LYAPUNOV STABILITY CONTROL OF INVERTED PENDULUMS WITH GENERAL BASE POINT MOTION

A methodology of Lyapunov stability control is presented to achieve th e upright balance of a base-excited inverted pendulum with two degrees of rotational freedom. The inclusion of the base point movement leads to the dynamic system of such a pendulum which is non-autonomous and is under persistent disturbance. An idealized piecewise continuous con trol strategy is first designed. Such a controller guarantees the solu tion trajectories to be arbitrarily close to the upright position. How ever, non-idealities in its implementation result in chattering of the controller. To rectify this, how the continuous control law can be us ed to approximate such a discontinuous controller is shown. The contin uous control law guarantees that the solution trajectories are kept in a controlled region around the upright position. We trade off the sta bility with a weaker stability to prevent chattering. The precise natu re of such a trade-off is analyzed. The robustness of the controllers with respect to certain class of uncertainties is also examined. (C) 1 998 Elsevier Science Ltd. All rights reserved.