Program a spreadsheet to calculate the controller output, system output, and contributions of the PID

components.

Create columns:

A$)$ Time increment, $t_i$

B$)U(t_i)$

C$)U(t_i)$

D$)E(t_i)$

E$)$ Integral control component

F$)E(t_i)$

G$)$ Proportional control component

H$)[E(t_i)]$

I$)$ Derivative control component

J$)Y(t_i)$

K$)($empty column$)$

Create a small table $($columns $L$&$M)$ to the right side for constants:

$I=1$

$h=0\mathrm{.}4$

$P=0\mathrm{.}5$

$D_g=0\mathrm{.}01$

$R=100$

Using the equations shown above, program the spreadsheet to calculate up to $i=44($note that your

first line of "true" calculations will occur at $t_i=2$ since this is a feedback system$).$

$)$

Create a chart with Time on the ordinate axis and Feed Rate on the coordinate axis and graph the

functions $U(t_i),E(t_i),$ and $Y(t_i).$ This displays your output, plant, and error.

Create a chart with Time on the ordinate axis and Component Value on the left coordinate axis and

Feed Rate on the right coordinate axis. Graph the integral, proportional, and derivative components and

the feed rate, both versus time. This displays the contributions of each component of PID control.

Print the charts from Parts $(4)$ and $(5),$ each on a separate $8-\frac{1}{2}"11"$ paper, and compose a one

paragraph summary of how PID can be used to automate processes.