Impulsive Dynamics and Control of the Inertia-Wheel Pendulum

The dynamics of the inertia-wheel pendulum, when subjected to impulsive inputs, can be described by algebraic equations. Optimal sequences of these inputs, that minimize their infinity norm, are designed for rest-to-rest maneuvers. The results are applied to the well-studied swing-up problem, and high-gain feedback is used for continuous approximation of the inputs and simulation of the impulsive dynamics. Analytical and simulation results establish a direct link between high wheel velocities during swing-up and control strategies that take the pendulum directly to the upright configuration. They also indicate that optimal trajectories resemble those of energy-based controllers and can be designed to satisfy the torque constraint of the actuator.