ece580 lecture 02

ece580 lecture 02 - Sept. 8, 2011 Feedback Control Systems...

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Unformatted text preview: Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 2 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø Email sent Ø Problem set 1 available on course website – Due Thursday, Sept. 15 in class Ø Access to website: problems? http://ece580.ecs.umass.edu/ Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 3 Last Time Ø Discussed the general feedback problem – Components • Control inputs Exogenous inputs • Measurements Performance signal System z y d r η u Input Disturbance Reference Measurement Noise Measurement Performance Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 4 Ø One-sided Laplace transform ( 29 ( 29 st F s f t e dt- ∞- = ∫ ( 29 { } L f t ≡ { } L f ≡ Ø Inverse Laplace transform ( 29 ( 29 c c j st j f t F s e ds σ σ + ∞- ∞ = ∫ ( 29 { } 1 L F s- ≡ { } 1 L F- ≡ – Partial fraction expansion Review of Laplace Transforms ( 29 ( 29 1 1 i n p t i i f t C e t = = ∑ ( 29 1 1 n n C C F s s p s p = + +-- L Block Diagram Construction Ø Electrical – Bridged tee circuit (FPE Example 2.8) Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 5 1 R 2 R 2 C 1 C i v + + + + + +------ o v Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 6 Today Ø Effect of pole locations – Single real pole response – Complex poles Ø Reading – FPE, Chapter 3.3-3.4 Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 7 Effect of Pole Locations Ø Linear system ( 29 u t ( 29 y t G – Transfer function of system ( 29 ( 29 ( 29 Y s G s U s = – Response ( 29 ( 29 ( 29 Y s G s U s = – System poles pi • Zeros of denominator d ( s ) – System zeros zi • Zeros of numerator n ( s ) ( 29 ( 29 n s d s = Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 8 Ø Step response – Assume there are n distinct non-zero poles: – Laplace transform of Step ( 29 { } 1 1 L t s = – Laplace transform of output ( 29 ( 29 ( 29 ( 29 1 Y s G s U s G s s = = – Output (inverse Laplace transform) ( 29 ( 29 1 1 y t L G s s- = i j p p i j ≠ ≠ ≠ Sept. 8, 2011 Feedback Control Systems (I) © Douglas Looze 9 ( 29 1 2 1 2 n p t p t p t n y t C C e C e C e = + + + + L ( 29 1 1 2 1 2 n n C C C C y t L s s p s p s p- = + + + + --- L – Use partial fraction expansion { } ( 29 i i p t p t st i i L C e C e e dt ∞- = ∫ ( 29 i p s t i C e dt ∞- = ∫ ( 29 1 i p s t...
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ece580 lecture 02 - Sept. 8, 2011 Feedback Control Systems...

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