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FAQ (Frequently Asked Questions)
Category:
CDS 101/110 Fall 2004
Identifiers: H0 H1 H2 H3 H4 H5 H6 H7 H8 L0.0 L1.1 L1.2 L2.1 L2.2 L2.3 L3.1 L3.2 L4.1 L4.2 L5.1 L5.2 L6.1 L7.1 L9.1
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How does overshoot relate to phase margin?
Submitted by: haomiao
Submitted on: November 21, 2004
Identifier:
H7
You can approximate the system as a 2nd order system by looking at the 2 dominant poles. Note that since poles on the real axis do not contribute to oscillatory behavior, they have no effect on the phase margin. Then, using the equations shown in Wednesday's lecture, you can get a requirement for the damping ratio zeta. Zeta is related to the phase margin through a somewhat complicated formula, which we can approximate to the linear relationship zeta is roughly PM/100.
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Is it OK for a system to have infinite gain margin?
Submitted by: waydo
Submitted on: November 22, 2004
Identifier:
H7
Absolutely. This just means that the phase never crosses -180, and we can turn up the gain as much as we like without causing instability (although in the real world turning up the gain too much will still lead to problems).
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What's the difference between calculating the tracking error with mag(L) vs. the sensitivity function?
Submitted by: asa
Submitted on: November 29, 2004
Identifier:
H7
, H8
For exact calculations of the frequency at which the error is less than a certain bound, you should use H_{er}, the sensitivity function. This gives you a measure of the error directly related to the input. The magnitude of L can be used as a quick approximation -- generally, 1/(1+mag(L)) will be close to mag(1/(1+L)). However, for precise work (i.e. not approximations), you should use H_{er}.
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