MECH466 - Lecture18-RelativeStability2009W

MECH466 Lecture18-

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: lot is much simpler.) We translate GM and PM defined in Nyquist plot into those in Bode plot! 2008/09 MECH466 : Automatic Control 21 2008/09 Relative stability on Bode plot MECH466 : Automatic Control 22 Notes on Bode plot Advantages Advantages Without computer, Bode plot can be sketched easily. Without GM, PM, crossover frequencies are easily determined GM, on Bode plot. Controller design on Bode plot is simple. (Next week) Controller ωg GM Disadvantage Disadvantage ωp If OL system is unstable, we cannot use Bode plot for If closed-loop stability analysis. closed- PM 2008/09 MECH466 : Automatic Control 23 2008/09 MECH466 : Automatic Control 24 6 An example Relative stability with time delay 20 0 GM GM 0 -50 -20 -1 10 -100 10 0 ωg 1 10 ωp 2 10 10 -90 Time delay reduces relative stability! PM -180 0 10 3 PM -180 -270 10 2008/09 -1 10 0 1 10 2 0 10 3 10 Delay time 10 MECH466 : Automatic Control 25 2008/09 Unstable closed-loop case MECH466 : Automatic Control 26 Summary and exercises Relative stability: Closeness of Nyquist plot to Relative the critical point -1 GM Gain margin, phase crossover frequency Gain Phase margin, gain crossover frequency Phase ωp Relative stability on Bode plot Relative We normally emphasize PM in controller design. We Exercises Exercises ωg Read Sections 10.6 & 10.7. Read Obtain GM, PM for open-loop Bode plots in Figures Obtain openP10.7, P10.8, P10.10 (pages 593-595). 593- PM 2008/09 MECH466 : Automatic Control 27 2008/09 MECH466 : Automatic Control 28 7...
View Full Document

This document was uploaded on 03/05/2014 for the course MECH 466 at University of British Columbia.

Ask a homework question - tutors are online