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lecture 20

lecture 20 - the fictitious frequency in w plane...

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1 Digital Compensator Design based on the frequency response method Frequency response of a linear time invariant discrete time system The frequency response of can be obtained by substituting : ) ( z G T j e z ω = ) ( T j e G ω ) ( ) ( ) ( ) ( T j T j e G e G M M ω ω ω θ θ ω = = = = Since the a transform maps the primary and complementary strips of the left half of the s plane into the unit circle in the a plane, conventional frequency response methods, which deal with the entire left half plane, do not apply to the z plane.

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2 Bilinear Transformation and the w plane w T w T z ) 2 / ( 1 ) 2 / ( 1 - + = 1 1 2 + - = z z T w
3 By replacing w by , where

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Unformatted text preview: the fictitious frequency in w plane, conventional frequency response techniques can be used to draw the Bode diagram for the transfer function in w plane. υ j 4 However, the fictitious frequency and actual frequency are related as follows: υ ω 2 tan 2 2 1 1 2 1 1 2 ) 2 / 1 ( ) 2 / 1 ( ) 2 / 1 ( ) 2 / 1 ( T j T e e e e T e e T z z T j w T j T j T j T j T j T j e z j w T j = +-= +-= +-= =--= = 2 tan 2 T T = Example 1. Example 2 Design in w plane...
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