Notch filter feedback control of a chaotic system

A recent method for suppressing chaos uses time-varying perturbations in accessible system parameters. A new method is presented using a notch filter output feedback, with fixed controller parameters and without affecting the original system parameters. The motivation for using a notch filter in the feedback is to disturb the balance of power dynamically at the lower end of the participating frequencies in the power spectrum. To select the controller parameters, both a harmonic balance method and a numerical optimal parameter selection scheme are presented to choose the notch filter parameters to achieve desired k-period motions. The procedures are tested on Duffing's oscillator with a notch filter feedback. It is shown that not only can chaotic motion be transformed into k-period motion, but also that the resulting controller is robust with respect to changes in the forcing amplitude.