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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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Suppose P(jw) = a + jb, and I compute phase as arctan(b/a) and get -30 deg, how do I know if this is a lag of 30 deg, or a lead of 330 deg?
Submitted by: mreiser
Submitted on: December 1, 2003
Identifier:
L10.1
We typically are interested in phase lag, because we expect the systems we are dealing with to be causal. Causality means that outputs of a system depend only on current and previous inputs (and states) of the system, and not on future inputs. Thus a phase lead would correspond to a system whose output leads the input, and thus is non-causal. If we think of one point on the Bode plot as the result of driving a system with a sinusoidal input at a fixed frequnecy, then the input is periodic (and so is the ouput for a linear system), and in this case we prefer to look at phase lead as a convention used because of the above reason.
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Is the closed loop transfer function the same as Hyr?
Submitted by: lars
Submitted on: December 1, 2003
Identifier:
L10.1
Yes, we call Hyr the closed loop transfer function.
Consider the case where we have a feedback control system with a plant P, compensator C and some delay or sensor effect G.
The transfer function in this case (which we also call the closed loop TF) is Hyr = PC / (1 + PCG). This can be checked through careful block diagram algebra.
In general, for a single negative feedback loop, the closed loop (r to y) transfer function is F/(1+L), where F is the forward path transfer function, and L is the (open) loop transfer function, which includes any blocks on the feedback path.
NB: The initial response posted to this question was erroneous.
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What properties does L need to satisfy Bode's integral formula?
Submitted by: lars
Submitted on: December 3, 2003
Identifier:
L10.1
L needs to be of relative degree (degree of the denominator minus degree of numerator) greater than or equal to 2.
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