Robust tracking control of a shaking table with dry friction

Abstract

In this paper, the design, analysis, implementation, and evaluation of two tracking algorithms to control the motion of a shaking table are described. This mechanism is a component of an experimental platform used to study the effect of oscillatory signals on mechanical structures. The table, driven by a linear brushless motor, presents high dry friction. It is intended to attenuate the negative effects due to this phenomena. The first algorithm is a classical PD controller with friction and disturbance compensation. This controller requires a prior modeling of the mechanism and a good tuning of the control parameters. The second algorithm is a sliding-mode controller based on a non-connected switching surface. This controller makes the system produce a combined sliding motion of first order in a first stage and then a second-order sliding motion. It makes the system converge to the desired trajectory in finite time. The platform instrumentation provides only the measurement of the table position; thus, a discontinuous observer has been included to estimate the velocity. It is shown that both controllers display a good tracking, although the discontinuous algorithm exhibits a better performance.