Nonlinear feedback control of the rotary inverted pendulum

Abstract

The inverted pendulum, a popular problem of study, is presented in many textbooks as a nonminimum phase system. The majority of control algorithms for this problem include linearizing the system about a fixed operating point. In this thesis, a nonlinear form of control is considered. A model for the rotary inverted pendulum system was derived and validated by comparing simulations using the derived equations to experimental data. The system parameters were tuned until the simulation and experimental data fit. A feedback linearization controller was then designed based on the model derived. The simulated implementation of the feedback linearization was successful but indicated continuous motion of the system. The experimental results of the feedback linearization controller were less successful than simulations. The simulated results also indicated unstable zero dynamics of the system, which were characterized and confirmed to be unstable. Finally, an intuitive fix was applied to add terms to the feedback linearization controller to account for the zero dynamics. The results of this controller in simulation were successful but did not produce a substantially different response in the experimental system