l28 - 16.06 Lecture 28 Principle of the Argument November...

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16.06 Lecture 28 Principle of the Argument November 12, 2003 Today’s Topics: 1. D Contours 2. The Principle 3. Zeros of G(s)+1
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An important and useful approach to control system design is obtained by considering closed D contours in the s plane. The D contour looks like this Notice that the vertical portion of the contour travels up the imaginary axis, which we know yields the system frequency response in the G ( s ) plane. For example, consider the first order system, which is a pole in the left half plane The term s ± ( ± 2) is the vector from the pole at ± 2 to the point s in the plane. In polar form the transfer function becomes 2
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s plane, it produces a G ( s ) contour Note that the G ( s ) contour does not enclose the origin. In fact, if there are N poles in the left half plane then there will be N loops but none of them will enclose the origin. Now consider a system with a pole in the right half plane (RHP) so Note that there is one counterclockwise encirclement of the origin by the G ( s ) contour. If there are N poles in the right half plane then there will be N counterclockwise encirclements of the origin by the G ( s ) contour. 3
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l28 - 16.06 Lecture 28 Principle of the Argument November...

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