Next, you can choose to set up the MATLAB code in a few different ways. First make sure that both the numerator and denominator are in acceptable forms.

[1 2 3] is the same as saying

Using an example:

We can write the numerator and denominator MATLAB codes as:

>>numerator=[1];

>>denominator=[1 8];

For a more complex problem we can bypass the long and tedious expansion process and use the convolution function in MATLAB.

Here, the denominator is also represented by (s+1)*(s+3+3j)*(s+3-3j). Being three seperate parts, we can use convolution once for two of them, then use convolution again with the remaining part. Just look at the example:

conv( A , conv( B , C ) )  —> denominator = conv( [1 1], conv( [1 3+3*j], [1 3-3*j] ) );

After we define our numerator and denominator in MATLAB, we can use the root locus function then set our axis parameters as follows.

>>rlocus( numerator, denominator )

>>axis([-10 10 -10 10])

Your plot should look similar to the following for this example:

RULE 1:

This is a scalar product that is equal to the two magnitudes multiplied together and multiplied by the cosine of the angle between them.  If  the two vectors are perpendicular to each other then the angle between them is 90 degrees, which will make the dot product equal zero.  This is an equivalent equation.

RULE 2:

When you finish your dot product, you should have a number, not a directional vector.  So if you get something like this you did something wrong: .  If you ended up with (any #) then you don’t have to completely rule out your answer.

A few vectors to practice with:

Okay, now we have found our dot product by applying RULE 2 above.  We can use this value along with our individual vector magnitudes to apply RULE 1 and obtain the angle .

We can calculate the projection of the vector A onto the vector B by this relationship:

Note that this is a scalar quantity, and that we can also define the projection of B onto vector A in a similar fashion:

Perform a dot product in MATLAB like so:

>>A = [ 1 2 3];

>>B = [2 3 4];

>>dot(A,B)

Enjoy

Vector

In MATLAB: >>A = [1 2 4];

Vector

In MATLAB: >>B = [2 3 4];

When you add vectors together, you add each individual directional component ().  Subtraction works the exact same way.  Lets go ahead and do a few, C will represent the vector that results from the addition and subtraction.

These vectors are all in 3-dimensional space with a X, Y and Z component.  The number in front of each directional component is the weight or magnitude of that particular directional component of the vector.  There it is, short and sweet

rmax = 1;
V = 0;
step = 0.02;
A = 5;

B = 10;
C = 15;
for x= -5 : step : 5
for y = -10 : step : 10
for z = -15 : step : 15
if((x/A).^2 + (y/B).^2 + (z/C).^2) < rmax
V = V + step.^3;
end
end
end
end
disp(V)

it should spit out , approximately