To reveal the mechanism of the friction torque on the system stability, the system nonlinear coupled dynamic model is established based on the Lagrange–Maxwell equation, in which the influence of electromechanical parameters and terminal load is considered. The end friction torque is selected as the bifurcation parameter, and its influence on the system stability is studied. At the same time, in order to reduce the impact of the end friction torque on the stability of the system, from the electrical point of view, the motor q-axis voltage is selected as the control variable to construct a nonlinear state feedback controller to improve the stability of the system. In the process of building the controller, the sufficient and necessary conditions for the dynamic Hopf bifurcation and the type of system bifurcation are determined, and the system controller parameters are determined. Through numerical simulation verification, it is found that the designed controller has a better control effect, which provides a reference for practical applications.

为揭示摩擦力矩对系统稳定性的作用机理，基于拉格朗日-麦克斯韦方程建立系统非线性耦合动力学模型，考虑机电参数和终端负载的影响。选取端部摩擦力矩作为分岔参数，研究其对系统稳定性的影响。同时，为了减小端部摩擦力矩对系统稳定性的影响，从电学角度选取电机q轴电压作为控制变量，构建非线性状态反馈控制器，提高系统的稳定性。在构建控制器的过程中，确定了动态Hopf分岔的充要条件和系统分岔的类型，并确定系统控制器参数。通过数值仿真验证，发现所设计的控制器具有较好的控制效果，为实际应用提供了参考。