【作者】 郎华威；

【导师】 杨建华；

【作者基本信息】 大连理工大学 ， 控制理论与控制工程， 2005， 硕士

【摘要】 测厚仪在板轧厚度控制系统中起着非常重要的监测作用,它的测量精度将直接影响产品的质量。原有同位素测厚仪存在着设备落后,监测系统功能不完善,测量精度不高,以及标定方法繁琐等不足。 本文主要从两个方面改进原有同位素测厚仪:一是完善监测系统,使之监测界面美观大方,监测功能多样化,测量操作简易方便;另一方面,改进原有的标定方法,简化标定过程,提高标定精度。 传统的标定方法主要是通过最小二乘法进行一般多项式的曲线拟合,这种方法的拟合精度受标定点的个数以及测量范围影响较大,不利于工作人员对测厚仪进行多次反复的标定工作。为了改进原有的标定方法,首先,本文对传统最小二乘法进行了改进,改进的最小二乘法是以相对误差的平方和最小为运算条件,可以提高拟合精度。其次,在测厚仪原理公式基础上,本文还提出了一个新的数学模型作为拟合函数,该数学模型主要是用两个补偿多项式对原理公式进行斜率和偏移的补偿,其拟合精度主要决定于标定片的精确度,受标定点数以及测量范围影响不大。在拟合过程中,为了方便计算,非线性拟合函数被分解成了三部分线性化的函数,分别为原理公式拟合,斜率补偿拟合,偏移补偿拟合,然后用改进的最小二乘法分别对每一部份函数依次进行线性曲线拟合,最终的结果为拟合结果。 仿真试验结果表明,这种曲线拟合方法受标定点的个数和测量范围影响小,在0.015cm-0.256cm测量范围内,用了4个标定点,可以使精度达到要求(±0.5%)。因此用这种方法进行标定,可以在减少标定点的基础上,保证标定的精度,使标定的工作变得简单,有利于测厚仪的测量精度保证。更多还原

【Abstract】 A thickness gauge plays an important role in the thickness measuring monitoring system, its measuring precision will influence product quality directly. The old isotope gauge has a lot of shortcoming, such as the unadvanced equipment, the imperfect monitoring system, the fussy calibration method and so on.The old gauge is mainly improved from two aspects. One side is that the monitoring system will be perfected, about the beautiful interface, the diversiform function, and the easy manipulation. On the other hand, the old calibrating method will be improved, simplifying the calibration process, improving the calibration precision.The polynomial curvefitting is a conventional calibrating method which is influenced seriously by the thickness range and the number of the standard plates, and makes calibration work trouble. For improving the old method, firstly, the least squares method is improved, and the improved method makes it a condition that the sum of the relative errors square is the least, which can improve the fitting precision. Next, a new mathematical model based on the theoretical mathematical mode is proposed and is regarded as the fitting function. The proposed mathematical model adds two compensation polynomials to compensate the theoretical mathematical model: one polynomial compensates slope, another compensates offset. During the fitting progress, the nonlinear fitting function is divided into three linear portions: the theoretical formula fitting, the slope compensation fitting, the offset compensation fitting. And then the improved least squares method is used to fit every linear function in turn.The simulation result shows that this method is influenced less by the thickness range and the number of the standard plates, the measuring precision can get between ±0.5% only by 4 standard plates in the thickness range from 0.015cm to 0.256cm. So using less standard dots to keep the better precision by this method is feasible, which simplifies calibrating work, and makes for ensuring the measuring precision.更多还原