Spline-based nonlinear controller for the Duffing oscillator

The forced Dulling oscillator is a mathematical model of the nonlinear pendulum. It is formulated by a second-order, nonlinear, nonautonomous, ordinary differential equation. First, a review of designing a nonlinear controller with an exact feedback linearization method is given. Then a 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 for example linear, quadratic and cubic. The cubic spline allows each segment to have a unique cubic polynomial while constraining the curve fit to the data properties. Controller efforts for different orders of polynomial interpolants and power spectral densities of the controller signals are compared with the exact feedback linearization method.