NONLINEAR CONTROL OF A SWINGING PENDULUM

We propose a nonlinear controller to regulate the swinging energy of t he pendulum for a cart and pendulum system. Roughly speaking, the cont roller is designed to regulate an output (the swing energy) while prov iding internal stability (regulating the cart position). It is difficu lt to apply many of the standard nonlinear control design techniques, since the output zeroing manifold does not contain any equilibrium poi nts and the relative degree of the system is not constant In contrast to controllers that use a command generator and possibly a time-varyin g feedback, our control law is a simple autonomous nonlinear controlle r. We analyze the stability of the closed-loop system using an L(infin ity) small-gain approach on a transverse linearization of the system a bout the desired periodic orbit. One can easily extend this approach t o analyze the robustness of the control system with respect to disturb ances and parameter variations. Experimental results demonstrate the e ffectiveness of the nonlinear controller.