MECH466 - Lecture18-RelativeStability2009W

3 routh hurwitz is not applicable routh200809 10

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Unformatted text preview: ve mathematical model is never accurate. How to measure relative stability? How Use a “distance” from the critical point -1. Use distance” Gain margin (GM) & Phase margin (PM) Gain 15 2008/09 MECH466 : Automatic Control 16 4 Gain margin (GM) Examples of GM Im Phase crossover Phase frequency ωp: Gain margin (in dB) Gain Indicates how much Indicates OL gain can be multiplied without violating CL stability. 2008/09 Im Re Nyquist plot of L(s) L(s) MECH466 : Automatic Control 17 2008/09 Reason why GM is inadequate Same gain margin, but different relative stability MECH466 : Automatic Control Gain crossover Gain frequency ωg: Gain margin is often inadequate to indicate relative stability 19 Nyquist plot of L(s) L(s) Indicates how much Indicates OL phase lag can be added without violating CL stability. Phase margin! MECH466 : Automatic Control 18 Phase margin (PM) Phase margin Phase 2008/09 Re 2008/09 MECH466 : Automatic Control 20 5 An example Notes on Nyquist plot Advantages Advantages Nyquist plot can be used for study of closed-loop Nyquist closedstability, for open loop systems which is unstable and includes time-delay. time- Disadvantage Disadvantage Controller design on Nyquist plot is difficult. Controller (Controller design on Bode p...
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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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