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

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.

I. Introduction

Mathematical models of dynamical systems generally involves uncertain components due to the presence of environmental disturbances, parameter fluctuations, approximations, etc. Therefore it is important to take into account of these uncertainties in controller design process. One of the effective ways to improve the controller performance is to estimate the disturbance variables and eliminate them in the control design process. There are various methods available to design disturbance observer for dynamical systems. A based technique is proposed in [15] to design disturbance observer whereas the authors of [26] utilized approximate differentiation type method to design disturbance observers. Variable structure based nonlinear disturbance observer design is proposed in [3] for minimum phase systems.