Graphical Data Representation$-$ Histogram $$ Normal Distribution

To create a histogram from a simulation of a normal distribution, the randn function is needed. The

format is as follows:

Variable$\_$name $=$ mu$+$sigma$*$randn$([$array$])$

ESET $329$ Six Sigma and Applied Statistics

where mu is the mean and sigma is the standard deviation. This variable will act as your frequency axis,

or as vector Y$,$ for your histogram. The function for plotting the histogram on MATLAB is hist$($Y$,$X$).$ X$,$ in

this case, will be the individual range of your frequencies. This is defined as a vector with constant

spacing.

$1.$ With this in mind, plot a histogram with the following constraints:

A $50$ x $1$ randomly generated array with a mean of $1($mu$)$ and a standard deviation of $2\mathrm{.}5$

$($sigma$),$ and a bin width array that increments by one from $-8$ to $8.$

Save your $.$m file with your initials as $$Lab$2\_$MATLAB$\_$Initials$$ and save the histogram figure as a

separate image file. Does this graph look symmetrically bell$-$shaped, or normal?

$2.$ Now change the number $50$ to $5000$ and repeat the same steps. Compare the histogram with the

one you get the step $1.$ Does this graph look symmetrically bell$-$shaped, or normal?

Simulink$-$simulation for dynamic systems such as motors

$1.$ Run a model in Simulink

$$ Copy the Simulink model DCPMmotorNonParametrized from eCampus to the Current

Folder window in MATLAB. In the Current Folder double click the file

DCPMmotorNonParametrized. Exam the values for parameters such as Jinv, Vbatt, and

Linv by double clicking the corresponding blocks. For example, double click on the Jinv

gain block, you will find the Gain is defined as $1/0\mathrm{.}042.$

$$ Click the green Run button, then double click the Scope and Scope$1$ blocks to look at the

motor current and motor speed.

$$ Try to zoom in$/$out and change the scale X$/$Y axes limits

ESET $329$ Six Sigma and Applied Statistics

Fig. $1.$ Motor speed trace

$2.$ Run a model from an $.$m file

Copy the file $$MfileforSimulink$.$m$$ from eCampus to the Current Folder of MATLAB, then double

click it in the Current Folder. You should see the m file open with lines of codes. Read the code

and try to understand what each line does. Use help command$\_$name in the command window

to read the documentation $($For example, help sim, help plot, help figure$).$

Explore the Simulink model by double clicking DCPMmotor in the Current Folder and then

double clicking each block in it$.$ Do you find the value for the parameter in each block?

Now run the mfile MfileforSimulink.m$.$ You should see plots.

Set all the parameters, such as Linv, Jinv, etc., in these two methods to be the same, then you

have the same result from these two methods. The mfile method allows the user to easily

change parameters and rerun the model. For example, you can add code to the m file so that a

for loop is created to change parameter values.

$3.$ Use the mfile to plot the steady$-$state speed $($the limit of the speed when time goes to infinity$)$ as

a function of the voltage applied $($Vbatt$).$

First define a voltage vector: Vbatt$\_$i$=[6$:$0\mathrm{.}5$:$14]$;

Then create a for loop:

for i$=1$:N$,$

Vbatt$=$Vbatt$\_$i$(1,$i$)$;

$[$T$,$X$,$Y$]=$sim$(\text{'}$DCPMmotor$.$mdl$\text{'},[0$:$0\mathrm{.}02$:$3])$;

Vbatt$\_$j$($i$,1)=$ Vbatt;

Speed$1($i$,1)=$max $($Y$($:$,1))$;

end

figure$(3)$

plot$($Vbatt$\_$j$,$ Speed$1)$

grid on

Test your code with N $=4.$ If your code works as you expected, insert the following before the for

loop:

N$=$size$($Vbatt$\_$i$)$;

N$=$N$(2)$;

Change the values of the second and third parameters in

sim$(\text{'}$DCPMmotor$.$mdl$\text{'},[0$:$0\mathrm{.}02$:$3])$

$($Try $[0$:$0\mathrm{.}001$:$3],[0$:$0\mathrm{.}1$:$3],[0$:$0\mathrm{.}01$:$0\mathrm{.}1],$ and other values. Discuss what you observed in the two

scopes.$)$