(untitled) (Advances in Applied Mathematics and Mechanics, 2020)
Lightweight and flexible structures are often used in the engineering field which may produce the long time residual vibration of flexible appendages. In order to reduce the residual vibration of the flexible manipulator, a control method of combining the multi-impulse robust shaper with the linear quadratic regulator controller is put forward in this paper. The Lagrange equation and assumed mode method are used to obtain the dynamic equation of the manipulator. Then the dynamic equation is rewritten in state space, and the state equation of the closed-loop system is obtained after the optimal control is used. The multi-impulse robust shaper is designed according to the system frequency and damping ratio and is used to shape the required angle. The input torque is obtained by the linear quadratic regulator controller. The proposed combination controller is compared with the combination controller of ZVD shaper and the optimal control method, the combination controller of the EI shaper and the optimal control method, and optimal controller. The robustness of the proposed controller is then investigated. The simulation results show that the proposed combination controller has a better advantage in suppressing residual vibration than other controllers and has a good performance in the robustness of natural frequency.