MECH466 - Lecture18-RelativeStability2009W

E if ls has no pole in open rhp if ls cl stable we

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Unformatted text preview: (s) has no pole in open RHP) IF L(s) CL stable We assume P=0 from now on! 2008/09 MECH466 : Automatic Control 5 Example of L(s) with an integrator When open loop poles When lie on the imaginary Im axis, we modify Nyquist path, by path, detouring to the right of the poles. (very small) Ex: 2008/09 Re CL unstable MECH466 : Automatic Control 6 L(s) for modified Nyquist path For small |s|, For Im s s Re (very small) When s moves as When L(s) moves as L(s) Re L(s) L(s) (very large) Note: If L(s) has no open RHP pole, L(s) we are interested in (and draw) Nyquist plot ONLY around the critical point -1. 2008/09 MECH466 : Automatic Control 7 2008/09 MECH466 : Automatic Control 8 2 Bode plot of L(s) Example of L(s) with an integrator dB -20 15 10 5 -40 0 deg -5 -10 -15 -1 2008/09 MECH466 : Automatic Control 9 2008/09 -0.8 -0.6 -0.4 -0.2 MECH466 : Automatic Control 0 10 Bode plot of L(s) Example of L(s) with double integrator dB -40 5 -60 deg 0 -5 -5 2008/09 -4 -3 MECH466 : Automatic Control -2 -1 0 11 2008/09 MECH466 : Automatic Control 12 3 L(s) with a time-delay Bode plot of a time delay (review) 0.5 1 0.5 0 0 -0 . 5 -0.5 -1 -2 10 -1 10 -1 10 0 10 1 10 2 Huge phase lag...
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This document was uploaded on 03/05/2014 for the course MECH 466 at University of British Columbia.

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