Experiments on output tracking with internal stability by learning for a one-link flexible arm

In this paper we present the experimental results of the implementation of a novel finite-dimensional learning algorithm for output zeroing with internal stability. The end point trajectory control of a flexible link moving on a horizontal plane is considered. Given a desired end point trajectory generated by a finite-dimensional exosystem, by means of successive trials, the algorithm implemented learns the initial state and the control needed to exactly track the desired trajectory. An internal stability constraint is enforced, which prevents undesirable excessive vibrations and control effort. Initialization of the flexible link state is automatically accomplished as a part of the same learning process. The experimental results presented show the effectiveness of the algorithm introduced and its robustness with respect to nonlinear plant perturbations and unmodeled high frequencies dumped modes of vibration.