lecture13b

lecture13b - MAE 171A: Dynamic Systems Control Lecture 13b:...

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MAE 171A: Dynamic Systems Control Lecture 13b: Stability Margins Goele Pipeleers
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Stability Criteria feedback control configuration D ( s ) G ( s ) u y r e open-loop system L ( s ) = D ( s ) G ( s ) closed-loop system T ( s ) , Y ( s ) R ( s ) = L ( s ) 1 + L ( s ) 1
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When is the closed loop (BIBO) stable? T ( s ) is stable Z 0 | h T ( t ) | dt < T ( s ) is stable ⇔ <{ p T,i } < 0 , i Routh-Hurwitz criterion: T ( s ) is stable all entries in the first column of its Routh-Hurwitz table are positive root locus: let L ( s ) , kL ( s ) , compute the closed-loop poles p T,i as a function of k from the open-loop poles p L,i and zeros z L,i Nyquist stability criterion: determine closed-loop stability from the open- loop poles p L,i and FRF L ( ) 2
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Absolute versus relative stability absolute stability: “Is the system stable, yes or no?” e.g. Routh-Hurwitz criterion, Nyquist stability criterion, . . . relative stability: “How stable is the system?”
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This note was uploaded on 08/08/2011 for the course MAE 171 taught by Professor Pipeleers during the Summer '11 term at UCLA.

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lecture13b - MAE 171A: Dynamic Systems Control Lecture 13b:...

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