Quiz_4_sol

# Quiz_4_sol - D * 1 ) D * 2 R * . Plugging into the...

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ECE 483 Quiz # 4 Solution Problem 1. (20 points) For each of the two sampled-data control systems above, ±nd the transfer function C ( z ) R ( z ) . If such a transfer function does not exist, derive C ( z ) instead. Solution: For system (a), we have C ( z ) R ( z ) = 1 + G ( z ) 1 + [ GH 1 ]( z ) H 2 ( z ) . For system (b), label the input of the sampler on the right as V ( s ). Then C = G [ D * 1 ( R * - D * 2 V * ) - D * 2 V * ] = GD * 1 R * - G (1 + D * 1 ) D * 2 V * C * = G * D * 1 R * - G * (1 + D * 1 ) D * 2 V * . On the other hand, from V = HC , we have V = GH [ D * 1 ( R * - D * 2 V * ) - D * 2 V * ] = GHD * 1 R * - GH (1 + D * 1 ) D * 2 V * V * = [ GH ] * D * 1 R * - [ GH ] * (1 + D * 1 ) D * 2 V * V * = [ GH ] * D * 1 1 + [ GH ] * (1 +
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Unformatted text preview: D * 1 ) D * 2 R * . Plugging into the previously obtained equation, we get C * = G * D * 1 R *-G * [ GH ] * (1 + D * 1 ) D * 1 D * 2 1 + [ GH ] * (1 + D * 1 ) D * 2 R * C ( z ) R ( z ) = G ( z ) D 1 ( z )-G ( z )[ GH ]( z )(1 + D 1 ( z )) D 1 ( z ) D 2 ( z ) 1 + [ GH ]( z )(1 + D 1 ( z )) D 2 ( z ) = G ( z ) D 1 ( z ) 1 + [ GH ]( z )(1 + D 1 ( z )) D 2 ( z ) . 1...
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## This note was uploaded on 04/15/2011 for the course ECE 483 taught by Professor Evens during the Spring '08 term at Purdue University.

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