Sliding mode observers and unknown input estimations for nonlinear systems - Veluvolu Kalyana Chakravarthy (2008)
This thesis presents a new perspective for the analysis of sliding mode observers (SMO) and unknown input estimations of nonlinear uncertain systems. The main idea lies with exploiting the observability of the unknown inputs from the measured outputs. This allows us to design appropriate robust terms to estimate the unknown inputs from the sliding mode and thereby estimating the states in the presence of unknown inputs/disturbances. The first part of the thesis addresses the continuous time problems of linear and nonlinear uncertain systems. A sliding mode observer for linear MIMO systems with unknown inputs is proposed and the complete disturbance rejection properties of the observer are established. By the proposed method, the unknown inputs can be directly estimated from the corresponding sliding surfaces. The observer design of linear MIMO is then extended to a class of Lipschitz nonlinear systems. The stability conditions are established and the observability of unknown inputs from the sliding mode is further analyzed. To handle the state estimation problem for a more general class of SISO nonlinear systems perturbed by an unknown input, SMO is incorporated into the partially linearized system via nonlinear transformation. The measurable output estimation error is the sliding surface. In the sliding mode, the disturbance can be estimated from the equivalent control, and the convergence of the estimation error dynamics is proven. To further extend the development to a generic class of MIMO nonlinear systems perturbed by multiple unknown inputs, we propose a new nonlinear transformation to structurally classify the original nonlinear system into two subsystems so as to facilitate the design of multiple sliding mode observer. By construction, the unknown inputs are structurally reconstructible from the chosen sliding surfaces. The second part of the thesis focuses on the development of discrete-time observers for the same continuous-time problems discussed earlier.