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

Questions

• What is the definition of bandwidth?

• How do I calculate "steady state error"?

• For problem 1, do we plot bode and nyquist plots for the open-loop or closed-loop system?

• What is the definition of bandwidth?
  Submitted by: waydo
  Submitted on: November 10, 2004
  Identifier: L7.1 , H6

  Bandwidth is the frequency at which the *closed-loop* transfer function has a gain of 1/sqrt(2) its DC value. That is, if G(s) is the closed-loop transfer function, the bandwidth is the frequency w at which |G(jw)|/|G(0)| = 1/sqrt(2). You may see it mentioned that the bandwidth is the frequency at which the *open-loop* transfer function has gain 1 (0 dB), but this is only a useful approximation for design purposes. The approximation rougly works because the closed-loop gain is about 1/(1+1) = 1/2 when the open-loop gain is 1, but an error is introduced by the phase of the open-loop transfer function at the crossover frequency. After doing a design, you should always verify the bandwidth of the closed-loop system.

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• How do I calculate "steady state error"?
  Submitted by: asa
  Submitted on: November 14, 2004
  Identifier: H6

  There is no direct Matlab command to calculate the steady state error. However, if you look at the block diagram for our standard PC feedback loop, you'll see that the error is the input to the control block. You should then be able to calculate a transfer function H_{er} very straightforwardly. Think a bit about "steady state" and you'll see what value of s you need to evaluate this at to get the steady state error.
  
  Also, if you know the final value theorem, and think about the final value of H_{er} for a step input, you should get the same answer. Note, however, that this analysis requires that the system is stable -- if it's not stable, then there is no limit for the final value, and "steady state error" isn't defined.

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• For problem 1, do we plot bode and nyquist plots for the open-loop or closed-loop system?
  Submitted by: waydo
  Submitted on: November 14, 2004
  Identifier: H6

  We always generate these plots for the open-loop system. One of the remarkable things about these plots is that the open-loop plots can be used to tell us everything we will need to know about the closed-loop system.

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