Model-based Friction Compensation

Abstract: Friction is present in all mechanical systems and causes a wide range of problems for control. The development of model-based strategies accounting for Friction in the designed control has been a vast area of Research since these last decades. A promising Friction model which received a lot of attention these last years is the so-called LuGre model, which originates in the collaboration between the two control Research groups of Lund (Sweden) and Grenoble (France). This model is quite simple and is capable of capturing a wide range of well known friction phenomena, such as the Stribeck effect or the frictionnal lag. In particular this model is used in [Robertsson et al., 2004], where a general method for friction compensation for nonlinear systems is presented. The compensation strategy is simple: it just consists in adding to the control signal a friction estimate, computed using a LuGre model based observer. This thesis deals with the application of the theory of this article on a real experiment: the stabilization of the Furuta pendulum in the upright position. First, attention is paid so that the initial hypothesis of this article be satisfied. These hypotheses consist in finding a stabilizing control for the system when Friction is neglected, and an associated Lyapunov function verifying some properties. Then, Friction is included by following the procedure presented in the article. The friction estimate is computed according to the discretized LuGre form, presented in fFreidovich et al., 2006g, and the main result of the article is verified both in Simulation and on the real process, the simulations being carried out with Matlab-Simulink and the real experiments by using a dSPACE device. From a practical point of view, the implemented compensation scheme works perfectly in Simulation: the limit cycles originating from an uncompensated friction are totally annihilated, while for real experiments this oscillating behaviour is still remaining, but happens to be significantly reduced. From a theoretical point of view, the results of [Robertsson et al., 2004] are fully verified in Simulation, while for real experiments the presence of remaining limit cycles prevents a perfect verification of the theory.