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针对非完整约束系统的高非线性和强耦合性导致整个系统存在着动力学特性复杂及运动稳定性难以分析等问题,通过空间算子代数方法建立系统的动力学模型,在此基础上采用李雅普诺夫指数方法分析了系统的运动稳定性,建立了动力学参数与系统稳定性之间的量化关系.最后以小车倒立摆为例,对整个算法的有效性进行验证.该方法与李雅普诺夫第二法相比,主要优点在于其可构建性,并能够量化分析系统动力学参数与运动稳定性之间的关系,可为机械结构设计及控制系统优化提供参考.
Due to the high nonlinearity and strong coupling of the nonholonomic constrained system, the whole system has the problems of complex dynamics and difficult to analyze the stability of the motion. The dynamic model of the system is established by the space operator algebra method. Based on this, Nov index method is used to analyze the stability of the system and to establish the quantitative relationship between the dynamic parameters and the system stability.At last, the validity of the algorithm is verified by the example of the car inverted pendulum.The method is compared with Lyapunov Compared with the second method, the main advantage lies in its constructability and the quantitative analysis of the relationship between system dynamics parameters and motion stability, which can provide reference for mechanical structure design and control system optimization.