Nonlinear Vibration Control of Flexible Structures Using Nonlinear Modified Positive Position Feedback Approach

A new Nonlinear Modified Positive Position Feedback (NMPPF) controller is proposed in this paper to suppress the nonlinear resonant vibrations in flexible structures. The NMPPF uses a nonlinear second-order feedback compensator to overcome the vibrations at exact primary resonance frequency, and a first-order integrating term to lower the remaining peak amplitudes in the frequency domain. For the closed-loop system, an innovative implementation of the Method of Multiple Scales is employed to obtain the modulation equations. Results demonstrate the superior performance of the NMPPF controller compared to the conventional approach i.e. Positive Position Feedback (PPF), as the suppression performance is improved by 62% in the peak amplitude reduction. The presented parameter analysis of the NMPPF controller also proposes the optimal controller parameters to provide the highest suppression level in the nonlinear oscillatory system.