设计金属加热的控制策略,首先要获得金属导热体的开环系统模型.针对一个带有矩形孔的金属薄板上的热传导问题,采用PDE Toolbox进行求解和仿真,并用最小二乘方法进行热传导系统的建模与仿真,以获得模型中的参数.将此参数与求解微分方程方法所得到的数据进行对比,结果表明,采用最小二乘法可以更清楚地了解金属板的外部特性,并获得输入输出信号的差分方程,而求解微分方程的方法则显示了金属板的内部特性,两种方法是等效的.%To design the control strategy for heating metal, the open loop system model of the metal heat conductor shall be obtained first. Aiming at the heat conduction issue of the metal sheet with rectangular hole, the solution and simulation are conducted by adopting PDE Toolbox;and modeling and simulation of the heat conduction system are completed with the least square method for getting parameters of the model. Comparing the data obtained from the model and resolving the differential equation, it is shown that by using the least square method, exterior characteristics of the metal sheet can be learnt more clearer, thus the difference equations of the input and output signals can be obtained, while the resolving method reveal its interior characteristics, both methods are equivalent.
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