Dual Time-Scale Control of Flexible Manipulator Based on Double-Power Sliding Mode and LQR

Trajectory tracking and vibration suppression of flexible manipulators are addressed in this paper. A control method combining double-power sliding mode and linear quadratic regulation is proposed. Firstly, the hypothetical modal method is used to describe the vibration mode of the flexible manipulator, and then the Lagrange dynamic equation is used to establish the dynamic model. The singular perturbation method is applied to reduce the order of the system model, and a dual time-scale model is obtained. For the slower part of the dynamics, the double-power sliding mode control is utilized for trajectory tracking and for the fast part of dynamics an optimal controller is designed for vibration suppression. The dual time-scale combination controller for the flexible manipulator is constructed. Feasibility and effectiveness of the combination control is verified by MATLAB/Simulink simulation.