Friction induced hunting limit cycles: an event mapping approach

This paper studies the occurence of limit cycles for a simple PID-controlled motion system subjected to different shapes of static frictional damping functions. The friction characteristics are compared with respect to the so-called hunting phenomenon. In particular, a classification with respect to the ability to predict both stable and unstable limit cycles is obtained. Furthermore, the local stability of the equilibrium points is discussed and attractor basins are given. To perform this analysis, the closed-loop dynamics are represented with an equivalent one-dimensional map representing a so-called event map

Friction induced hunting limit cycles : an event mapping approach

This paper studies the occurence of limit cycles for a simple PID-controlled motion system subjected to different shapes of static frictional damping functions. The friction characteristics are compared with respect to the so-called hunting phenomenon. In particular, a classification with respect to the ability to predict both stable and unstable limit cycles is obtained. Furthermore, the local stability of the equilibrium points is discussed and attractor basins are given. To perform this analysis, the closed-loop dynamics are represented with an equivalent one-dimensional map representing a so-called event map

High-performance regulator control for mechanical systems subjected to friction

Several control strategies are compared with respect to their performance for regulator tasks on mechanical systems that exhibit friction. For this purpose a classic PID-controller combined with mass and frictional feedforward is compared to (i) a PID-controller combined with a model-based friction compensation using the dynamic LuGre friction model and (ii) a gain-scheduled optimal PD-controller based on a polytopic linear model (PLM). The latter consists of a feedforward part and an optimal nonlinear feedback part. The controllers are compared to the classic PID-controller by means of experiments on a rotating arm subjected to friction. The performance for three third order point to point setpoints shows that the gain-scheduled optimal PD-controller outperforms the other controllers with respect to settling time and maximal error after setpoint. The tracking performance is comparable for the LuGre-based controller and the classic PID-controller where the tracking performance of the gain-scheduled PD-controller is limited