具有多个饱和非线性的系统分析与设计

提出了一种在状态空间中分析非线性系统的精确方法。对于具有多个非线性的分段线性系统来说，系统的状态空间被各非线性所对应的超平面分隔，系统在各超平面之间的状态轨迹可以用数值积分来求解，根据状态轨迹束穿过各超平面时截面之间的映射关系，可以分析是否存在自振荡。对于饱和非线性来说，给出了一种确定超平面的简便方法，因此本方法特别适合于分析具有多个饱和非线性的系统。最后给出了一个应用于高精度伺服系统设计的例子。

Analysis and design of systems with multiple saturation nonlinearities

A state space-based method for nonlinear system analysis is presented in this paper. For a piecewise linear dynamic system with multiple nonlinearities, the state space of the whole system is divided by hyperplanes of the corresponding nonlinearities. The state trajectory between the hyperplanes can be calculated by numerical integration.Based on the sequential mapping relationship of the cross-sections formed by the state trajectories with these hyperplanes, it is possible to determine whether or not a sustained oscillation is existantA simple method to construct the hyperplane for saturation nonlinearity is proposed. An example of application to a high precision servo design is also given.