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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online