Sensitivity analysis of the Nonlinear Integral Positive Position Feedback and Integral Resonant controllers on vibration suppression of nonlinear oscillatory systems

A new Nonlinear Integral Positive Position Feedback (NIPPF) approach and the Integral Resonant Control (IRC) method are implemented and analyzed for nonlinear vibration control. The performances of both controllers are compared to the Positive Position Feedback (PPF) method. A comprehensive form of the nonlinear feedback controller that includes all three approaches is considered for the closed-loop system; this form is then solved innovatively using the Method of Multiple Scales. The particular form of the modulation equations for each controller is obtained via the calculated comprehensive solution. Sensitivity analysis is performed on the controller parameters of each approach, and the influence of the parameters on the system response is studied. Results demonstrate that controller structure has the most salient role in the suppression performance. Even by selecting the optimal control parameters for each approach, improvements in the control performances are limited. The NIPPF controller delivers superior results compared to the other two approaches in the frequency and time domains. Using this approach, not only is the vibration amplitude at the exact resonant frequency sufficiently suppressed, but the subsequent peaks in the frequency domain are also reduced significantly compared to the PPF method.