l32 - 16.06 Lecture 32 Gain and Phase Margins November 20,...

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Unformatted text preview: 16.06 Lecture 32 Gain and Phase Margins November 20, 2003 Today’s Topics: 1. Definitions of phase and gain margins 2. Interpretation of distance from –1 3. Examples Commonly, in situations where there are no open loop poles in the RHP the criteria of gain and phase margins are used to evaluate the performance of feedback control systems. Typically the Nyquist diagram may look like this in the region near –1. Now consider the vector from the –1 point to any point on the G ( j Z ) contour. It is in fact G ( j Z ) ¡ 1 . Thus the magnitude of the closed loop response at the frequency Z is always the ratio of these two vectors. Clearly, if the contour passes through the –1 point then the ratio goes to infinity, at which point the system is at the threshold of instability, and it will have a resonant peak of infinite magnitude at that frequency. Gain and phase margin are measures of the changes in magnitude and phase of the open loop system that would cause the contour to just pass through the –1 point. In particular they are defined as Gain Margin-the magnitude of increased open loop gain that would...
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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l32 - 16.06 Lecture 32 Gain and Phase Margins November 20,...

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