Nonlinear feedback anti-control of limit cycle and chaos in a mechanical oscillator: theory and experiment

Abstract

Though engineers believe that self-excited oscillation and chaos is detrimental, recent research has revealed that self-excited periodic and chaotic oscillation can be effectively utilized in many engineering processes and devices for significant benefits. Then a simple nonlinear acceleration feedback controller is proposed to generate self-excited periodic and chaotic oscillation in a mechanical oscillator. Analytical expressions relating the amplitude of limit cycles and control parameters are obtained by the method of multiple time scales. Analytical results are verified by numerical simulations performed in MATLAB–SIMULINK. Existence of chaotic oscillations is confirmed by numerical simulations. An extensive parametric study is carried out to reveal the nature of the chaotic oscillations and its dependence on the controller parameters. Theoretical results are finally verified by experiments. It is generally observed that the same controller can be used to induce both periodic and chaotic oscillations just by flipping the phase of the controller. This is possibly the first example where the same controller can be utilized to generate periodic and chaotic oscillation in a mechanical system. The findings of the paper are believed to be used in macro- and micro-mechanical systems.