Nonlinear model predictive control of a flexible beam with multiple moving actuators

Precise motion of key optical payloads on flexible structures has wide application prospects in future space missions such as variable baseline earth observation. In this paper, a cantilever beam with multiple moving actuators is selected as the basic model, and a nonlinear model predictive control is designed to control the trajectory of the payload installed on one of the actuators and to achieve vibration suppression of the flexible structure. Firstly, the dynamic equation of the rigid-flexible coupling of the system is established based on the assumed modal method and the second order Lagrange equation. Then, a nonlinear model predictive controller is designed in which the performance index comprehensively coordinates the load trajectory tracking error, the vibration amplitude of the flexible beam and the smoothness of the payload motion trajectory. In particular, considering the high computational cost of the overall structural vibration suppression, an improved optimization strategy is proposed that focuses on the vibration damping of the structural segment covered by the expected load trajectory within the prediction step. Numerical simulation results verify the feasibility and effectiveness of the designed controller and control strategy. In addition, in order to analyze the appropriate number of actuators, this paper also compares the overall control effect of the system under the action of different numbers of actuators based on energy consumption.