Notes-3A

Notes-3A - 3. Stability and Stabilization 3.1 Concept of...

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3. Stability and Stabilization 3.1 Concept of Stability Peak magnitude Stability of a polynomial : all roots have negative real parts. BIBO Stability : output is bounded for each bounded input . BIBO Stability : G(s) is proper and all poles have negative real parts.
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3.2 Routh Criterion
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Routh Criterion
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Routh Criterion
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Routh Criterion
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Routh Criterion
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Routh Criterion
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Routh Criterion
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Routh Criterion
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3.3 Routh Hurwitz Criterion Hurwitz matrix
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Routh Hurwitz Criterion
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3.4 Robust Stability Kharitonov Theorem is stable if and only if the following four are stable are all stable.
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3.5 Stability of Closed Loop Systems All transfer functions must be stable. Stable: if the characteristic polynomial is stable. 1 () 1 () () 1 : ( ) , ( ) , stable, 1( ) 1 ( ) 1 ( ) ( ) 2 ()() ( 1 ) ( 1 ) ( 1 ) Example ( 2) is unstable. bs s qs PsCs Ps Cs sa s s p s P s C s s asps bsqs s s s s s == = −+ + + += + + = +
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More Stability Tests The following are equivalent: 1. The closed-loop is stable () 2. and are stable 1( ) ( ) ) ( ) 3. Suppose ( ) is stable. Then is stable.
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This note was uploaded on 02/03/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.

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Notes-3A - 3. Stability and Stabilization 3.1 Concept of...

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