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 S1, exhibiting unpredictable jumps of 2π. 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.

I. Introduction

Observers are fundamental building blocks in control when facing output feedback problems. Many strategies have been proposed in order to estimate the plant state starting from its output, such as Luenberger observers [4], passivity-based observers [2], and high-gain observers [14]. Among these, high-gain observers are a well established tool when the process to be observed contains some unmodelled dynamics. They are also used in order to estimate the time derivative of the plant’s output, making use of the high-gain scaling parameter as a tuning parameter allowing one to trade off between responsiveness and noise sensitivity of the observer [8], [17]. Recently, the hybrid dynamical system framework of [12] has been exploited in order to enhance the performance or extend the use of classical continuous-time observers, both in the high-gain scheme [5], [10], and in cases where hybrid dynamical system are at stake (see [7] and references therein).