Optimal control and sensitivity analysis of two links flexible arm with three degrees of freedom

The modeling and control method for a flexible robotic arm with three degrees of freedom is described. Under the assumption that the links vibrate both transversely and torsionally, the dynamics of the three degrees of freedom flexible robotic arm is derived. To estimate the state of the system, an observer is employed. The control algorithm is designed by using optimal control theory based on the quadratic performance index approach. This control method is shown to suppress the coupled vibrations. Sensitivity analysis is carried out when there are some inaccuracies in the payload´s weight or the link´s length. The way to find the stable domain of these parameters is presented, and some simulation results are provided