- Published 2008 in Int. J. Control

We design an exact output tracking control law for a four degree of freedom spherical inverted pendulum based on the nonlinear stable inversion tool proposed by Devasia, Chen and Paden. The pendulum is a slim cylindrical beam attached to a horizontal plane via a universal joint; the joint is free to move in the plane under the influence of a planar force. The upright position is an unstable equilibrium of the uncontrolled system because of gravity. The objective is to design a controller so that the pendulum can be steered to track some smooth desired translational trajectories while keeping the pendulum tightly around the upright position. The design proceeds in three steps: 1) identification of the internal dynamics; 2) feedforward control design for achievable trajectories; 3) feedback design to stabilize the achievable trajectories. The computer simulations show that the proposed controller can deliver excellent tracking performance.

@article{Liu2008NonlinearSI,
title={Non-linear stable inversion-based output tracking control for a spherical inverted pendulum},
author={Guangyu Liu and Dragan Nesic and Iven M. Y. Mareels},
journal={Int. J. Control},
year={2008},
volume={81},
pages={116-133}
}