hwsln-421-s06-06

hwsln-421-s06-06 - ECE 421, Spring 2006 Solutions to HW...

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ECE 421, Spring 2006 Solutions to HW Assignment #6 Problem # N Step ( q =1) Ramp ( q =2) Parabola ( q =3) 1 0 1 1+ K x ,K x = 168 K 9 2 1 0 1 K x x = 7 K 25 3 2 0 0 1 K x x =7 K 4 3 0 0 0 5 0 1 K x x = K 6 2 0 0 1 K x x = K 7 1 0 1 K x x = 8 K 5 8 0 1 K x x = 2 K 5 9 1 0 1 K x x = 2 K 13 10 2 0 0 1 K x x = 427 K 4 11 0 1 K x x = 304 K 3 12 1 0 1 K x x = 182 K 5 13 2 0 0 1 K x x =96 K 14 3 0 0 0 15 0 1 K x x = K 16 2 0 0 1 K x x = K 17 1 0 1 K x x = 85 K 6 18 0 1 K x x = K 2 19 1 0 1 K x x = K 3 20 2 0 0 1 K x x = 143 K 2 21 0 1 K x x = 209 K 6 22 1 0 1 K x x = 990 K 7 23 2 0 0 1 K x x = 525 K 2 24 3 0 0 0 25 0 1 K x x = K 1
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Problem B-5-30 For a unity-feedback system with forward transfer function G ( s ) , the closed-loop transfer function T CL ( s ) is given by T ( s )= G ( s ) 1+ G ( s ) (1) so G ( s ) can be determined from T ( s ) . T ( s )[1+ G ( s )] = G ( s ) G ( s T ( s ) 1 T ( s ) (2) For this system, G ( s ) is G ( s μ Ks + b s 2 + as + b 1 μ + b s 2 + as + b = + b ( s 2 + as + b ) ( + b ) = + b s [ s +( a K )] (3) This is a Type 1 system, so the steady-state error for a ramp input is e ss = 1 K v ,K v = lim s 0 [ sG ( s )] = lim s 0 + b s a K ) ¸ = b
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hwsln-421-s06-06 - ECE 421, Spring 2006 Solutions to HW...

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