Notch filter feedback control of a chaotic system

Understanding chaotic motion has become an important challenge in the research community due to its complexity and recently found wide variety of applications. The motion can sometimes be desirable or undesirable, and hence control over such a phenomenon has become an issue in the literature. Currently available methods involve making systematic time-varying small perturbations in the accessible system parameters. A new method, which uses a notch filter output feedback, is presented here to achieve control over chaotic motion. The notch filter controller uses an active negative feedback with fixed controller parameters instead of time variation of the original system parameters.;A notch filter is a linear device which eliminates a single frequency from the input signal. 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. The harmonic balance method is used to show that a single participating frequency can indeed be eliminated. To deal with relatively complex nonlinear plants, a numerical optimal parameter selection scheme is presented to choose the notch filter parameters. It is shown that the notch filter controller can be used not only to eliminate chaos but also to achieve a desired periodic motion. In addition, the notch filter parameters remain fixed at all times while the controller is on.;The notch filter controller is used to eliminate chaos from a dynamically rich nonlinear system, a harmonically forced Duffing's oscillator. A detailed study of notch filter parameters is presented. Notch filter parameters are presented for different periodic motions with periods up to ten times the forcing period.