ece580 lecture 14

# ece580 lecture 14 - Lecture 14 ECE 580 Feedback Control...

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Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 14 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze

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Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø PS 5 due today Ø Office hours Tue 4:00 – 5:00 PM
Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 3 Announce (cont.) Ø Exam Wednesday, October 26 7–9 PM Hasbrouck Lab Add 124 Open book, notes No calculators/computers/cell phones Covers material in FPE 1 – 4.3, 6.3 (through Lecture 12) Ø No class Thursday, Oct. 27

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Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 4 Today Ø Exam review
Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 5 System Response Ø Convolution System ( 29 u t ( 29 y t ( 29 ( 29 ( 29 y t g t u d τ -∞ = - ( 29 u t ( 29 y t ( 29 g t ( 29 ( 29 ( 29 Y s G s U s = Ø Laplace transform ( 29 u t ( 29 y t G ( 29 y t ( 29 g t ( 29 u t System transfer function

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Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 6 Ø Frequency response ( 29 ( 29 j t Y j e G j ϖ = Laplace transform of g ( t ) Fourier transform of g ( t ) Frequency response ( 29 u t ( 29 y t ( 29 g t ( 29 j t U j e ϖ=
Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 7 Ø Second-Order Systems Transfer function ( 29 2 2 2 2 n n n G s k s s ϖ ζϖ = + + natural frequency n damping ratio ζ≡ DC gain k ( 29 2 1 2 1 1 1 1 sin tan 1 n t d y t e t k ζ - - - ÷ ÷ = - + ÷ ÷ - Response ss y

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Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 8 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Step Response Time (sec) Amplitude Ø Step response (2nd order system) ss y p y p t r y r t d y d t s t ±4% p ss p ss y y M y - =
Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 9 0.3 0.7 ζ < < Ø Rise time for 2nd order system Damping ratio 0 1 < < r d t π β ϖ - = 100 % Damping ratio 1.8 r n t = Empirical 10 - 90% Ø Peak time and value p d t = 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0 0.2 0.4 0.6 0.8 1 Damping Ratio Peak Overshoot 2 1 p M e πζ - - @

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Oct. 25, 2011 Feedback Control Systems (I) © Douglas Looze 10 Ø Settling time
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ece580 lecture 14 - Lecture 14 ECE 580 Feedback Control...

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