ece580 lecture 23

ece580 lecture 23 - Lecture 23 ECE 580 Feedback Control...

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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 23 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø PS 8 available Due Thursday, December 8 Ø Final Exam Monday, December 12 10:30 AM ELAB 323 Open book No electronic devices
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 3 Last Time Ø Design example RPV
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 4 Today Ø Begin sampled-data systems Discrete-time control Ø Effects of sampling within control loop Ø Reading FPE 8.1–8.2
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 5 ( 29 D s ( 29 G s - Sampled-Data Systems Ø Standard unity feedback architecture Continuous time ( 29 r t ( 29 e t ( 29 u t ( 29 y t ( 29 m y t ( 29 t η
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 6 - A/D Digital control unity feedback architecture ( 29 D s ( 29 G s - ( 29 r t ( 29 e t ( 29 u t ( 29 y t ( 29 m y t ( 29 t η ( 29 G s - ( 29 D z D/A A/D ( 29 r kT ( 29 e kT ( 29 u kT ( 29 u t ( 29 y t ( 29 m y t ( 29 t ( 29 m y kT Sample period T Discrete-Time Continuous-Time ( 29 r t
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 7 Continuous-time system Discrete-time system ( 29 G s - ( 29 D z D/A A/D ( 29 r kT ( 29 e kT ( 29 u kT ( 29 u t ( 29 y t ( 29 m y t ( 29 t η ( 29 m y kT Cont. Time Controller ( 29 u t ( 29 m y t Discrete Time Plant ( 29 u kT ( 29 m y kT Not time-invariant No inter-sample information
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 8 Analog-to-Digital Converter Ø Terminology A/D ( 29 x kT ( 29 x t ( 29 x t t  sampler ( 29 x kT ( 29 x t T T s sampling period 2 sampling frequency 1 s T T f T π ϖ = = T 2 T 3 T 4 T 5 T
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 9 Representation: Discrete-Time Signal ( 29 0 x t T 2 T 3 T 4 T 5 T ( 29 1 x ( 29 2 x ( 29 3 x ( 29 4 x ( 29 5 x ( 29 6 x ( 29 x k k 1 2 3 4 5 ( 29 * x t t T 2 T 3 T 4 T 5 T
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 10 * k k k k k x x t x t kT δ = - = - = - ± ( 29 * x t t T 2 T 3 T 4 T 5 T ( 29 x k k 1 2 3 4 5 Equivalent Representations { } ( 29 ( 29 * k k k k x x t x t kT = ∞ = - ∞ = - ± * k k k k k x x t x t kT ±
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 11 Ø Z-transform of discrete-time signal ( 29 k k k x z x z - =-∞ = ( 29 ( 29 { } * kTs k k k k x s x t kT x e δ ∞ ∞ - = - ∞ = - ∞ = - = ∑ ∑ L Ø Laplace transform of continuous-time signal Ø Relationship ( 29 ( 29 * sT z e x s x z = = ( 29 ( 29 { } * kTs k k k k x s x t kT x e - = - ∞ = - ∞ = - = L
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 12 ZOH Digital-to-Analog Converter Ø Usually done with zero-order hold (ZOH) Hold continuous value at value of most recent sample ( 29 x kT ( 29 ZOH x t T ( 29 ZOH x t t T 2 T 3 T 4 T 5 T ( 29 ( 29 ZOH 1 k x t x kT t k T = < +
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 13 Ø Suppose { } is result of sampling k x ZOH ( 29 x kT ( 29 x t ( 29 ZOH x t ( 29 ( 29 ZOH Would like x t x t ( 29 ( 29 ZOH How is related to ? x t x t ( 29 * x t
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Dec. 6, 2011 Feedback Control Systems (I) © Douglas Looze 14 Ø Relationship Unit step ( 29 { 1 0 0 0 t t t σ = <
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ece580 lecture 23 - Lecture 23 ECE 580 Feedback Control...

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