Design and implementation of sliding mode control with the modified force for an inverted pendulum with nonlinear friction

The purpose of this study is to present a method for controlling an inverted pendulum in the presence of nonlinear and indeterminate friction force between the moving cart and its straight guide rail. Control of an Inverted pendulum, as an Under-actuated Mechanical System, is facing challenges from theoretical and experimental aspects. To deal with such challenges, a new method is proposed in this paper. The method is based on an approximate input-output linearization of the inverted pendulum dynamic model for which a modified sliding mode control is proposed. For experimental determination of the bound of friction force, an inverted pendulum with a moving cart is designed and built. The moving cart and its rail are intentionally designed and built such that the resulting friction force is nonlinear, uncertain, and state-varying. The upper bound of the friction force is obtained experimentally and its average value is added to the control input obtained from the conventional sliding mode controller. Experimental verifications depict the success of the proposed control method in preserving the closed-loop stability under the challenging case of dealing with a large nonlinear friction force.