4-sol - ECE 483 Homework #4 Solution These problems are...

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 Homework #4 Solution These problems are from the textbook. Problems 4-13 Solution: (a) The transfer function from e ( kT ) to m ( kT ) is D ( z ) = . 2 1 . 9 z- 1 = . 2 z z . 9 . Thus, the transfer function from e ( kT ) to c ( kT ) is C ( z ) E ( z ) = D ( z ) G ( z ) , where G ( z ) is the z-transform of the combined plant and data hold transfer function: G ( z ) = Z bracketleftbigg 1 e- sT s G p ( s ) bracketrightbigg = Z bracketleftbigg (1 e- sT ) 1 s ( s + 0 . 2) bracketrightbigg = (1 z- 1 ) Z bracketleftbigg 5 s 5 s + 0 . 2 bracketrightbigg = z 1 z bracketleftbigg 5 z z 1 5 z z e- . 2 T bracketrightbigg = 5(1 e- . 2 T ) z e- . 2 T = . 9063 z . 8187 . Thus, the system transfer function is C ( z ) E ( z ) = D ( z ) G ( z ) = . 2 z . 9 . 9063 z . 8187 = . 1813 z ( z . 9)( z . 8187) . (b) The DC gain of the system is D ( z ) G ( z ) | z =1 = . 1813 (1 . 9)(1 . 8187) = 10 . (c) Alternatively, the DC gain can be computed as D ( z ) | z =1 G p ( s ) | s =0 = . 2 1 . 9 1 . 2 = 10 . (d) The steady-state value of the output under unit step input is 10. 1 (e) Under unit step input e ( t ) = u ( t ), we have E ( z ) = z z- 1 , and C ( z ) = . 1813 z ( z . 9)( z . 8187) z z 1 = . 1813 z 2 ( z . 9)( z . 8187)( z 1) = 20 . 07 z z . 9 + 10 . 07 z z . 8187 + 10 z z 1 . Thus, c ( kT ) = 20 . 07 (0 . 9) k + 10 . 07 (0 . 8187) k + 10 , k = 0 , 1 , 2 , . . ., which approaches 10 and k ....
View Full Document

Page1 / 6

4-sol - ECE 483 Homework #4 Solution These problems are...

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