Nonlinear suppression using time-delayed controller to excited Van der Pol–Duffing oscillator: analytical solution techniques

Abstract To suppress the nonlinearity of an excited Van der Pol–Duffing oscillator (VdPD), time-delayed position and velocity are used throughout this study. The time delay is supplemental to prevent nonlinear vibration considered system. topic work extremely current because technologies with a have been subject several studies in latest days. classical homotopy perturbation method (HPM) utilized extract approximate systematic explanation for system at hand. Furthermore, modification HPM reveals more accurate solution. This accuracy tested through comparison numerical practical analytical methodology makes possible qualitatively evaluate results. histories obtained solutions drawn various values natural frequency parameters. Discussion results presented light plotted curves. On other hand, multiple scale procedure examines organized prototypical approach. influence diverse regulatory restrictions on organization’s performances explored. Two important cases resonance, sub-harmonic super-harmonic, examined according cubic nonlinearity. modulation equations achieved these graphically impact