Vibration Suppression of a High-Speed Macro-Micro Integrated System Using Computational Optimal Control

This article considers a dynamic modeling and computational optimal control for vibration suppression of a new high-speed macro-micro integrated system, which is mainly consisted of a macrostage and a pair of flexible microbeams (FMs). In this article, we model the FM motion by a partial differential equation (PDE) system and model the dynamics of the macro-micro integrated system based on the Hamilton's principle. Then, a computational optimal control problem for the vibration suppression of the FM is proposed. To solve this optimal control problem, we first use the assumed mode method to obtain an ordinary differential equation model based on the original microbeam PDE system. Some theoretical analysis is given to try to avoid spillover instability based on the assumed model using infinitely many modes and characteristics of a microbeam. Then, we apply the control parametrization approach to approximate the trajectory of the macrostage motion by piecewise-quintic functions and derive the gradient of the objective function with respect to the decision variables. Finally, we conclude this article with numerical simulations and experimental results to validate the effectiveness of the proposed dynamic model and computational optimization approach.