Frequency Response based Adaptive Vibration Control of Nonlinear Systems∗

The problem of active vibration control for a class of nonlinear mechanical system is addressed. A recently developed nonlinear frequency response analysis technique is utilized for the vibrational analysis and controller design. Unlike the linear case, the nonlinear system oscillations are complex, which can be observed via the nonlinear Frequency Response Function (FRF). In order to achieve a satisfactory vibration attenuation, an adaptive tuning method based on the FRF, for selecting the controller gains is proposed. The proposed algorithm performs sufficiently well for a given range of input excitation magnitudes and frequencies. A physically motivated example is given to demonstrate the application of these results. Finally, the feasibility of the proposed algorithm in a satellite vibration control application has been examined.