Coexisting attractors in a fractional order hydro turbine governing system and fuzzy PID based chaos control
Karthikeyan Rajagopal, Hadi Jahanshahi, Sajad Jafari, Riessom Weldegiorgis, Anitha Karthikeyan, Prakash Duraisamy
Abstract
ABSTRACT A fractional order model of a hydro turbine governing system (FOHTGS) is derived using the Grunwald‐Letnikov's (GL) method. This model is developed using its integer order. Dynamical properties of FOHTGS, such as equilibrium point and its stability, Hopf bifurcation, and Lyapunov exponents (LEs) are investigated. Different dynamics of FOHTGS with respect to changing fractional order of the system and its parameter are studied. The FOHTGS shows multistability and coexisting attractors. To support the existence of multistability, some coexisting attractors are presented. A fuzzy PID based chaos control algorithm is designed and proposed in a hydro turbine governing system (HTGS). Numerical simulations are conducted to validate the effectiveness of the derived controller.