Convergence analysis of high gain disturbance observer based backstepping control: A contraction theory approach

摘要

Backstepping design is a powerful method for stabilization and tracking of strict feedback nonlinear systems which find applications in practical fields like robotics, aerospace, process control, etc. However the presence of uncertainties in system dynamics complicates the control design procedure. In recent past, high gain disturbance observer based backstepping design has received considerable attention. Due to the use of large observer gains, the closed loop system possess a time scale separation between the system dynamics and the observer dynamics. This paper analyzes the performance of high gain disturbance observer based backstepping controller using contraction framework. In doing so the steady state error bounds are obtained in terms of design parameters which can be exploited to tune the closed loop system performance. Unlike the quadratic Lyapunov based methods, the stability analysis does not require any interconnection conditions. Furthermore the convergence results are shown to hold for less conservative choice of observer gain. The effectiveness of the proposed controller is verified through simulation example.