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hw-421-s06-06 - ECE 421 Spring 2006 HW Assignment#6 Due...

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ECE 421, Spring 2006, HW Assignment #6 Due Tuesday, March 7, 2006 1. Textbook problems B-5-30 and B-5-32 2. For each of the following systems, determine the closed-loop steady-state errors for unit step, unit ramp, and unit parabolic reference input signals, expressing the errors in terms of K. You may assume that the closed-loop systems are stable in each case. G 1 ( s ) = K ( s + 6) ( s + 7) ( s + 0 . 75)( s + 1)( s + 3) (1) G 2 ( s ) = K ( s + 1) ( s + 3 . 5) s ( s + 1 . 25)( s + 2)( s + 5) (2) G 3 ( s ) = K ( s + 3) ( s + 7) s 2 ( s + 0 . 75)( s + 2) 2 (3) G 4 ( s ) = K ( s + 1) ( s + 5) ( s + 12) s 3 ( s + 0 . 625)( s + 2)( s + 3) (4) G 5 ( s ) = K ( s/ 3 + 1) ( s/ 15 + 1) ( s/ 0 . 5 + 1)( s/ 6 + 1)( s/ 9 + 1) (5) G 6 ( s ) = K ( s/ 3 + 1) ( s/ 4 + 1) s 2 ( s/ 5 + 1)( s/ 6 + 1)( s/ 7 + 1) ( s/ 0 . 25 + 1) (6) G 7 ( s ) = K ( s/ 5 + 1) ( s/ 40 + 1) ( s 2 + 8 s + 32) s ( s/ 0 . 5 + 1)( s + 20)( s/ 3 + 1) (7) G 8 ( s ) = K ( s/ 5 + 1) ( s/ 7 + 1) ( s/ 0 . 25 + 1)( s/ 9 + 1) ( s + 2 . 5) ( s/ 4 + 1) (8) G 9 ( s ) = K ( s/ 3 + 1) ( s/ 5 + 1) s ( s/ 0 . 625 + 1) ( s + 6 . 5) ( s/ 4 + 1)( s/ 0 . 25 + 1) (9) G 10 ( s ) = K ( s/ 3 + 1) ( s + 7) ( s 2 + 10 s + 61) s 2 ( s/ 0 . 25 + 1) ( s + 4) ( s/ 12 + 1)( s/ 0 . 12 + 1) (10) G 11 ( s ) = K ( s + 19) ( s + 20) ( s + 0 . 625)( s + 2)( s + 3) (11) 1
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G 12 ( s ) = K ( s + 7) ( s + 13) s ( s + 0 . 25)( s + 2)( s + 5) (12) G 13 ( s ) = K ( s + 3) ( s + 4) s 2 ( s + 2)( s + 0 . 25) 2 (13) G 14 ( s ) = K ( s + 10) ( s + 12) ( s + 13) s 3 ( s + 0 . 5)( s + 3)( s + 7) (14) G 15 ( s ) = K ( s/ 7 + 1) ( s/ 8 + 1) ( s/ 0 . 125 + 1)( s/ 9 + 1)( s/ 15 + 1) (15) G 16 ( s ) = K ( s/ 3 + 1) ( s/ 7 + 1)
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