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DO YOU EXCEL IN ELECTRONICS?

Part 3: The Bottom Line
by Aubrey Kagan

Start ý Calculating The Odds ý Strange Occurrences ý Can You Relate? ý Nothing Up My Sleeve ý Source and PDF

CAN YOU RELATE?

Regression is a technique derived from statistical applications where you try to find a linear relationship between a single output and several inputs. Statistically, this may be a method of predicting the performance of an athlete based on his weight, height, and foot size. An engineering application may be predicting the angular speed of a motor driving a water impeller based on the control signal and the fluid pressure.

Often the relationship is not known, but you can empirically measure the output for a given input. Letýs assume your application is to control the above pump though a PWM signal that can be adjusted from 0% to 100%. Also assume that the fluid pressure has a negligible effect on the revolutions per minute of the motor. Youýd apply the PWM signal to the motor and measure the revolutions per minute for different PWM inputs. Example6a.xls (download Excel files ) shows some fictitious results (see Photo 2). I have also added a graph to compare the prices (download Example9a.xls from Excel files ).

To use the regression for a linear relationship, make sure you click in the spreadsheet away from the graph. Go to Tools/Data Analysis, scroll down, and select Regression. Enter the data as shown in Photo 3. The y-axis is the dependent range, and the x-axis is the independent variable. The output range will put all the results on the same page.

On completion, the results appear as shown in Photo 4. Looking at cells C32 and C33, it is apparent that the linear formula is rpm = 129.3 ý PWM ý 2655. I added the calculation in column D (see Example9b.xls (download Excel files)) in order to add the line on the graph (=$C$33*A5+$C$32 in cell D5 and so on). Photo 5 shows the resultant line with the original curve.

It may be that the linear relationship is OK to the first approximation, so you can leave it at that. Between you, me, and the lamppost, I derived the revolutions per minute from a quadratic equation, rpm = 1.2 ý PWM² ý 2.7 ý PWM ý 15.

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