一类抛物型分布参数系统的边界控制

Boundary Control for a Class of Parabolic Distributed Parameter Systems

利用经典李对称理论,研究一类抛物型分布参数系统的边界控制问题,分别设计开环和闭环形式的边界控制律,实现系统状态的定态控制。借助于无穷小生成元作为分析工具,应用微分方程的不变性条件,确定系统经典李对称的具体表示形式,即其所对应的无穷小生成元表达式。之后,分别针对开环和闭环控制结构,设计出系统解析形式的边界控制条件。通过设定系统参数、初始条件和控制目标,开环和闭环边界控制都能实现设定的控制要求。相比较而言,开环控制的输出误差收敛速度较慢;闭环控制收敛速度较快,不过入口附近有无法完全避免的超调现象。提供的研究结果,对于一类包含传导和对流特性的温度或浓度模型的定态控制问题有一定指导意义。

Using classical Lie symmetry theory, boundary control for a class of parabolic distributed parameter systems has been stud- ied, and the control laws on open loop and closed loop have been designed to control the system reaching the fixed stationary state. By means of infinitesimal generators and invariance condition, the analytic control conditions on open loop and closed loop are presented af- ter having the classical Lie symmetry of the system, which is expressed by infinitesimal generators. The control purpose can be satisfied under the two types of control laws by setting system parameters, initial condition and control purpose ahead. Comparatively, from the simulation, the convergence of output error under open loop control is slower than that under closed loop control, and however there are overshoot phenomena nearby the intake under closed loop control. The resuh proposed in the paper can be applied for controlling a class of temperature or concentration models with conduction and convention characteristics.