A Class of Hybrid Velocity Observers for Angular Measurements with Jumps

We propose a hybrid nonlinear high-gain observer to estimate the speed of rotary systems equipped with potentiometer-based, capacitive or hall-effect rotary sensors or providing angular measurements evolving in $\mathbb {S}-{1}$ , exhibiting unpredictable jumps of $2\pi $. A hybrid measurement model is proposed, based on which a hybrid high-gain observer is synthesized, which does not require the knowledge of the jump times. Asymptotic tracking of the proposed observer is proven. A sampled-data approximation of the proposed observer is developed as well, based on which an experimental validation shows suitability for real-time applications.