Oscillation Control in Delayed Feedback Systems

The control of limit cycle oscillations is discussed for nonlinear delayed feedback systems. Through a center manifold reduction the effects of the control parameters on the periodic behavior are determined. The results are applied to the perturbed harmonic oscillator under the action of delayed feedback of position, which is a prototype system commonly arising in diverse biological and industrial settings. It is shown that, using a cubic feedback function, unwanted periodic solutions can be annihilated, and an asymptotically stable limit cycle can be created oscillating at an arbitrary prescribed amplitude. The frequency of the oscillations can also be controlled to a limited extent. The presence of the delay in the control signal turns out to be crucial for achieving these goals using position feedback .