Friction analysis based on integral quadratic constraints

One of the most important nonlinearities in mechanical control systems is friction. Friction may cause steady state errors, as well as unwanted oscillations. The purpose of this paper is to demonstrate how recently developed tools for nonlinear system analysis can give us a better understanding of these effects. One of the most common approaches to analysis friction systems is passivity theory. The main theoretical contribution of this paper is to prove a new set of integral quadratic constraints for a so called “stiction”. As an application, we consider stiction induced oscillations in a servo system with a PID controller. The phenomenon is analysed using integral quadratic constraints, and the quantitative relationship between the stiction level and the necessary amount of leakage is computed. The response to periodic inputs is also studied