On the Design of Backstepping Controller for Acrobot System Based on Adaptive Observer

Abstract

The present work has addressed the output control problem using backstepping controller based on adaptive observer for control and stabilization of underactuated system, represented by planar Acrobot system. The backstepping control strategy is a procedural approach based on the passivity concept used for upright stabilization of Acrobot, while the adaptive observer has been used for speed and mass estimation in presence of uncertainties. The planar Acrobot system is two Degree of Freedom underactuated system. It moves in the vertical plane and it works like a gymnast on a high bar, where the first and the second joints are analogous to hands and hips of the gymnast respectively. This paper is devoted to design and develop an observer-based backstepping control algorithm in order to stabilize and balance the links of Acrobot at their upright angular positions. Therefore, two design algorithms have been presented; one is developed for the backstepping control and the other one for adaptive observer. The stability of the observer-based backstepping controlled system has been analyzed based on Lyapunov direct method. The robustness characteristic of the adaptive observer has been evaluated under the variation of the mass of unactuated link an amount of 10% over the nominal value. Computer simulation based on MATLAB programming format has showed that the backstepping control algorithm could successfully stabilize and balance the Acrobot's links at the desired upright position. In addition, the adaptive observer could keep good robustness characteristics in estimation of unmeasured state in the presence of uncertainty in system parameter.