This thesis is in two parts, both considering the absolute stability of nonlinear systems. In the first two chapters the stability of certain classes of nonlinear time invariant systems involving several nonlinearities is considered. A number of graphical methods are given for testing the stability of these systems. The graphical tests are equivalent to a weakened form of the Popov criterion. The third chapter derives a stability condition for nonlinear systems involving a linear time-varying gain. The time-varying gain is assumed to satisfy conditions on its magnitude and rate of change. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The focus of this thesis is to research, analyze, and design a reliable and economical control system for the Cal Poly Wind Energy Capture System (WECS). A dynamic permanent magnet generator model is adopted from [1] and [2] and combined with an existing wind turbine model to create a non-linear time varying model in MATLAB. The model is then used to analyze potentially harmful electrical disturbances, and to define safe operating limits for the WECS. An optimal operating point controller utilizing a PID speed loop is designed with combined optimization criteria and the final controller design is justified by comparing performance measures of energy efficiency and mitigation of mechanical loads. The report also discusses implications for a WECS when blade characteristics are mismatched with the generator. Finally, possible ways to improve the performance of the Cal Poly WECS are addressed.

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Master of Arts / Department of Economics / Steven P. Cassou / This report shows the mathematics behind the solution to continuous time optimization problems. It shows how to specify the Hamiltonian function, how to use the Hamiltonian to obtain the optimal conditions for a typical economic optimal control problem and applies these techniques to several optimal control problems commonly encountered in macroeconomics. An appendix shows how to set up the optimal conditions for the case in which the state and co-state variables are both vectors. A second appendix shows how to approach the control situation for a system of optimal control problems where the co-state variable for the first sub-optimal control problem is the state variable for the second sub-optimal control problem.

Vita. / Digitized by Kansas Correctional Industries

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