分别推导出了基于线性模型和非线性模型的水轮机调节系统闭环比例积分微分(proportional-integral-derivative，PID)控制的微分方程。以水轮发电机组转速偏差相对值的时间乘误差绝对值积分指标作为粒子群优化算法的适应度函数，分别实现了采用这2种不同数学模型的水轮机调速器PID参数的优化设计。计算结果表明，PSO优化算法对于非线性系统控制参数的优化设计是一种有效的方法；采用不同数学模型的水轮机调节系统，其PID参数的优化结果是不同的；水轮机调节系统采用非线性模型时的优化结果相对较好。

The differential equations of the closed-loop system with proportional-integral-derivative (PID) control law for hydro turbine regulating system based on linear model, as well as nonlinear model were deduced, respectively. Then, the integral of time multiplied by the absolute value of error (ITAE) performance criterion of hydro turbine speed relative error was applied as fitness function of particle swarm optimization (PSO) algorithm to optimize tuning hydro turbine governor PID gains based on different mathematical models. The calculating results indicate that PSO algorithm can effectively optimize the control parameters for nonlinear control system. Additionally, the optimized PID gains are different between linear model and nonlinear model. The results are relatively better if the nonlinear model is applied.

国家自然科学基金项目(60874013)；河海大学自然科学基金项目(2008429311)。