基于Dark Aeyels定理的非线性PID控制稳定性分析

Stability Analysis for Nonlinear PID Control System Based on Dark Aeyels Theorem

针对非线性PID控制系统的稳定性提出一种工程近似判据。引入Dark Aeyels定理并进行了简要的分析;利用该定理对非线性PID控制器和线性PID控制器的稳定性进行了比较分析,得到了一个非线性PID控制系统稳定性的近似判据,该方法有效克服了常规稳定性分析方法的保守性;利用这一结果对PID控制参数进行了仿真检验,证明了判据的工程有效性。

An approximative and practical stability criterion is presented for nonlinear PID control system. The Dirk Aeyels stability theorem is introduced and some simple analysis is given firstly. Based on this theorem, a comparative stability analysis for the nonlinear PID controller and linear PID controller is investigated. As a result, an approximative stability criterion for nonlinear PID control system is deduced. This stability criterion overcomes the conservation when those conventional methods of the stability analysis are used. The PID control parameters are tested by simulation to verify this stability criterion and its engineering validity.