In this paper we shall address the oscillation control problems in certain classes of non-linear systems whose outputs are required to follow their inputs. It is assumed that the non-linear systems can be well represented by a set of state-space equations and undergo Hopf bifurcation at some particular value of their parameters or their inputs. A simple first-order output feedback controller is proposed for oscillation control in these non-linear systems. First it is shown that in most cases the first-order controller is effective in locally stabilizing a second-order non-linear system which is undergoing Hopf bifurcation. Then a state separation method based on the solution of the associated Riccati equation is applied to the oscillation control of higher-order non-linear systems and a second-order approximated model is developed for the purpose of designing an oscillation controller. The closed-loop stability of the reduced-order model based design is analysed and some sufficient stability conditions are provided. Finally, a detailed application example of a stepper motor is given to show how the controller design method developed in this paper is applied to practical oscillation control problems.
International Journal of Control
Department of Systems and Computer Engineering

Cao, L. (Liyu), & Schwartz, H.M. (2002). Oscillation control in non-linear systems using a first-order filter. International Journal of Control, 75(18), 1504–1524. doi:10.1080/0020717021000032069