Robust Adaptive Backstepping Control of Inverted Pendulum on Cart System

Abstract

In this paper a design methodology for a novel robust adaptive backstepping controller for the stabilization control of an inverted pendulum on a movable cart, which is a benchmark control problem in the nonlinear control system paradigm, has been presented in a systematic manner. The proposed control law provides a systematic iterative formulation of a Lyapunov energy function for the inverted pendulum system to ensure its stabilization and convergence of the angle tracking error as well as the estimation error of its unknown parameters towards zero. For easier parameter adaptation, the model of the inverted pendulum has been transformed into a motion control model. The effectiveness of the proposed algorithm has been verified in simulation studies. The controller design has been evaluated not only for the tracking performance but also for the parameter convergence rate of the system. It is quite interesting to note that during the simulation it does not require any prior information about the parameters of the mathematical model of the inverted pendulum.