Controlling an Inverted Pendulum with Bounded Controls

The dynamical behaviour of a simple underactuated mechanical system with a bounded continuous control law is analyzed. The system consists of a pendulum with an inertia disk mounted on its free extreme. It is driven applying torques to the inertia disk by means of a DC motor. The closed-loop system exhibits a rich and complex dynamic when a control parameter is varied. A numerical analysis reveals Hopf, fold and homoclinic bifurcations as the main phenomena. It is shown that the pendulum can be stabilized in its inverted position with zero velocity of the disk if the controller’s gains are appropriately chosen.

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