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Lect8 - Routh stability, properties of feedback

Lect8 - Routh stability, properties of feedback - outh’s...

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Lecture Note 8 : Routh Stability Criterion & Basic Properties of Feedback AE353, Spring 2010 Prof. Soon Jo Chung Prof. Soon Jo Chung ([email protected])
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Stability You derived a system transfer function G(s)=Y(s)/U(s) B h d i h bili ? But how to determine the stability?
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Linear Time Invariant System Linear Time Invariant System The linear system: what we are dealing with in this class For such systems: the system is stable if all the roots of the transfer function denominator polynomial have negative real parts
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Routh’s test Routh s test A system is stable if and only if all the elements in the first column of the Routh array are positive
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Routh Stability Criterion
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Examples
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Control Design
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Continued
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Stability vs. Two Control Gains
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Unformatted text preview: outh’s st Routh s test • system is stable if and only if all the A system is stable if and only if all the elements in the first column of the Routh ray are positive array are positive outh ability Criterion Routh Stability Criterion xamples Examples ontrol Design Control Design ontinued Continued ability vs. Two Control Gains Stability vs. Two Control Gains • enT [1 3 2+K KI] denT=[1 3 2+K KI] • numT=[K KI] 1.4 Fig. 3.35 Transient responses • sysT=tf(numT,denT) • Step(sysT) 1 1.2 K=10, K I =5 0.6 0.8 y(t) K=1, K I =1 2 0.4 K=1, K I =0 1 2 3 4 5 6 7 8 9 10 0.2 Time (sec)...
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