ME 475
HOMEWORK #2
Solutions
Spring 2012
PROBLEM 1:
GIVEN:
A rapid transit train car weighs 63000 lb. The combined effects of air resistance and wheel rolling
resistance provide equivalent viscous damping of 147 lb/(ft/sec). The dc traction motors that pr
ME 475
HOMEWORK #10
SOLUTION
Spring 2013
PROBLEM 1:
FPE, Prob. 6.45, p. 403.
Notice that you do not have to satisfy a steady-state error specification. Therefore, you are
allowed to introduce a gain to help you meet the specifications. Please note that th
ME 475
HOMEWORK 12 SOLUTIONS
Spring 2013
PROBLEM 1:
FPE, Prob. 8.2, p. 593.
Given:
where
Find: solution
.
Solution:
From Table 8.1:
Alternatively, you could use synthetic division:
Since
, y(k) can be read off as the coefficients of zk in the quotient.
2
Problem 1:
Let
1
s+a
and
D( s ) = K
( s + 2 )( s + 3)
s+b
Using root-locus techniques, find values for the parameters a, b, and K of the
compensation D(s) that will produce close-loop poles at s = ! 1 j for the system shown
in the figure.
G(s) =
Problem 2
ME 475
HOMEWORK #7
SOLUTION
Spring 2013
PROBLEM 1:
Given:
R(s)
G(s)
Y(s)
Find:
(a)
Plot frequency response of G(s) in MATLAB.
(b)
Static gain of G(s) from frequency response.
(c)
yss(t) when r(t) = A sin(t).
(d)
(e)
Output at steady state if r(t) = 10sin(
ME 475
HOMEWORK 11 SOLUTION
Spring 2013
PROBLEM 1:
FPE, Prob. 6.64 (part (b) only), p. 409.
Given:
Find:
Range of K for which the system is stable.
Solution:
Generate frequency response plots for G(s) with K = 1 and the time delay included:
G=tf(1,[1 2 0]
ME 475
HOMEWORK 8 SOLUTION
Spring 2013
PROBLEM 1:
FPE, Prob. 6.20, p. 394.
Given:
Find:
Nyquist plot with contour to the right of singularities on the j axis.
Nyquist plot with contour to the left of singularities on the j axis.
Range of gain K for stabil
Solution:
(a) Start by reducing the block diagram and in turn solving for Y.
or
to solve part (a) Let W = 0
But for a unit ramp input R = 1/s2
But if D as a pole at the origin
D must have a pole at the origin.
Part (b):
now let R = 0
There is a zero at th
Solution:
If the system were "second order" the equations in the text like 3.64 and 3.65 (6th ed) on
page 118 would apply. ( Equations 3.51 and 3.52 (5th ed) page 117 -188.)
this leads to :
from the 10% overshoot
and from the 1% settling time and a settli