Lecture Notes(9)

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Unformatted text preview: nd asymptotic stability condition are different. For linear time-invariant (LTI) systems (to which For we can use Laplace transform and we can obtain a transfer function), the conditions happen to be the same. In this course, we are interested in only LTI In systems, we use simply “stable” to mean both BIBO and asymptotic stability. Impulse Response 5 4 3 Amplitude 2 1 0 -1 -2 -3 -4 0 2 4 6 Time (sec) 8 10 12 6 4 2 0 -2 -4 -6 13 -5 0 14 5 Remarks on stability (cont’d) Examples Marginally stable if Marginally Repeated poles Repeated G(s) has no pole in the open RHP (Right Half Plane), & G(s) G(s) has at least one simple pole on -axis, & G(s) G(s) has no multiple poles on -axis. G(s) Does marginal stability imply BIBO stability? Does Marginally stable NOT marginally stable TF: TF: Unstable if a system is neither stable nor Unstable marginally stable. Pick Pick Output Output 15 16 Feedback Technique Positive Feedback K K will depends on the distance between the guitar and the amplifier. 17 Stability summary 18 Mechanical examples: revisited Let si be poles of G. Then, G is … K f(t) f(t) M (BIBO, asymptotically) stable if (BIBO, Re(si)<0 for all i. marginally stable if marginally Re(si)<=0 fo...
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This document was uploaded on 03/02/2014 for the course ME 451 at Michigan State University.

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