Analysis of Control Relevant Coupled Nonlinear Oscillatory Systems

The paper proposes and analyzes two prototype structures of coupled generalized van der Pol equations able to describe self-excitation of simultaneous oscillations with distinct frequencies. These structures are relevant for describing oscillations phenomena which may be encountered on systems subject to control. These structures are analyzed using the Krylov-Bogoliubov averaging method. This analysis allows to establish conditions for the occurrence of the various operation regimes. The usefulness of the results is illustrated by their application to the straightforward analysis of the properties of a combustion instability model. keywords nonlinear oscillating systems, van der Pol equation, coupled oscillators, Krylov-Bogoliubov method.