MECH466 - Lecture17-NyquistStabilityCriterion-2009W

15 1 200809 08 06 04 02 0 mech466 automatic

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Unformatted text preview: Routh27 2008/09 MECH466 : Automatic Control 28 7 Bode plot of a time delay (review) 1 0.5 0 -0 . 5 -1 -2 10 10 -1 10 0 10 1 10 2 Huge phase lag! 0 Summary and exercises Nyquist plot (Matlab command: “nyquist.m”) Nyquist (Matlab Nyquist stability criterion for feedback stability Nyquist Examples for Nyquist stability criterion Examples Exercises: For (half of) Nyquist plot below, Exercises: count N for each case. • A=-1 (Ans. N=2) A=- (Ans. • B=-1 (Ans. N=0) B=- (Ans. -2 0 0 0 -6 0 0 0 -2 10 10 -1 10 0 10 1 10 • C=-1 (Ans. N=2) C=- (Ans. B D F -4 0 0 0 2 E C A The phase lag causes instability of the closed-loop closedsystem, and thus, the difficulty in control. 2008/09 MECH466 : Automatic Control • D=-1 (Ans. N=0) D=- (Ans. • E=-1 (Ans. N=2) E=- (Ans. • F=-1 (Ans. N=0) F=- (Ans. 29 2008/09 MECH466 : Automatic Control 30 Exercise Read Sections 10.3-10.5. Read 10.3Exercise: Suppose L(s) is stable and has Exercise: L(s) Nyquist plot below. Find the range of OL gain K>0 for which CL system is stable. -1 -3.3 -2 -0.5 (Ans. 0<K<1/3.3, 1/2<K<2) 2008/09 MECH466 : Automatic Control 31 8...
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