Adaptive Sliding Mode Vibration Control of a Nonlinear Smart Beam: A Comparison with Self-Tuning Ziegler-Nichols PID Controller

Abstract

This paper investigates the vibration control of geometrically nonlinear beam with Macro Fiber Composite (MFC) actuators using two different adaptive control algorithms. A complete mathematical modeling is presented in order to find the dynamic equation of motion. Then, a robust adaptive fuzzy control algorithm for controlling the proposed mechanical structure is introduced. This controller includes a fuzzy scheme and a robust controller. Based on sliding mode controller a fuzzy system is introduced to mimic an ideal controller. The robust controller is designed based on compensation of the difference between the fuzzy controller and the ideal controller. The parameters of the fuzzy system and uncertainty bound of the robust controller are adjusted adaptively. The adaptive laws are designed based on the Lyapunov stability theorem to reach the stability of the closed-loop system. Meanwhile, for comparison purposes the presented controller is compared with self tuning Ziegler-Nichols PID controller for both robustness and vibration suppression performance aspects. Effectiveness of these two control strategies is evaluated by numerical simulations. Detailed analysis for the closed-loop system is carried out to evaluate the vibration controlling performance under different output excitation, robustness of the closed-loop system under sudden loading and the effect of initial condition on vibration characteristic.