A Stabilizable Control Laws For a Rotational Pendulum: A Trajectory Planning Approach

We propose two simple controls for the regulation of an under actuated rotational pendulum. Both controllers are based on the Lyapunov approach; the first is a simple passive control which makes the closed-loop solution converges asymptotically to an equilibrium manifold. The second approach is a combination of the Lyapunov and the off-line trajectory planning approaches to move the pendulum from an equilibrium point to another equilibrium point, both point belonging to an equilibrium manifold. The last task is accomplished in an approximated fashion. The results are illustrated by means of digital computer simulations.