Solutions to Homework Set 1 - MAE143B, Summer II, 2009
1.1 First we try to solve for y2 , as this is part of the feedback. Substitution of the rst connection equation u2 = yc into the dynamic equation (in Laplace form) y2 (s) = Q21 (s)u1 (s) + Q22 (s)u2 (
Solutions to Homework Set 2 - MAE143B, Summer II, 2009
1.1 First, we multiply denominator and numerator of G(s) by 1 G (s ) = k s2 + We can write
d m k m d s m 1 m
and k to reach the desired form
+
k m
as 2
k 1 d m 2 mk
=
d m k m
1 This way, by dening K =
Final - MAE143B, Summer II 2008
September 5, 2008 3:00pm-6:00pm, Center 115
Name: Student #:
open-book and open-notes nal exam use the available space to derive your results, attach extra paper if necessary use of any electronic equipment (calculator, pho
Solutions to Homework Set 3 - MAE143B, Summer II, 2009
1.1 Consider y (s) = G1 (s)u(s), G1 (s) = then substitution of s = j in G1 (s) yields G1 (j ) = and with > 0 this makes 1 + (1 )2 |1 + j1 | = |j |1 + 2 | 1 + (2 )2 G1 (j ) = (1 + j1 ) (j ) (1 + j2 ) =
Name:
Student #:
Midterm - MAE143B, Fall 2005
November 15, 2005 11:00am-11:50pm, HSS1330
Solutions
open-book and open-notes midterm exam
use the available space to derive your results, attach extra paper if necessary
use of any electronic equipment (calcu