l27 - rl A = magnitude of the vector from the zero at ± z...

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16.06 Lecture 27 Polar Plots November 6, 2003 Today’s Topics: 1. First order system polar plot 2. Second order system polar plots 3. Other examples

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Recall from last time that if the system G ( s ) receives a steady sinusoidal input of amplitude A , so then the steady state output will be a sinusoid of magnitude A ± M ( Z ) with its phase shifted by I ( ) where Now let’s pause for a bit and think about some interpretations of G ( j ) . 2
G ( j Z ) =the transfer function G ( s ) evaluated at the point s j on the imaginary axis of the “ s ” plane. In particular, if then Now the term ( j ± z 1 ) is the vector from the zero at z to the point 1 j on the imaginary axis of the “ s ” plane 3

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Similarly, if the poles p 1 and p 2 are complex conjugates then In general where- k root locus gain

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Unformatted text preview: rl A = magnitude of the vector from the zero at ± z to the point j Z z i i A magnitude of the vector from the pole at ± p i to the point j p i I angle of the vector from the zero at ± z to the point j z i i angle of the vector from the pole at ± p i to the point j p i 4 Example-first order system As Z goes from zero to plus infinity G ( j ) traces a contour in the complex plane 5 Example: second order system 6 Some typical second order system polar plots for k G ( s ) 2 rl 2 s ± 2 GZ s ± Z n n Critical damping ( G 1 )-Medium damping ( 0.7 ) 7 Light damping( G 0.1 ) Zero damping ( ) 8 The Quanser An integrator (pole at the origin) 9 A differentiator (zero at the origin) 10...
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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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l27 - rl A = magnitude of the vector from the zero at ± z...

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