Abstract
This chapter discusses the sensitivity analysis of self-excited oscillations in nonlinear control systems. The need for useful method of analysis in the relative stability of self-excited oscillations and the transient response of nonlinear systems has been felt for a long time. The majority of studies investigated the stability and the response by subjecting the system to small perturbations of the sustained oscillations. The Krylov–Bogoliubov approach was used under certain restrictions in the study of the relative stability of self-excited oscillations. The application of this approach to the analysis of higher-order nonlinear control systems requires, however, the use of a graphical procedure that is usually cumbersome to perform. It is shown that by sensitivity analysis based on the modified Krylov–Bogoliubov approach, it is possible to obtain information about the relative stability of self-excited oscillations, and the transient response of nonlinear control systems. The proposed analytical procedure applies readily to the stability investigation of sustained oscillations.
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