10. Using Nonlinearity for Output Vibration Suppression: An Application Study

A frequency domain approach to the analysis and design of nonlinear feedback controller for suppressing periodic disturbances is studied and some preliminary results in this subject are provided by applying the theory and method established before. Although there are already some time-domain methods, which can address nonlinear control problems based on Lyapunov stability theory, few results are available for analysis and design of a nonlinear feedback controller in the frequency domain to achieve a desired frequency domain performance. Based on the analytical relationship between system output spectrum and controller parameters defined by the OFRF, this chapter demonstrates a systematic frequency domain approach to exploiting the potential advantage of nonlinearities to achieve a desired output frequency domain performance for the analysis and design of vibration systems. Compared with other existing methods for the same purposes, the method in this chapter can directly relate the nonlinear parameters of interest to the system output frequency response and the designed controller may also be realized by a passive unite in practice.