ece580 lecture 08 - Lecture 8 ECE 580 Feedback Control...

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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 8 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø PS 3 due today Ø Next PS next week
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 3 Last Lecture - ( 29 D s ( 29 G s ( 29 Y s ( 29 U s ( 29 R s ( 29 E s ( 29 o W s ( 29 N s Ø Proportional-plus-Integral Controller Combine elements (add responses) I k s p k ( 29 E s ( 29 U s ( 29 D s ( 29 ( 29 ( 29 0 t p I u t k e t k e d σ σ = + ( 29 ( 29 I p k U s k E s s = + PI Controller
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 4 Ø Derivative element ( 29 ( 29 D u t k e t = & ( 29 ( 29 D U s sk E s = Note: improper Implement ( 29 ( 29 1 dominant poles D D D sk U s E s T s T τ = + = Effect Add damping to system Make stabilization easier Increases control amplitude
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 5 Today Ø PID controllers Ø System type Ø Reading FPE 4.2, 4.3
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 6 Ø Proportional-Integral-Derivative (PID) Control What if we also want zero steady-state response? Add integrator I k s p k k D k s ( 29 E s ( 29 U s ( 29 D s ( 29 ( 29 ( 29 ( 29 0 t p I D u t k e t k e d k e t σ σ = + + & ( 29 ( 29 I p D k U s k k s E s s = + + ( 29 I p D k D s k k s s = + +
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 7 Ø Example: DC motor position PID control - ( 29 G s I p D k k k s s + + ( 29 Y s 1 s ( 29 I p D k D s k k s s = + + ( 29 ( 29 1 m m k G s s s τ = + Closed-loop transfer function ( 29 ( 29 ( 29 cl Y s G s W s = ( 29 ( 29 1 1 1 m m m I p D m k s s k k k k s s s s τ τ + = + + + ÷ + ( 29 U s ( 29 2 1 m s s τ + g
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 8 ( 29 ( 29 3 2 1 m cl m D m p m I m k s G s s k k s k k s k k τ = + + + + Proportional, integral and derivative gains affect different terms in characteristic polynomial Can use RH to specify parameter regions for stability Use insights from effects of elements to select initial parameters Use insights to iteratively improve parameters
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 9 0 2 4 6 8 10 12 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 Step Response Time (sec) Amplitude k i = 0 k i = 0.5 k i = 2 k i = 4 k i = 10 5 2 p D k k = =
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 10 0 2 4 6 8 10 12 -0.1 -0.05 0 0.05 0.1 0.15 Step Response Time (sec) Amplitude k d = 2 k d = 4 k d = 10 k d = 15 5 10 p I k k = =
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Sept. 29, 2011 Feedback Control Systems (I) © Douglas Looze 11 0 2 4 6 8 10 12 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 Step Response Time (sec) Amplitude 0 2 4 6 8 10 12 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 Step Response Time (sec) Amplitude k p = 10 4 10 10 D I p k k k = = =
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Sept. 29, 2011
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