Integral (PI) sliding mode technique can reduce the controller steady state error. In the fuzzy design, a low number of membership functions are selected, which will help speed up the performance of the processors. By combining proportional-integral sliding mode and fuzzy logic, the final controller is designed. It is proved that the derived robust controller based on Lyapunov stability theory can guarantee that all states of the closed-loop system are globally uniformly ultimately bounded, and lead the system tracking error to zero. In numerical simulation, the controller signal is depicted. It shows that the proposed method can be built and implemented in the real world, because it has low amplitude and oscillations. Finally, simulation results are provided to show the effectiveness of the proposed approach.