Tracking control of moving flexible system by incorporation of feedback-based vibrational energy sink in model predictive control algorithm

This paper proposes a new approach towards the nonlinear problem of tracking control for mobile multivariable vibrational structure featuring an Euler-Bernoulli vibrational beam. The control scheme involves obtaining interactions between flexural and rigid motions of the multivariable continuum mechanics system with actuator force limitation both regarding domain and frequency bandwidth. To this end, the boundary control inputs are selected prioritizing two tasks, satisfying actuator limitations and obtaining minimum possible tracking error. The former is employed as hard constraint in model predictive control (MPC) scheme while the latter is considered as soft constraint. The control scheme is adjusted such that when actuator limits are exceeded, the soft constraints are relaxed to maintain stability. In order to provide smooth tracking, Euler-Bernoulli transverse vibration is attenuated by incorporating Feedback Vibrational Energy Sink (FVES) method in obtaining control law. Hence, actuators are manipulated such that total vibrational energy of flexible beam is damped without using passive or conventional active dampers. The accuracy of the proposed method has been verified via FEA-based simulations.