Control of mechanical systems with Stribeck friction and backlash

In this paper the control of mechanical systems in the presence of nonlinear friction and backlash is treated in a hybrid system approach. To deal with friction induced nonlinearities, the Stribeck friction model is linearized and the resulting model of the controlled plant is a hybrid system, the dynamics of which is given by linear models in the different partitions of the state space. During controller design it is assumed that the size of the backlash gap is unknown and the load side position and velocity cannot be measured. For motion control an LQ controller is applied. A condition is formulated for the control law parameters to guarantee the asymptotic stability of the control system. The LQ control algorithm is also extended for trajectory tracking tasks. Simulation results are presented to show the applicability of the theoretical results.