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# l37 - stable systems Root locus or Nyquist diagrams should...

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16.06 Lecture 37 Bode Design Karen Willcox December 4, 2003 Today’s Topics 1. Gain and phase margin 2. More Bode Examples Reading : 7.6, 7.7 1

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1 Gain and Phase Margin Recall the deﬁnition of gain margin and phase margin we saw with Nyquist plots: Now consider the translation of these concepts to the Bode diagram. We note the following: The crossover frequency, ω c , is the frequency where Phase margin, φ m = Gain margin, GM = Gain margin in dB, GM dB = 2
On a Bode diagram: 1. ω c is the frequency where 2. φ m is 3. GM dB is Note : Bode digrams do not show the encirclements speciﬁed by the Nyquist criterion. Therefore, Bode plot stability analysis is limited to open-loop

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Unformatted text preview: stable systems. Root locus or Nyquist diagrams should be used for open-loop unstable systems. 3 2 Examples The phase and gain margins can be calculated from either a Bode diagram, or from tabulated Bode data. Example 1: Insert Matlab ﬁgure here 4 Example 2: Insert tabulated data here. Do calculation in log units and in dB. 5 Example 3: 100(0 . 1 s + 1) G ( s ) = s ( s + 1) 6 Example 4: 10( s + 1) G ( s ) = s (10 s + 1) 7...
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l37 - stable systems Root locus or Nyquist diagrams should...

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