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FAQ (Frequently Asked Questions)
Category:
CDS 101/110 Fall 2003
Identifiers: FN H0 H1 H2 H3 H4 H5 H6 H7 H8 L0.0 L1.1 L1.2 L10.1 L2.1 L2.2 L3.1 L3.2 L4.1 L4.2 L5.1 L5.2 L6.2 L8.1 L9.1 L9.2
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What is Td in HW6, #3?
Submitted by: waydo
Submitted on: November 14, 2003
Identifier:
H6
Td is the same as τ (tau) in the earlier expression for time delay.
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Can you explain the Final Value Theorem again?
Submitted by: waydo
Submitted on: November 17, 2003
Identifier:
L6.2
, H6
For a signal f(t) with Laplace transform F(s), the Final Value Theorem says that
lim(t->infinity) f(t) = lim(s->0) s F(s)
Note that this is only true if F(s) has no poles in the right-half-plane, which makes sense - this is when f(t) will have a well-defined asymptotic value. Be careful - if the system is unstable (or marginally stable), the Final Value Theorem will still give you an answer, but it will be incorrect.
With this in mind, if you have plant P(s) and controller C(s), then your closed-loop transfer function is P(s)C(s)/(1 + P(s)C(s)). The Laplace transform of a step input 1(t) is 1/s. Applying the Final Value Theorem (calling the output y(t)) we have
lim(t->infinity) y(t) = lim(s->0) s (1/s) P(s)C(s)/(1 + P(s)C(s)).
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On HW6, #3, the pade approximation listed doesn't match what MATLAB says. What gives?
Submitted by: waydo
Submitted on: November 17, 2003
Identifier:
H6
MATLAB's pade function scales the numerator and denominator such that the coefficient of s^n is 1 for an nth order approximation, while on the HW it is scales so the coefficient of s^0 is 1. The only difference between MATLAB and the HW is then multiplying the numerator and the denominator by a constant factor, so the two transfer functions are equivalent.
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