Kybernetika 38 no. 2, 217-232, 2002

Rotary inverted pendulum: trajectory tracking via nonlinear control techniques

Luis E. Ramos-Velasco, José J. Ruiz-León and Sergej Čelikovský


The nonlinear control techniques are applied to the model of rotary inverted pendulum. The model has two degrees of freedom and is not exactly linearizable. The goal is to control output trajectory of the rotary inverted pendulum asymptotically along a desired reference. Moreover, the designed controller should be robust with respect to specified perturbations and parameters uncertainties. A combination of techniques based on nonlinear normal forms, output regulation and sliding mode approach is used here. As a specific feature, the approximate solution of the so-called {\sl regulator equation} is used. The reason is that its exact analytic solution can not be, in general, expressed in the closed form. Though the approximate solution does not give asymptotically decaying tracking error, it provides reasonable bounded error. The performance of the designed feedback regulator is successfully tested via computer simulations.