## Homework 10, due April 20, 2005.

Due Wednesday, April 20, 2005.
goodwine
Posts: 1596
Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
Contact:

### Homework 10, due April 20, 2005.

1. Find the transfer function Y(s)/R(s) for the following block diagram.
• 2. Find the transfer function Y(s)/R(s) for the following block diagram.
• 3. Consider the block diagram illustrated in the following figure.
• Compute the step response of the system (i.e., find y(t) assuming R(s)=1/s) for the following values of a and b and verify the answer using the matlab step() command. Hint: it is easiest to do the partial fraction expansion using the variables a and b and then substituting the values instead of computing a partial fraction expansion multiple times.
1. a = -1, b = 1;
2. a = -2, b = 1;
3. a = -1, b = 2; and,
4. a = 1, b = 1.
What general conclusions can you draw regarding the effect of changing a and b?
4. Consider the block diagram in the following figure.
• Compute the step response of the system for the following values of a and b and verify your answer using the matlab step() command:
1. a = -1, b = 1;
2. a = 1, b = 1;
3. a = -1, b = -1; and,
4. a = 1, b = -1.
What general conclusions can you draw regarding the effect of changing a and b?
5. For the transfer function in problem 4 let a=-1 and b=-3. Compute the partial fraction expansion by hand and plot the three terms in the response (the term due to A/s, the term due to B/(s-a) and the term due to C/(s-b)) and verify that the response from the step() command is the sum of these three terms.
Last edited by goodwine on Thu Jun 15, 2006 4:17 pm, edited 4 times in total.
mightyduck
For number 4, letters a) and d) contain the same values for a and b. I'm assuming d) should be a = 1 and b = -1??
goodwine
Posts: 1596
Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
Contact:
mightyduck wrote:For number 4, letters a) and d) contain the same values for a and b. I'm assuming d) should be a = 1 and b = -1??
Yes. Thanks.
Bill Goodwine, 376 Fitzpatrick
kp316
For problem 4, parts b & c, I am finding that the denominators of several of the y(t) terms are zero, which makes little sense to me. If a and b are the same then isn't 1/(a^2 - ab) undefined? I don't know if I'm missing the point to this problem or what, but if someone could point me in the right direction it would be much appreciated.
goodwine
Posts: 1596
Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
Contact:
kp316 wrote:For problem 4, parts b & c, I am finding that the denominators of several of the y(t) terms are zero, which makes little sense to me. If a and b are the same then isn't 1/(a^2 - ab) undefined? I don't know if I'm missing the point to this problem or what, but if someone could point me in the right direction it would be much appreciated.
If a=b you can't use the partial fractions that I did in class since there was a division by (a-b) or (b-a) at some point in it.

If a=b you need to partial fraction

A/s + (Bs+C)/(s+a)^2 = 1/(s(s+a)^2).

You can either do it twice with the numbers substituted, or try it with just an a or b so you only have to do it once, but I'm not sure how bad the algebra gets in the latter case.
Bill Goodwine, 376 Fitzpatrick
NDChevy07

### step function

I went to do the step function analysis on Matlab and it said that there is not function called step.m???
goodwine