| Systems described by nonlinear ordinary differential equations that admit an observer with linear error dynamics, termed integrable systems, rarely arise in practice. However, any nonlinear system can be expressed as the sum of non-integrable and integrable parts. We find coordinates where the size of the system's non-integrable part is minimized uniformly over a compact operating region. Provided the control-affine, multi-input, multi-output system's non-integrable part satisfies a relatively weak structural condition, the design coordinates can be used to obtain an observer with approximately linear, locally stable error dynamics. The synthesis is constructive, and we perform the optimization numerically using an algorithm implemented in Mathematica. The procedure is generalized to the reduced-order case. Examples illustrate the constructive nature of the design method and its relatively low gains compared with a high-gain design.; The second part of this thesis considers the industrial application of estimating the span tension of a web processing machine using observers. After presenting the dynamic equations of a web machine, their structure is exploited to design a reduced-order, nonlinear observer with linear time-varying error dynamics. The stability of the error dynamics is discussed for the nominal model, and the design is generalized to multi-span web machines. The observer is compared with three other designs in three performance tests. In particular, the nonlinear observer's robustness to tension disturbances is compared to that of a sliding-mode design. The performance of the observers is experimentally verified on a real two-span web machine. |
