An Estimation and Compensation of the Friction in an Inverted Pendulum

This paper deals with a method to reduce oscillations that often appear in the steady-state response of a system, which is controlled by a linear controller based on the linearized system model. With an assumption that the oscillations shown in the steady-state are caused by the process of linearizing nonlinear systems, we improve the performance of stabilization and tracking by estimation and compensation of the friction omitted in the linearized system. Experimental results show that the control performance can be improved sufficiently by the proposed method, when it is applied to an inverted cart pendulum which is a multi-variable and unstable system. Even though the Coulomb friction model used in the estimation of the friction is simple, it is sufficient in validating the suggested method. To confirm proposed method to compensate the Coulomb friction, the friction in an inverted cart pendulum is estimated by nonlinear friction observer and the estimate of the friction observer is used to compensate a linear controller