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TIme Specs Lecture 3_31_09

# TIme Specs Lecture 3_31_09 - 1 Step Response Specifications...

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Unformatted text preview: 1. Step Response Specifications for Underdamped 2 nd Order Systems Step Response Time (sec) 2 4 6 8 10 12 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 ( ) t y final y 9 . final y 02 . ± r t final y max y t final y 1 . s t p t overshoot course) in this (neglect time rise ~ r t peak time ~ p t time settling ~ s t overshoot percent 100 % max = ⋅ − = final final y y y os 2. Basic Equations for Underdamped 2 nd Order Systems Step Response Time (sec) Amplitude 2 4 6 8 10 12 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 1 . = ζ 2 . = ζ 4 . = ζ 5 . = ζ 6 . = ζ 8 . = ζ ( ) ( ) ( ) 1 2 1 2 2 1 2 2 + + = + + = = s s s s s s s Y n n n n step ζ ω ζω ω ω z1=0.1; num=[1]; den1=[1 2*z1 1]; step(num,den1); hold on z2=0.2; den2=[1 2*z2 1]; step(num,den2); hold on z3=0.4; den3=[1 2*z3 1]; step(num,den3); hold on z4=0.5; den4=[1 2*z4 1]; step(num,den4); hold on z5=0.6; den5=[1 2*z5 1]; step(num,den5); hold on z6=0.8; den6=[1 2*z6 1]; step(num,den6); hold on grid axis([0 12 0 1.8]) hold off ( ) ( ) ( ) ( ) ⎟ ⎟...
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TIme Specs Lecture 3_31_09 - 1 Step Response Specifications...

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