Robustness and Tuning of Incremental Backstepping Approach

Abstract

Incremental Backstepping (IBS) approach is robust to the uncertainties in the plant dynamics term f(x). However, its robustness to the uncertainties in the control effectiveness term g(x) remains unknown especially in the presence of actuator dynamics. Furthermore, it requires the assumption of the availability of fast actuator dynamics. In this paper, the robustness is analyzed with and without the actuator dynamics. It is found that uncertainties with γ > 1 are advantageous for the stability of the complete system. Then, the tuning of the IBS is introduced. Two methods which can increase the robustness of the IBS are proposed: γ tuning and actuator compensator. The design of an actuator compensator requires the parameter of the actuator whereas the γ tuning methods does not. Finally, the robustness to model uncertainties is verified by simulation examples, which show the effectiveness of the proposed approaches.