Model error compensation and robust observer design. I. Theoretical formulation and analysis

A two-step observer design methodology is developed for a class of nonlinear, uncertain systems which can be separated into a linear, accurately modeled subsystem and a nonlinear uncertain subsystem. This class of systems is reasonably general and quite common in manufacturing systems. The first step includes the design of a model error compensator (MEC) to account for the effects of the uncertain subsystem. The second step includes the error dynamics analysis using a conventional observer based on the compensated system. The MEC is formulated as an input tracking problem and the existence of an MEC is guaranteed by the right-inverse and left-inverse of the linear subsystem. In general, the tracking stability of the MEC is not guaranteed; however, for systems with single-input and single-output (SISO) subsystems, the stability is achieved in this paper by choosing a suitable MEC gain based on the Popov circle criterion. This two-step observer design strategy may improve the estimation accuracy of conventional observers and simplify the design procedure.