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.

中文翻译：

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分数阶水轮机调节系统与基于模糊PID的混沌控制共存吸引子

水轮机调节系统（FOHTGS）的分数阶模型是使用Grunwald-Letnikov（GL）方法得出的。此模型是使用其整数顺序开发的。研究了FOHTGS的动力学特性，例如平衡点及其稳定性，Hopf分叉和Lyapunov指数（LE）。研究了FOHTGS相对于系统分数阶变化及其参数的不同动力学。FOHTGS显示出多重稳定性和吸引子并存。为了支持多重稳定性的存在，提出了一些共存的吸引子。在水轮机调节系统（HTGS）中设计并提出了一种基于模糊PID的混沌控制算法。进行了数值模拟，以验证派生控制器的有效性。