ece580 lecture 19

ece580 lecture 19 - Lecture 19 ECE 580 Feedback Control...

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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 1 Lecture 19 ECE 580 Feedback Control Systems (I) MIE 444 Automatic Controls Doug Looze
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 2 Announce Ø PS 6 due Friday By 5 pm In my office or my KEB mailbox Ø Next week No class Tuesday
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 3 Last Time Ø Unity feedback system - r u y η m y e ( 29 D s d ( 29 G s ( 29 ( 29 ( 29 z s r s y s = - Performance signal
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 4 Ø Specify bounds on magnitudes of spectra of exogenous signals (or their PSDs) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 r d r j W d j W j W η ϖ < < < ( 29 ( 29 p z j W < Ø Find a controller to achieve this The Control Problem Ø Specify desired bound on performance signal Ø Then ( 29 ( 29 ( 29 dr p S j W - r u y m y e ( 29 D s d ( 29 G s
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 5 Today Ø Analysis of the control problem Ø Approximate transfer functions in terms of loop transfer function Ø Summarize performance objectives in terms of loop transfer function Ø Reading FPE 6.5-6.6, 6.7.7-6.7.8
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 6 Ø There are 3 regions of frequency with fundamentally different control behaviors Active control ( 29 ( 29 1 disturbance rejection command following 1 S j T j ϖ = g g No control ( 29 ( 29 1 no disturbance rejection reject measurement errors 1 T j S j = g g Transition control ( 29 ( 29 , ? T j S j ( 29 ( 29 z j j η ( 29 ( 29 ( 29 z j r j d j - ( 29 ( 29 1 no disturbance rejection reject measurement errors 1 T j S j = g g ( 29 ( 29 ( 29 ( 29 ( 29 dr p S j W T j W W + ( 29 ( 29 1 S j T j + = 1 disturbance rejection command following
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 7 Ø Typically: Reference commands Low frequency energy Disturbances } Measurement errors High frequency energy ( 29 1 at low frequencies S j ϖ = ( 29 1 at high frequencies T j = Active Off Transition LOW MID HIGH 1 log , S T S T
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 8 Ø Another limitation For any minimum phase system with an open loop transfer function L ( s ) that has a 2-pole rolloff Consequence of stability ( 29 log 0 S j d ϖ -∞ = n-pole rolloff n more poles than zeros All real feedback systems 0 ( 29 log S j log A B A B = ( 29 ( 29 ( 29 z j S j d j =
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Nov. 15, 2011 Feedback Control Systems (I) © Douglas Looze 9 Approximation of Transfer Functions Ø Approximate in terms of loop transfer function Closed loop transfer functions depend nonlinearly on compensator Why?
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ece580 lecture 19 - Lecture 19 ECE 580 Feedback Control...

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