EN123 2002 Feedback Quiz #2: Take Home Honor System

name________________________________ 

Take an hour to try to answer the question below:
do not discuss with fellow students or any so-called Automatic Control Experts.
Consult any reference you like, including the EN123 archive website,
the EN166 website, and the supplemental notes on feedback on the main 123 index.

Your answer is due by noon, Thurs Dec 5, 2002.
Bring the test to my office, rm 355 B&H; hand it to me or slip it under the door.
For credit you must show some work, and derive the correct answer.

Study the feedback diagram below, where L is an external load.

Your problem: Find an expression for OUT(s) such that
OUT(s) = T1(s)*L(s) + T2(s)*IN(s)
you need to figure out Laplace transfer functions T1 and T2.
Make sure you reduce the transfer function answers to the ratios of
two polynomials in s. No need to convert to function of time for output.

There is derivative compensation on the negative feedback error signal.
(s stands for differentiation in Laplace transform notation)
Notice you have an inner positive feedback loop and an out negative feedback loop.
You might start by solving for the inner positive loop transfer function,
then work on the outer negative loop.
To handle the IN and LOAD inputs you can work through each case separately
then add the results, assuming linear superposition.

Check the solution to Quiz 1, posted on the website.