Takagi-Sugeno sliding mode observer for friction compensation with application to an inverted pendulum

To improve the dynamics in mechatronic systems an active friction compensation is usually necessary. However, a poor friction compensation action in the control scheme may lead to significant tracking errors, especially at low velocities. Different kinds of friction models are commonly used to compensate for the effects of friction. However, the friction modeling problem remains a very difficult and time-consuming task. In this work, a different approach is presented: the friction force acting in a dynamic system can be viewed as an unknown but bounded input with time-varying characteristics to be estimated and compensated for using a robust sliding mode observer scheme based on the Takagi-Sugeno model structure. The TakagiSugeno fuzzy observer scheme combined with sliding mode (TS SMO) deals with nominal nonlinear dynamics, unmeasurable premise variables, bounded uncertainties in the plant and enables friction estimation based on an equivalent output error injection approach. Thus, the limitations arising from the use of an explicit friction model are removed. The stability of the nonlinear error dynamics is ensured by sufficient linear matrix inequality (LMI) conditions. The approach is illustrated using a non-linear inverted pendulum with Stribeck friction and additional uncertainties due to a slight path angle. Simulation and experimental results demonstrate the effectiveness of the proposed scheme.