An immersion and invariance based speed and rotation angle observer for the ball and beam system

The present contribution introduces a nonlinear observer for the rotation angle and the velocities of the ball and beam system. It is based upon the Immersion and Invariance (I&I) methodology and it uses measurements of the relative rotation angle and the absolute ball position. Significant practical relevance of this contribution is due to the relative rotation angle measurement, provided by most commercially available encoders. Observability of the system is studied and the nonlinear observer is designed using the (reduced-order) observer theorem of the I&I technique. The asymptotical convergence of the observation error is proved by means of Lyapunov arguments. Simulation experiments illustrate the theory and show the effectiveness of the proposed design.