Date of Award
Doctor of Philosophy (PhD)
Frank R. Groves
Feedback linearization provides an effective means of designing nonlinear control systems. This method permits one to have an exactly equivalent linear system by using a coordinate transformation and state feedback. Once the nonlinear system is transformed to a linear system, one can proceed with well developed control technologies for linear systems. Feedback linearization is based on a model of the real system. If there is mismatch between the model and the real plant, feedback linearization does not yield an exactly linear system. The question of robustness then arises: will a controller based on the model be stable when applied to the real plant? We have developed a theoretical approach to analyze robustness of feedback linearization of SISO (Single-Input Single-Output) systems. We have also considered the dimensional reduction of a high dimensional model which is not a standard singularly perturbed system. Specifically we have found sufficient conditions for boundedness and convergence of the system trajectories when feedback linearization based on a nominal mathematical model is applied to an uncertain real plant which may have parametric and structural uncertainties as well as unmodeled dynamics. The developed approach does not require the restrictive conditions which are commonly used in the previously developed methods of robustness analysis. Furthermore, for parametric uncertainties a nonlinear adaptive control of feedback linearizable processes is proposed. The main feature of the proposed nonlinear adaptive control system is that it is relatively straightforward and simple. For this adaptive control system we have found sufficient conditions for stability of the output regulation and tracking of feedback linearizable systems using the second method of Lyapunov. Examples of the robustness analysis and the adaptive control for unstable chemical and biochemical reactors are given.
Kim, Weon Ho, "Feedback Linearization of Nonlinear Systems: Robustness and Adaptive Control." (1991). LSU Historical Dissertations and Theses. 5130.