5173 fall 2009 HW07 solutions

5173 fall 2009 HW07 solutions - EEL5173 HW # 7, Page 7-3 2....

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Unformatted text preview: EEL5173 HW # 7, Page 7-3 2. The Nyquist Diagram (for z = ejωT with 0 < ωT < π) of the open-loop gain, G(z)H(z), of a single-loop feedback control system is shown. The open-loop gain is of the following form N 0 ( z) G( z) H ( z) = k , ( z − 1) 2 ( z + 0.87) where N0(z) is a polynomial of degree not higher than 3. Complete the Nyquist Diagram and use the Nyquist Criterion to determine the range of k in which the closed-loop system is stable. We have Po = 0. The multiplicity of the open-loop pole at z = 1 equals to 2. Hence, Δ ρ ∠GH = − mπ = −2π GH-plane 0+ ← ωΤ A B -8k C 3.5k ωΤ = π For k > 0, Case A: When -1 < -8k, Po = 0, Nc = 2, Zo = Po + Nc = 2, unstable. Case B: When -8k < -1, Po = 0, Nc = 1 – 1 = 0, Zo = Po + Nc = 0, stable, i.e. when k > 1/8 For k < 0, Case C: When 3.5k < -1, Po = 0, Nc = 1 – 1 = 0, Zo = Po + Nc = 0, stable, i.e. when k < -1/3.5 = -2/7 Case D: When -1 < 3.5k, Po = 0, Nc = 1 = 1, Zo = Po + Nc = 1, unstable. D ...
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This note was uploaded on 07/15/2011 for the course EEL 5173 taught by Professor Tung during the Fall '09 term at FSU.

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5173 fall 2009 HW07 solutions - EEL5173 HW # 7, Page 7-3 2....

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