Spline based controller for nonlinear systems

The objective of this thesis is to apply spline theory to implement controllers for nonlinear systems. Two different systems, forced Duffing oscillators and power systems, are investigated. The spline method is used to mimic the controller which drives a state of the Duffing system toward a desired path. The spline-based nonlinear controller has piecewise polynomial segments with different order of polynomials on each segment. Controller efforts for different order of polynomial interpolants and power spectral densities of the controller signals are compared with the exact feedback linearizaton method.;The first objective for power systems is to design nonlinear excitation controllers for a multi-machine power system using Direct Feedback Linearization. The designed controllers, whose parameters are obtained, require the internal variables of the machines. These variables are verified by using a proposed internal variable identifying algorithm. The objective is to design nonlinear excitation controllers for power system stability enhancement. Spline techniques are used to approximate the nonlinear controllers obtained through feedback linearization by piecewise polynomials while enhancing the stability of the system