End-point control of a flexible-link manipulator using state-dependent Riccati equation technique

The problem of modeling and controlling the tip position of a one-link flexible manipulator is considered. The paper discusses the control strategy based on the nonlinear state Dependent Ricatti Equation (SDRE) design method in the context of application to robotics and manufacturing systems. Lagrangian Mechanics and the Assumed Mode Method have been used to derive a proposed dynamic model of a single-link flexible manipulator having a revolute joint. The model may be used in general to investigate the motion of the manipulator in the horizontal plane rest-to-rest rotational maneuver. The nonlinear SDRE control law is derived as minimizing a quadratic cost function that penalizes the states and the control input torques. Simulation results are presented for a single-link flexible manipulator to achieve a desired angular rotation of the link while simultaneously suppressing structural vibrations, and the effect of payload on the system response and vibration frequencies is investigated. The results are illustrated by a numerical example.