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Analyzing the Nyquist Curve for a 5th Order System
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[QUOTE="Karl Karlsson, post: 6550250, member: 667628"] They come to the conclusion that there are 2 zeros by ##wi## becoming dominant for large values of w and each ##wi## in the denominator gives a phase shift of -90° and each ##wi## in the numerator gives a phase shift of +90°. Thus there must be 2 zeros because you see that ##G(iw)## phase shift -270° for large w. The problem I have with it is that the expression will probably be approximately ##a\cdot(wi)^2/(b \cdot (wi) ^ 5 )##, ie we do not know if the constants a and b are negative and then we get a completely different phase shift. Then there are also many solutions, eg if G(s) were ##\frac{-s ^ 4} {(s + 1)(s + 2)(s + 3)(s + 4)(s + 5)}##, here you see that ##G (iw)## phase rotates -270 degrees for large values of w and there is only one zero (I do not know if they in the task count double root as two zeros) The way I have learned it is that the number of poles with positive real part to the feedback system ##1/(1+G_0(s))## is equal to the number of poles with positive real part of ##G_0## plus the number of encirclements of the point -1 in a nyquist diagram. Not sure if that is in a nyquist diagram where w goes from ##-\inf## to ##\inf## or 0 to ##\inf##. Does anyone know which it is? [/QUOTE]
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Analyzing the Nyquist Curve for a 5th Order System
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