Backstepping-like control using sliding modes for a single flexible-link robot

The model of a single flexible-link robot arm with a payload attached to its tip is represented in a cascade-like fashion using a proper coordinate transformation of the system state. The new system representation makes possible to find a way to assign a convenient dynamics for the overall system to control its tip position by using the joint shaft angular position as a virtual control input for the controlled output dynamics as it is used in Backstepping approaches. The rigid dynamics of the system is found to be perturbed due to the flexural effects of the flexible link, so a sliding mode control scheme is employed to deal with both, system uncertainties and perturbations while achieving good performance on a trajectory tracking task at the tip. The flexible-link model is considered as an Euler-Bernoulli beam and no gravity effects are taken into account. Simulations result which show the system performance are presented in this work.