In the process of optimizing the automatic generation control (AGC) of steam turbines using single-parameter bifurcation tools, steam flow-induced vibrations cause irregular rotor motion trajectories and high dynamic uncertainty, resulting in poor stability of steam turbine units. To solve this problem, this paper proposes a chaotic motion suppression control method for steam turbines that integrates binary genetic parameter tuning and Runge-Kutta numerical solution. Differential equations are constructed for the chaotic dynamic system of steam turbines to accurately describe the dynamic characteristics of rotor chaotic motion. The Runge-Kutta method is adopted to solve the equations, and the binary genetic algorithm is used to simulate natural selection and genetic mechanisms for global optimization in the parameter space. Parameter combinations close to the optimal values are obtained, which synchronously improves the precision of parameter tuning and optimization speed and optimizes the chaotic motion control effect. Experimental results show that the proposed strategy can convert the chaotic motion of steam turbine rotors into stable periodic motion, significantly reduce motion uncertainty, and improve the operational stability of steam turbines.