# lecture12 - 12.NyquistStabilityTheorem...

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1 12.  Nyquist Stability Theorem We know that if the poles of a system are all on  the LHP, then the system is stable. We also know that any poles on the imaginary  axis must be single for stability. Recall poles are roots of the characteristic  equation. The characteristic equation is formed by   1+  L(s) = 0, where L(s) is the open-loop transfer  function. Using the Routh-Hurwitz Criterion, we can  determine stability without solving for roots.

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2 L(s) = K(s)G(s)H(s) Substitute s with j ϖ . Decompose L(j ϖ ) into real and imaginary parts. This is the Bode function for the open-loop  transfer function. Plot the real part against imaginary part on a  complex plane – This is the Nyquist plot. Stability Based on L(s) R(s) K(s) Y(s) H(s) G(s)
3 Nyquist Stability Theorem Suppose we have plotted the Bode function of the

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## This note was uploaded on 11/09/2009 for the course ENG 91301 taught by Professor Lui during the Spring '08 term at Hong Kong Institute of Vocational Education.

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lecture12 - 12.NyquistStabilityTheorem...

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