Midterm_2_Fa10

# Midterm_2_Fa10 - ECE 483 Midterm 2 Solution Problem 1 (20...

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Unformatted text preview: ECE 483 Midterm 2 Solution Problem 1 (20 points) For the above sampled-data system, find the transfer function C ( z ) R ( z ) . Solution: We write C = G 2 ( G 1 E + HC ) C = G 1 G 2 1 G 2 H E C = bracketleftbigg G 1 G 2 1 G 2 H bracketrightbigg E . (1) On the other hand, using the above expression of C , we obtain E = R D A = R D ( HC ) = R D bracketleftbigg G 1 G 2 H 1 G 2 H E bracketrightbigg = R D bracketleftbigg G 1 G 2 H 1 G 2 H bracketrightbigg E . Solving for E , we have E = R 1 + D bracketleftBig G 1 G 2 H 1 G 2 H bracketrightBig . Pluggint this into (1) yields C = bracketleftBig G 1 G 2 1 G 2 H bracketrightBig 1 + D bracketleftBig G 1 G 2 H 1 G 2 H bracketrightBig R . Therefore, the transfer function is C ( z ) R ( z ) = bracketleftBig G 1 G 2 1 G 2 H bracketrightBig ( z ) 1 + D ( z ) bracketleftBig G 1 G 2 H 1 G 2 H bracketrightBig ( z ) . D ( z ) T Data Hold G p ( s ) C ( s ) R ( s ) +- Problem 2 (35 points) In the above system, suppose T = 0 . 1 s; the data hold is a zero-order data hold; D ( z ) = K for K 0; and the plant is such that G ( z ) = Z bracketleftbigg 1 e sT s G p ( s ) bracketrightbigg = z . 5 z 2 z + 1 . 25 . 1 (a) (5 pts) Write the characteristic equations on both the z-plane and the w-plane....
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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-West Lafayette.

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Midterm_2_Fa10 - ECE 483 Midterm 2 Solution Problem 1 (20...

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