An experimental result on stabilization via Immersion and Invariance: The cart-pendulum system

The Immersion and Invariance (I&I) methodology for stabilization of nonlinear systems has shown a great efficiency from a theoretical point of view. Nevertheless, it is important to show its applicability level. This paper is thus devoted to the experimental validation of the application of a state-feedback controller derived by the I&I methodology. The application consists of the well-known academic example of the inverted pendulum on a cart. First, it is shown that theoretically the I&I controller can stabilize the system by considering an initial position of the pendulum angle very close to the horizontal axis, condition which cannot be met previously by means of other control schemes. Moreover, it is shown that the controller designed herein is simpler than others described in previous research works. Finally, it is pointed out that taking into consideration the presence of friction in the experimental set-up is crucial for attaining the required performance and maintaining a good level of stabilization robustness.