End-point control of a flexible-link manipulator using H∞ nonlinear control via a state-dependent Riccati equation

The problem of modeling and controlling the tip position of a single-link flexible manipulator is considered. In a flexible-link manipulator in general the effect of some parameters such as payload, friction amplitude and damping coefficients can not be exactly measured, One possibility is to consider these parameters including uncertainty. Recent results may then be applied on nonlinear robust regulators using a nonlinear H_∞ via state dependent Ricatti equation (SDRE) design method. Lagrangian mechanics and the assumed mode method have been used to derive a proposed dynamic model of a single-link flexible manipulator having a control joint. The full state feedback nonlinear H_∞ SDRE control law is derived to minimize 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 the desired angular rotation of the link whilst simultaneously suppressing structural vibrations. The effect of payload on the system response and vibration frequencies is also investigated. The results are illustrated by a numerical example.