旧文备份:热电偶/热电偶分度表生成

设计热电偶/热电阻式温度采集电路,将采集值转换成温度值是件麻烦事,因为其温度关系曲线不是线性的,可以近似看作高次方程曲线,而一般采集得到的数据都是用单片机来做温度值转换,让单片机去求解高次方程显然不现实,所以一般都是采用分段线性化的方法来计算温度值,这个分段方法技巧就不去介绍了,这里主要来探讨分段线性化对应表(分度表)的生成,网络上有不少这种表格,但是这种表格一般精度不高,而且不一定符合我们的分段要求,所以这里介绍程序生成分度表.以B型热电偶为例:

其温度-电压关系曲线方程为:



t90=c0+c1E+c2E+2+c3E+3…ciE+i

其中t90是温度值(计算所得),E是热电偶产生的电动势(采集所得),c是常量,下面是c的取值表:

 

温度范围:	250 to 700°C	700 to 1,820°C
电压范围:	291 to 2,431 m V	2,431 to 13,820 m V
c0	=	9.842 332 1 x 10+1	2.131 507 1 x 10+2
c1	=	6.997 150 0 x 10-1	2.851 050 4 x 10-1
c2	=	-8.476 530 4 x 10-4	-5.274 288 7 x 10-5
c3	=	1.005 264 4 x 10-6	9.916 080 4 x 10-9
c4	=	-8.334 595 2 x 10-10	-1.296 530 3 x 10-12
c5	=	4.550 854 2 x 10-13	1.119 587 0 x 10-16
c6	=	-1.552 303 7 x 10-16	-6.062 519 9 x 10-21
c7	=	2.988 675 0 x 10-20	1.866 169 6 x 10-25
c8	=	-2.474 286 0 x 10-24	-2.487 858 5 x 10-30
错误范围:	0.03 to -0.02°C	0.02 to -0.01°C

(表中如-2.474 286 0 x 10-24后面可是-24次方, -2.131 507 1 x 10+2后面是2次方)

下面是根据温度求电动势的逆方程:



E=c0+c1t90+c2t90+2….cit90+i

常量取值表如下:

温度范围:	0 to 630.615°C	630.615 to 1,820°C
c0= c1= c2= c3= c4= c5= c6= c7= c8=	0.000 000 000 0 .... -2.465 081 834 6 x10-1 5.904 042 117 1 x 10-3 -1.325 793 163 6 x 10-6 1.566 829 190 1 x 10-9 -1.694 452 924 0 x 10-12 6.229 034 709 4 x 10-16	-3.893 816 862 1 x 103 2.857 174 747 0 x 101 -8.488 510 478 5 x 10-2 1.578 528 016 4 x 10-4 -1.683 534 486 4 x 10-7 1.110 979 401 3 x 10-10 -4.451 543 103 3 x 10-14 9.897 564 082 1 x 10-18 -9.379 133 028 9 x 10-22

 

根据公式可以设计程序来完成计算,下面是一个计算分段为1摄氏度和1uV的小程序:

#include <math.h>

#include <stdio.h>

#define C00 0.0000

//0-630.615

#define C10 -2.4650818346e-1

#define C20 5.9040421171e-3

#define C30 -1.3257931636e-6

#define C40 1.5668291901e-9

#define C50 -1.6944529240e-12

#define C60 6.2290347094e-16

//630.615-1820

#define C01 -3893.8168621

#define C11 28.571747470

#define C21 -8.4885104785e-2

#define C31 1.5785280164e-4

#define C41 -1.6835344864e-7

#define C51 1.1109794013e-10

#define C61 -4.4515431033e-14

#define C71    9.8975640821e-18

#define C81 -9.3791330289e-22

//291-2431uV;250-700

#define C02 98.423321

#define C12 6.9971500e-1

#define C22 -8.4765304e-4

#define C32 1.0052644e-6

#define C42 -8.3345952e-10

#define C52 4.5508542e-13

#define C62 -1.5523037e-16

#define C72 2.9886750e-20

#define C82 -2.4742860e-24

//2431-13820uV;700-1820

#define C03 213.15071

#define C13 2.8510504e-1

#define C23 -5.2742887e-5

#define C33 9.9160804e-9

#define C43 -1.2965303e-12

#define C53 1.1195870e-16

#define C63 -6.0625199e-21

#define C73 1.8661696e-25

#define C83 -2.4878585e-30

int main(void)

{

    double t,e;//t=temperature e = electronictive force

    int i,j;

    for(i=0;i<631;i++)

    {

        t = (double)i;

        e = C00+C10*t+C20*t*t+C30*t*t*t+C40*t*t*t*t+C50*t*t*t*t*t+C60*t*t*t*t*t*t;

        printf("t = %g, e = %g\n",t,e);

 

    }

    printf("t from 0-630 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");    

for(i=631;i<1821;i++)

{

t = (double)i;

e = C01+C11*t+C21*t*t+C31*t*t*t+C41*t*t*t*t+C51*t*t*t*t*t+C61*t*t*t*t*t*t+C71*t*t*t*t*t*t*t+C81*t*t*t*t*t*t*t*t;

printf("t = %g, e = %g\n",t,e);

}

printf("t from 631-1820 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");

for(j=291;j<2432;j++)

{

e = (double)j;

t = C02+C12*e+C22*e*e+C32*e*e*e+C42*e*e*e*e+C52*e*e*e*e*e+C62*e*e*e*e*e*e+C72*e*e*e*e*e*e*e+C82*e*e*e*e*e*e*e*e;

printf("e = %g, t = %g\n",e,t);

}

    printf("t from 291- 2431 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");

for(j=2432;j<13821;j++)

{

e = (double)j;

t = C03+C13*e+C23*e*e+C33*e*e*e+C43*e*e*e*e+C53*e*e*e*e*e+C63*e*e*e*e*e*e+C73*e*e*e*e*e*e*e+C83*e*e*e*e*e*e*e*e;

printf("e = %g, t = %g\n",e,t);

}

     printf("t from 291- 2431 ended!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!\n");

}

对于热电阻,方法一样,公式为(PT100):



R=R0(1+AT+BT+2+CT+3(T-100))

R是采集的阻值,T是求得的温度值,R0=100, A = 3.90830 x 10 -3. B = -5.775 x 10 -7. C = 0 如果 T > 0 否则C= -4.183 x 10 -12.(注,那个-3是-3次方)

程序实现就略了,通过该公式开可以计算分段误差.

上面的程序在Linux下编译运行通过.其他类型的那些个公式可以在网上找到,曾经想做个小软件,用Qt写个界面,计算8种热电偶和几种热电阻的分度表,可以设置精度自动分段,可惜没时间.

(2007.1.25)