Trajectory Tracking Control in a Single Flexible-Link Robot using Finite Differences and Sliding Modes

In this article it is shown how the end effector position of a single flexible-link robot can be directly controlled by the angular position of its joint, so that, trajectory tracking in the end effector of the robot is possible by properly designing a reference trajectory for the joint angle. In order to ensure trajectory tracking of the angular position of the robot joint, a Sliding Modes Control (SMC) scheme is employed once the desired trajectory for the robot joint has been designed. SMC scheme is chosen because its known robust performance under dynamical disturbances and modeling inaccuracies. Then, the angular position of the robot joint plays the role of a virtual control input for the flexible dynamics of the link. Both, regulation and trajectory tracking of the end effector position are achieved by using the scheme devised in this work. The Finite Differences Method (FDM) is employed to simulate the closed loop performance of the flexible-link robot, because its dynamics are assumed to be governed by the undamped Partial Differential Equation (PDE) of the Euler-Bernoulli Beam (EBB).