低阶被控过程含延迟的饱和最优PID控制器设计方法  

A Design Method of Saturated Optimal PID Controller for the Low-order Controlled Processes with Time Delay

作　　者：李先宏[1] 于海斌[1] 曾鹏[1] 苑明哲[1] 孙兰香[1] 

机构地区：[1]中国科学院沈阳自动化研究所工业控制网络与系统研究室,辽宁沈阳110016

出　　处：《信息与控制》2015年第1期43-50,共8页Information and Control

基　　金：中国科学院重要方向资助项目(KGCX2-EW-104)

摘　　要：实际控制器的输出信号是有界信号,即控制器输出饱和问题.针对控制器输出饱和问题,本文提出了低阶被控过程含延迟的一种饱和最优PID控制器设计方法.将控制误差及1阶、2阶、3阶微分项,及它们的混合项作为优化性能指标,建立了含有状态约束、稳定性及代数约束的非线性最优控制问题.应用共同李亚普诺夫函数定理与李亚普诺夫定理,约束最优控制问题被转化为非线性约束最优化问题,通过求解相应的非线性约束最优化问题,可获得饱和最优PID控制器参数.仿真结果表明了设计方法的可行性和有效性.In actual control systems, the controller＇s output signal is bounded, which is the controller＇s output satu- rated problem. This paper presents a design method of saturated optimal proportional integral derivative （PID） controller for low-order processes with time delay. The controller error, first-order error derivative, second-order error derivative, third-order error derivative, and their cross-items are used to calculate perform- ance index. Subsequently, a nonlinear optimal control problem with the state constraint, and stability and al- gebraic constraint is proposed. The constraint optimal control problem is transformed into the nonlinear con- straint optimization problem using common Lyapunov functions and Lyapunov theorems. Thus, the saturated optimal PID controller can be obtained by solving the nonlinear constraint optimization problem. The simula- tion results illustrate effectiveness and usefulness of the proposed design method.

关 键 词：控制器输出饱和问题 饱和最优PID(proportional INTEGRAL derivative)控制器约束最优控制问题 非线性约束最优化问题 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]