Vibration control of nonlinear rotating beam using piezoelectric actuator and sliding mode approach

In this research, we develop a general methodology for the vibration control of a nonlinear rotating beam. The dynamic model of a rotating Euler-Bernoulli beam integrated with a piezoelectric actuator is formulated. An integral sliding mode approach is proposed for the vibration control of the system with nonlinear coupling effect between the hub rotation and the beam transverse vibration. The vibration control is achieved by using the piezoelectric actuator only, whereas the motor torque is treated as a time-dependent external input. In the sliding mode control design, the sliding manifold is constructed using only the partial states of the system that are associated with the beam vibration. Particularly, utilizing the internal dynamics analysis, the nonlinear coupling effect of the rigid-body rotation and the beam transverse vibration is decoupled, and the robust stability of the system is guaranteed. This integral sliding mode control is continuous in nature, which can alleviate or avoid the chattering problem. A series of simulation studies demonstrate that the proposed control method can effectively suppress the beam vibration induced by the hub rotation and the external disturbance.