by Katie Lilienkamp, (c)2000
You can review this by following the link for
hw5 Notes on the Problem Sets webpage for 2.010.
- Post-Quiz #1 Comments (Solutions to the quiz will be available on the psets webpage some time
AFTER it is returned on Tuesday, October 24.)
*** The main NEW IDEA covered this term (but not fully understood for the quiz) was, I think:
You have a PROPORTIONAL controller (C(s)=G) and some particular open-loop system.
(The open loop results from 'cutting' the feedback loop and getting
the transfer function (TF) for one circuit through the cut loop).
You are asked to study the relationship between the value of 'G' and the pole locations (and thus the stability) of the resulting close-loop system.
Specifically, you can look visually at the Bode plot of
an OPEN-LOOP system to predict the stability of the
CLOSED-LOOP system which would result from 'closing the loop'. (For our
standard control system model with C(s), P(s) and M(s), the open-loop transfer
function has been defined as "C(s)*P(s)*M(s)".)
Oh yeah, and in case I forgot to mention it, the MAIN IDEA people had probably not
fully grasped for Quiz #1 is that you can LOOK AT AN OPEN-LOOP BODE PLOT to predict the
range of G values valid for stability of the CLOSED-LOOP system that results from closing this loop.
Changing G just shifts the y-axis of the open-loop MAGNITUDE plot (without changing the PHASE plot at all)
You just ensure the gain is below 0dB whereever the phase has dropped below -180 degrees.
Yes, this involves GAIN MARGIN stuff...
I'm distributing some drill problems Tuesday, in class and on the web, to better explain this point.
This was (in my opinion) clearly the essential point in all problems in HW #3 (the
last assignment on which quiz #1 was based). Sorry I didn't explain this all more clearly
to everyone, but I'm going to attempt to get the point across more directly with the practice
problems. (These drill problems won't be graded; in fact, I'm giving them out with solutions attached.)
* WARNING* : Any (inadvertant) mis-information on these pages is your responsibility to catch (if you use it on problem sets, etc).
Double-check (for errors) whatever you find here!