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Chemical Engineering Department
University of Florida
ECH 4323
Process Control Theory
HOMEWORK No. 8 — SECONDORDER DYNAMICS
1.0
A forcemomentum balance on a mercury manometer results in the equation
4
d
2
x
dt
2
+
0.8
dx
dt
+
x
=
p(t)
where
x
is the displacement of the mercury column from its equilibrium position, and
p(t)
is the timevarying pressure acting on the manometer.
(a)
Find the transfer function relating
x
to
p
, assuming that the system is initially in
equilibrium.
(b)
Find the gain, timeconstant, and damping coefficient for the system. Classify the
system based on the value of the damping coefficient.
(c)
Calculate the response of the manometer to the pressure input
p(t)
= 2
e
4
t
S(t).
2.0
Modified version of Exercise 5.12 in Seborg, Edgar and Mellichamp (3
rd
. Edition)
Consider the linear differential equation
d
2
!
y
dt
2
+
"
d
!
y
dt
+
4
!
y (t)
=
!
u (t)
with initial condition
!
y (0)
=
0
and
!
u (0)
=
0
, and where
!
is a nonnegative real
number. The following questions regard the response of the system when input is the
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This note was uploaded on 07/14/2011 for the course ECH 4323 taught by Professor Crissale during the Spring '10 term at University of Florida.
 Spring '10
 Crissale

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