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ece580 lecture 17 - Lecture 17 ECE 580 Feedback Control...

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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 17 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø Problem set 5 available Due Thursday, Nov. 19
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 3 Last Time Ø Bode plots constructed by adding individual factors ( 29 ( 29 ( 29 1 1 m n zi pi i i G j q j q j ϖ ϖ ϖ = = = - R R R ( 29 ( 29 ( 29 1 1 log log log log m n zi pi i i G j K q j q j ϖ ϖ ϖ = = = + - ( 29 ( 29 ( 29 1 1 m zi i n pi i q s G s K q s = = =
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 4 Ø Individual factors Gain factor Pole/zero factor at origin 1st order factor (real pole/zero) 2nd order factor (complex pole/zero) Ø Approach to construction Add asymptotes Sketch plot Use computer (Matlab) for detail
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 5 Today Ø RHP poles/zeros Ø Interpretation of Bode plots of the open- loop transfer function of a feedback system Steady-state error constants Stability Ø Reading FPE 6.1-6.2, 6.4
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 6 Right Half-Plane Factors Ø First-order factor ( 29 1 0 q s s τ τ = - + Pole/zero at 1 τ Magnitude ( 29 ( 29 2 1 q j ϖ ϖτ = + Same as first order factor in LHP Phase ( 29 1 tan 1 q j ϖτ ϖ - - = ÷ R ( 29 1 tan ϖτ - = -
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 7 Note: Pole factors often written as ( 29 1 0 q s s τ τ = - Phase ( 29 ( 29 1 tan q j ϖ π ϖτ - = - R
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 8 -40 -35 -30 -25 -20 -15 -10 -5 0 Magnitude (dB) 10 -2 10 -1 10 0 10 1 10 2 -180 -135 -90 -45 0 Phase (deg) Bode Diagram Frequency (rad/sec) Ø Example ( 29 ( 29 1 2 1 1 1 1 G s s G s s = + = -
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Nov. 8, 2011 Feedback Control Systems (I) © Douglas Looze 9 Ø Example ( 29 2 4 4 G s s = - Inverted Pendulum Bode form ( 29 ( 29 ( 29 4 2
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