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

• Published in: Journal of the Franklin Institute 2017-10, Vol.354 (15), p.6651-6671
• Main Authors: Kuo, Chi-Wei, Suh, C. Steve
• Format: Article
• Language: English
• Subjects: Control systems design; Dynamic response; Feedback control systems; Fuzzy control; Fuzzy logic; Motion stability; Nonlinear feedback; Response time; Spectral sensitivity; Studies
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2017.08.023

•Linearization inevitably makes all inherent nonlinear effects inconspicuous.•Linearization of the time-delayed feedback oscillator conceals the underlying transition from bifurcation to chaos.•Control of the non-autonomous system is achieved by considering time and frequency responses simultaneously.•Time-frequency control renders unconditional stationarity and quasi-periodic stability.•PID and fuzzy logic controllers induce a high frequency component indicative of instability. 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.