lecture13a

lecture13a - MAE 171A: Dynamic Systems Control Lecture 13a:...

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Unformatted text preview: MAE 171A: Dynamic Systems Control Lecture 13a: Nyquist Stability Criterion Goele Pipeleers The General Picture 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 Determine the closed-loop systems absolute stability: Is the system stable, yes of no? relative stability: How stable is the system? performance: transient: t r , t s , M p steady state: e ss 2 Root Locus: answers these questions from poles and zeros of L ( s ) absolute stability: all points p T,i on the root locus corresponding to k = 1 in the LHP? relative stability: max i {<{ p T,i }} performance: transient: heuristics based on dominant poles steady state: ] poles of L ( s ) @ and error constants 3 Bode and Nyquist plot: answers these questions from FRF of L ( s ) absolute stability: Nyquist stability criterion relative stability: phase and gain margin performance: transient: phase margin and cross-over frequency steady state: ] poles of L ( s ) @ and error constants 4 Nyquist Stability Criterion L ( s ) y r e determine closed-loop stability from the FRF and the number of unstable poles of the open-loop system L ( s ) Nyquist criterion: Z = P + N , where...
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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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lecture13a - MAE 171A: Dynamic Systems Control Lecture 13a:...

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