Observer Design for a Variable Moment of Inertia System

Abstract

Variable moment of inertia systems are common, and a popular laboratory system of this type is the “ball-and-beam”. Such systems are, however, nonlinear and often unstable. Efficient control requires full state information (or at least partial velocities), which are generally difficult to measure. That is why the design of state observers is a relevant problem. In this paper, a new design of an observer is proposed. This new nonlinear observer uses partial output injection and the circle criterion to ensure semiglobal stability. Moreover, we present a complete modeling of the system and systematic testing of the observer in comparison to a baseline in the form of a linear observer. The results show that the designed observer outperforms its linear counterpart and does not impede control.