Local Bifurcation Analysis of One Parameter in the Greitzer's Model with a General Compressor Characteristic

Based on the Greitzer's reduced model, an analytical study on the instabilities phenomena of the operating point is presented using some basic properties of the nonlinear dynamic system. Moreover, a proposal of a general compressor characteristic curve, that suits the stationary system, is given. The Routh-Hurwitz theorem is applied to determine the stability conditions on the model parameters. An analysis along with a discussion is presented when the compression system goes to the Hopf bifurcation point during surge. For the Hopf bifurcation case, an approximate expression, for the periodic cycle of the system's solution from the equilibrium point, is obtained and the direction is determined using Lyapunov's stability theory. A numerical simulation is executed to illustrate the theoretical results.

Automated summary

Based on the Greitzer's simplified model, this article presents an analytical study on the instability phenomena of the operating point using fundamental properties of nonlinear dynamic systems. Furthermore, a general compressor characteristic curve suitable for stationary systems is proposed. The stability conditions of the model parameters are determined using the Routh-Hurwitz theorem. A numerical simulation is conducted to illustrate the theoretical results.