Hybrid adaptive Backstepping-Sliding mode control design for Non-linear Under-Actuated systems

Abstract

This paper focuses on studying the inverted pendulum as a case study of under-actuated systems, which has two degrees of freedom and a single actuator. The Lagrangian dynamic model of the system is non-linear and its internal dynamic is not asymptotically stable. The control of this system has been the subject to many studies because the dynamics of the inverted pendulum is closer to those of more complex systems. Besides, this mechanism is a low cost tool for implementation and practical illustration of new control approaches. For the stabilization of the system, it is first necessarily to bring the pendulum from its equilibrium stable position (pendulum pointing downwards) to its unstable equilibrium position. In this study, different control approaches were applied to the system such as sliding mode control, Backstepping method, and their combination. These studied techniques are very implementable for under-actuated systems, where their algorithms are designed with an appropriate choice of parameters. Moreover, the obtained results are very interesting; they show the effectiveness of the proposed hybrid approach in improving the performances, namely, the controller robustness and convergence stability. The hybrid control system has been designed for both stabilization and external disturbances rejection. Hence, the main contribution of this study is the hybridization of adaptive backstepping approach with sliding mode control for under-actuated systems