NONLINEAR CONTROL OF A SWINGING PENDULUM

We propose a nonlinear controller to regulate the swinging energy of the pendulum for a cart and pendulum system. Roughly speaking, the controller is designed to regulate an output (the swing energy) while providing internal stability (regulating the cart position). It is difficult to apply many of the standard nonlinear control design techniques, since the output zeroing manifold does not contain any equilibrium points and the relative degree of the system is not constant In contrast to controllers that use a command generator and possibly a time-varying feedback, our control law is a simple autonomous nonlinear controller. We analyze the stability of the closed-loop system using an L(infinity) small-gain approach on a transverse linearization of the system about the desired periodic orbit. One can easily extend this approach to analyze the robustness of the control system with respect to disturbances and parameter variations. Experimental results demonstrate the effectiveness of the nonlinear controller.