Lect8 - Routh stability, properties of feedback

Lect8 Routh - 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

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Lecture Note 8 : outh Basic Properties of Feedback AE353, Spring 2010 rof. Soon Chung Prof. Soon Jo Chung ([email protected])
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ability Stability u derived a system transfer function You derived a system transfer function (s)=Y(s)/U(s) G(s)=Y(s)/U(s) But how to determine the stability?
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near Time variant System Linear Time Invariant System e linear system: what we are dealing with in The linear system: what we are dealing with in this class r such systems: the system is stable if all the For such systems: the system is stable if all the roots of the transfer function denominator olynomial have negative real parts polynomial have negative real parts
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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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This note was uploaded on 04/12/2010 for the course AE 353 taught by Professor Voulgaris,p during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lect8 Routh - 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

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