A case of mitigating non-autonomous time-delayed system with cubic order feedback

Time-delayed feedback of a small magnitude can perturb a system to exhibit complex dynamical responses including route-to-chaos. Such motions are harmful as they negatively impact the stability and thus output quality. A non-autonomous time-delayed oscillator having several higher order nonlinear feedback terms is investigated using a novel concept featuring simultaneous control of displacement in the time-domain and spectral response in the frequency-domain. The concept is explored to formulate a control methodology feasible for the mitigation of the non-autonomous time-delayed feedback system. Because the control concept does not require linearization, the true dynamics of the non-autonomous delayed feedback system is faithfully preserved and properly construed in the control action. The validity of the controller design is demonstrated by evaluating its performance against PID and fuzzy logic in controlling displacement and frequency responses with the most chaotic dynamic response time-delay parameters.