Bounded Nonlinear Control of a Rotating Pendulum System

We are interested in the output feedback control of mechanical systems governed by the Euler-Lagrange formalism. The systems are collocated actuator-sensor controlled and underactuated. We present a design method by means of a specific example : the set point control of a rotating pendulum. We use constrained output feedback, whereby the control inputs satisfy a priori imposed upper bounds. The closed loop stability analysis relies on the direct method of Liapunov. This results in a frequency criterion on the controller's linear dynamic component and some restrictions on its nonlinearities. The control parameters are tuned for maximizing closed loop damping.