Quasi-time-optimal controller design for a rigid-flexible multibody system via absolute coordinate-based formulation

Previous studies have shown that the absolute coordinate-based formulation is an accurate modeling approach for the rigid-flexible multibody system subject to both large rotation and large deformation. However, it is almost impossible to design the complex controller for a rigid-flexible multibody system via the absolute coordinate-based formulation because of its high dimensions. The primary aim of this study is to design a quasi-optimal controller for a rigid-flexible multibody system via the absolute coordinate-based formulation. The design procedure includes two steps. As the first step, the simplified model for a rigid-flexible multibody system is established via the floating frame of reference formulation first, and then, a time-optimal controller is designed for the simplified model by using the Gauss pseudo-spectral method. In the second step, a quasi-time-optimal closed-loop tracking controller is achieved for the absolute coordinate-based formulation of the rigid-flexible multibody system by superposing a PD controller to track the pre-designed optimal trajectory. The paper presents two case studies for a hub-beam system, where only the motion of the rigid part is observable and driven. The numerical results of the two case studies well verify the effectiveness of the proposed controller.