A differential geometric approach for the nominal and robust control of nonlinear chemical processes

This thesis addresses the transformation of nonlinear systems to linear systems through the use of differential geometric methods. The transformations involved are state and input coordinate changes. Nominal and robust control of such transformed systems is investigated. The application of these transformations as well as new control synthesis methods are implemented on various chemical process models.In the first part, two transformation approaches are presented. The "internal" transformation considers the mapping of a nonlinear system without output to a controllable linear system. The "external" transformation addresses the mapping of a nonlinear system with output so that the transformed system exhibits linear input-output dynamics.In the second part, the nominal stabilization of transformed nonlinear systems is done through classical control techniques such as pole placement and the internal model control framework. Also an analysis study of the influence of disturbances (measurable or unmeasurable) on the internal and the external transformations is given.The last part of the thesis addresses the robustness of these transformation techniques. First an analysis study shows the effect of modeling errors on these techniques. Then, the synthesis of stabilizing controllers is proposed when uncertain nonlinear systems are transformed internally or externally.