非线性模型经P控制后的奇异性分析*

对于一类开环具有三个定态的非线性系统,应用三阶台劳级数近似表达式足以揭示经P控制后的闭环系统的奇异特性。特别当设定点是拐点时,闭环系统的定态解分支呈音叉型分枝特性。此方法能减少计算工作量,亦能揭示设定的误差所引起闭环系统定态解分枝的分裂现象。这样的简化模型有利于反应器的设计和调节。

Singularity Characteristics of a Nonlinear System Under Conventional P Control

For a nonlinear system with three steady states, the third order Taylor expansion of original system is enough to reveal closed-loop singularity under P control. If setpoint has inflection point characteristics during open-loop operation, pitch fork singularity can be viewed during closed-loop operation. Moreover, set-point error results in splitting phenomenon in closed-loop system. The technique and all the results in this paper are beneficial to controller design and regulation.