Robust Nonlinear Control of Positioning Systems with Stiction

Abstract

A robust, point to point, nonlinear controller for positioning systems is proposed. In the continuous domain the robustness is achieved through the use of a switching controller. To avoid chattering the switching had to be reduced as the controller was transformed into the discrete domain. The controller is designed to minimise the effect of stiction near the reference point. This is achieved by forcing the states to follow a parabolic trajectory as they approach the set point. Such a surface can be followed exactly in the continuous domain. In discrete time however the extent to which the states can be forced to follow a parabolic surface depends on the sampling time and the severity of the parameter uncertainties. The relationship between these variables is provided. Both the continuous and the discrete time controllers are simulated on a second order positioning system with stiction. A second order filter is also added to the simulation model in order to approximate the dynamics of the driver. Due to robustness, changes in inertia by as much as 200% result in minimal performance degradation. The controller in its discrete form is also applied to a single axis robot arm driven by NSK direct drive motor.