MECH 466 - Lecture22-DesignExamples-2009W

Feedback transform feedback stability analysis via

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Unformatted text preview: edback: Stability analysis via Routh-Hurwitz criterion Stability RouthSteady-state error analysis Steady- Design of lead-lag compensators Design leadRoot locus Root Frequency response Frequency 2008/09 MECH466 : Automatic Control 11 2008/09 MECH466 : Automatic Control 12 3 Steady-state error (cont’d) Outline For unit step: For System description and control objective System Modeling Modeling Analysis Analysis Stability analysis via Routh-Hurwitz criterion Stability RouthSteady-state error analysis Steady For unit ramp: For Design of lead-lag compensators Design leadRoot locus Root Frequency response Frequency For unit parabolic: For 2008/09 MECH466 : Automatic Control 13 2008/09 Gain design via root locus MECH466 : Automatic Control 14 Step response 25% overshoot! Find K required for Find 25% overshoot. For 2nd order systems 2008/09 MECH466 : Automatic Control By magnitude condition 15 2008/09 MECH466 : Automatic Control 16 4 Lead-lag design via root locus Lead compensator design Design specifications Design Locate desired poles Locate 25% overshoot 25% 2% settling time 2 seconds 2% Kv=20 Kv=20 Due to “2% settling time 2 seconds” Due seconds” Im In the previous gain design, In Angle condition Angle 25% overshoot 25% 2% settling time 4.8 seconds 2% Kv=2.49 (Verify this by yourself!) Kv=2.49 Not satisfactory! 2008/09 Re MECH466 : Automatic Control 17 2008/09 Lead compensator design MECH466 : Automatic Control 18 Lag compensator design Im Fix z=-2 (rather arbitrarily), Fix z=and obtain p s.t. s.t. Error constant Kv Error Find K Find Re 2008/09 MECH466 : Automatic Control 19 2008/09 MECH466 : Automatic Control 20 5 Step and ramp responses 1.4 Outline System description and control objective System Modeling Modeling Analysis Analysis 10 Ramp reference 1.2 9.8 1 Stability analysis via Routh-Hurwitz criterion Stability RouthSteady-state error analysis Steady 9.6 0.8 Gain compensated 0.6 0.4 Design of lead-lag compensators Design lead- 9.4 Lead compensated Root locus R...
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This document was uploaded on 03/05/2014 for the course MECH 466 at The University of British Columbia.

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