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- W2046300900 abstract "Consider a second examplewith one unstablepole. The objective here is to determinehowtomodify theopen-looptransferfunctionso that the closed-loop transfer functionwill be stable. The open-loop transferfunctionis givenby L.s/D K .sC 1/=.s2 C 9si 10/. Equation (2) states8D i.0:5P! C Pi1/180degmust be true for the system to be stable. The open-looppoles arei10 and 1. Because there are no poles on the imaginary axis and there is one unstable pole, P! D 0 and Pi1D 1. Thus, for a stable closed-loop system, we require that8Di180deg.TheNicholsplotof L.s/ is shown in Fig. 4 for a gain ofK D 10. The initialphaseat!D 0 is81 Di180deg.Of course, this is only true if the gain is raised slightly such that the initial magnitude is greater than 0 dB. If K D 0, the initial phase is not de ned by this technique. If K < 10, then81 Di180 deg because for s< 0 the 0 dB crossing is nearest 360 deg. The nearest multiple of 360 degwhen the magnitude of L.s/ is 0 dB is 0 deg. Thus, if the gain is greater than 10, then81 i83 Di180C 0Di180 deg as required for stability.The root locusof Fig. 5 shows this to be the case." @default.
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- W2046300900 date "1999-03-01" @default.
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- W2046300900 title "Optimal Control and Filtering for Nonstandard Singularly Perturbed Linear Systems" @default.
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