Homework 10, due April 25, 2012

[goodwine]

Reading: Chapter 9 through section 9.6. Chapter 10, sections 10.1 and 10.2.

Exercises: 9.18, 10.15 numbers 1 and 4 only, and 10.16 for the same two transfer functions as 10.15.

[pat]

For the 10.15 problems, I am running into the problem that we discussed at the end of class today. I cannot get a 5% overshoot, even if I crank up k or move the pole farther to the left. How do we accomplish this? I tried moving the zero, but then the angle from the added pole to the desired pole is negative.

[goodwine]

For the 10.15 problems, I am running into the problem that we discussed at the end of class today. I cannot get a 5% overshoot, even if I crank up k or move the pole farther to the left. How do we accomplish this? I tried moving the zero, but then the angle from the added pole to the desired pole is negative.

You may do two things: 1) say "the best I can get using a lead compensator is XXXXXXX" or 2) use two lead compensators. Doing 1) is ok for full credit, but doing 2) is probably the best pedagogically.

[#epsilon_zen]

I was able to surpass the specifications with one lead compensator after tinkering around in Simulink, but the Simulink response didn't match up with root locus numbers generated from a manual transfer function/lead compensator script using the same values (zero @ -1, pole @ -40, k = 250). Visually, the Scope output in Simulink definitely beat the specifications, but the root locus plot from the script gave wildly different frequency and overshoot numbers for the same k value. Is there some reason this might happen or am I doing something very wrong?

[goodwine]

I was able to surpass the specifications with one lead compensator after tinkering around in Simulink, but the Simulink response didn't match up with root locus numbers generated from a manual transfer function/lead compensator script using the same values (zero @ -1, pole @ -40, k = 250). Visually, the Scope output in Simulink definitely beat the specifications, but the root locus plot from the script gave wildly different frequency and overshoot numbers for the same k value. Is there some reason this might happen or am I doing something very wrong?

Just like the poll question in class today: the zero from the lead compensator is affecting the response.

[Jessie]

when designing the compensator do we need to be able to compute the value of the additional pole by had or is guessing and checking with matlab acceptable?

[goodwine]

when designing the compensator do we need to be able to compute the value of the additional pole by had or is guessing and checking with matlab acceptable?

You can use matlab to iterate to it, but in the end show that the angle of G(s) = =/- 180 for the point the root locus goes through.

[goodwine]

When designing the lead compensators, the root locus I calculate, using a specific point which meets the specifications, does not actually include the point used to calculate it. My understanding is that the root locus should automatically include the point which it is designed around. What might be causing this? I am reasonably certain that all of my calculations are correct.

If your computations indicate that the angle of G(s) should be 180 for a point but the root locus plot doesn't go through there, then you must have a computational error. Basically, the root locus is the set of all points where angle G(s) = 180.

[Jessie]

how do you get the output from the transfer function to go back to the sum and to the scope at the same time in simulink?

[goodwine]

how do you get the output from the transfer function to go back to the sum and to the scope at the same time in simulink?

Go backwards, i.e., start at the comparator and then you can place the endpoint wherever you want, including along the arrow from the transfer function that goes to the scope.