Dynamical behavior and Poincare section of fractional-order centrifugal governor system

The dynamic behavior of a fractional governor system is studied in this paper. The Stability and bifurcation of the equilibrium points of the system are investigated. We derive specific conditions for which the Hopf bifurcation of the fractional governor system may occur. It can be seen that different results are obtained compared to the classical mode. In the non-autonomous system, the tendency towards chaos is investigated using diagrams of bifurcation and Poincare maps analysis. Finally, the numerical results are given to illustrate the theoretical results. Analytical and numerical simulations result could be extended to other systems and ultimately, these results could be applied as a technical tool for the control and rotary machine designers. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the dynamic behavior of a fractional governor system, studying its stability, bifurcation, and Hopf bifurcation conditions. The results obtained differ from classical models, and chaos tendency in non-autonomous systems is explored using bifurcation diagrams and Poincare maps analysis. Numerical results are provided to illustrate theoretical findings, which can be applied as technical tools for control and rotary machine designers.