非线性系统的线性化

由于非线性系统线性化时采用泰勒展开式可能会得出错误的结果,指出了系统的线性化应该是在方程式推导过程中同时进行.对磁悬浮系统,在拉格朗日方程建立过程中求取相应的偏导数从而得出系统的线性化方程.给出了用Simulink的非线性系统仿真方法,并用非线性系统在小偏差下的仿真结果与线性化系统的结果进行对比.结果表明,这样的求取过程物理概念清楚、简单,有助于正确列写系统的方程式.

Linearization of a nonlinear system

If the linearizafion of a nonlinear system is carried out simply by using the Taylor series, sult may be incorrect. It was pointed out that the linearization must be carried out simultaneously the re during the derivation of the system equations. An electromagnetic levitation system was used as an example. It was shown that during the establishment of the Lagrange equations the relevant partial derivatives must be taken as constant values at the equilibrium point. A Simulink simulation method for nonlinear systems was also proposed. And the nonlinear simulation under small deviation was then used to verify the linearization process by comparison with the simulation results of the linearized system. It shows that the method is clear in physical meanings, simple, and is helpful for establishment of a correct system model.