An adaptive sliding mode observer for inverted pendulum under mass variation and disturbances with experimental validation

Abstract

In this paper, a new robust adaptive estimation approach is designed for the inverted pendulum. The estimation scheme is composed by an auxiliary high gain observer in cascade with an adaptive sliding mode observer. The auxiliary high gain observer is designed to estimate auxiliary outputs in order to solve the dissatisfaction of observer matching condition related to the presence of disturbances. Then, using the estimated auxiliary outputs, the adaptive sliding mode observer is synthesized to estimate conjointly the states, the unknown parameter (the pendulum mass which appears nonlinearly in the dynamics of the pendulum model) and the unknown disturbances. The stability analysis is established using the Lyapunov approach. Numerical simulations are carried out to validate theoretical results. Furthermore, experimental tests are realized using a real pendulum setup (a product of Feedback Instruments) to highlight the good performances of the proposed estimation method in practice.

Keywords: Adaptive observer; High gain observer; Inverted pendulum; Mass variation estimation; Sliding modes.