Nonlinear vibration suppression of flexible structures using nonlinear modified positive position feedback approach

This paper introduces Nonlinear Modified Positive Position Feedback (NMPPF) control approach for nonlinear vibration suppression at primary resonance. Nonlinearity in the system is due to large deformations caused by high-amplitude disturbances, while this control approach is applicable to all types of nonlinearities in resonant structures. NMPPF controller consists of a resonant second-order nonlinear compensator, which is enhanced by a lossy integrating compensator. The two compensators create a combination of exponential and periodic control inputs, which needs innovative time scaling for using the Method of Multiple Scales to obtain the analytical solution of the closed-loop system. The results of the analytical solution for the closed-loop NMPPF controller are presented and compared with the result of the conventional PPF controller. Effects of the control parameters on the system response are comprehensively studied by parameter variations. The approximate solution is then verified using numerical simulations. According to the results, the NMPPF controller provides a higher level of suppression in the overall frequency domain, as the peak amplitude at the neighborhood frequencies of the primary mode is reduced by 44 %, compared to the PPF method. The tunable control parameters also give more flexibility to create the expected type of system response.