水轮机调节系统的非线性模型、PID控制及其Hopf分叉

通过理论分析提出了水机电系统的非线性模型，该模型具有物理意义清楚、便于理论分析和计算机计算处理的特点；在此基础上应用基于遗传算法的PID控制方法优化控制参数，仿真表明，对非线性模型获得的控制性能是令人满意的；以PID调节参数作为系统分叉参数，运用Hopf分叉存在性的直接代数判据对该非线性模型的Hopf分叉行为进行了分析和仿真，对于水电站中所观察到的持续振荡现象，文中结果可作为一种可能的理论解释。

THE NONLINEAR MODEL OF HYDRAULIC TURBINE GOVERNING SYSTEMS AND ITS PID CONTROL AND Hopf BIFURCATION

Based on the theoretical analysis, a nonlineamodel of hydraulic-mechanical-electro systems is presentedwhich has clear physical meanings and is easy to be analyzedtheoretically and calculated by computer. By using the GA-basedPID controller, the control parameters are optimized and thecontrol performances are improved according to the simulationsFinally, the direct algebra criterion about the existence of Hopbifurcation is used to investigate the bifurcation behavior of thenonlinear model which takes the PID parameters as thebifurcation ones. The simulations show that the results of thispaper can be considered as one of the explanations to sustainedoscillations recorded in hydroelectric power station.