E1C12 09/14/2010
13:54:20 Page 558
We have provided an introduction to block-diagram representation of dynamic systems based
on Laplace transforms, and have provided a review of the application of Laplace transforms to the
solution of ordinary, linear differential equations. A discussion of open- and closed-loop control
methods provided examples of proportional, proportional-integral, and proportional-integralderivative control.
NOMENCLATURE
a
acceleration (l t
À2 )
c
damping coefficient (m t
À1 )
c c
critical damping coefficient (m t
À1 )
g
acceleration of gravity (l t
À2 )
k
spring constant (m t
À2 )
m
mass (m)
p
pressure (m l
À1
t
À2 )
r
radius, vector (l )
t
time (t)
dt
time interval for data sampling (t)
u
uncertainty
v
linear velocity (l t
À1 )
y
displacement (l )
y hs displacement of housing, seismic instrument (l )
y m
displacement of seismic mass (l )
y r
relative displacement between seismic mass
and housing in a seismic instrument (l )
dy
deflection (l )
A
amplitude
B
magnetic field strength (m C
À1
t
À1 )
C v
discharge coefficient
D c
coil diameter for magnetic pickup (l )
E i
input voltage (V )
E o
output voltage (V )
F
force, vector (m l t
À2 )
J
polar moment of inertia (l
4 )
L
length (l )
M
magnitude ratio
M
moment, vector (m l
2
t
À2 )
P
power (m l
2
t)
Q
volumetric flow rate (l
3 t
À1 )
R o
outer radius (l )
T
temperature (
)
T
torque (m l
2
t
À2 )
8
volume (l
3 )
z
damping ratio
t
time constant (t)
t max maximum shearing stress (m t
2
l
À1 )
f
phase angle
k
controller gain
v
rotational speed (t
À1 )
v n
natural frequency (t
À1 )
REFERENCES
1. Coltman, J. W., The transformer, Scientific American, 86, January 1988.
2. Herceg, E. E., Schaevitz Handbook of Measurement and Control, Schaevitz Engineering,
Pennsauken, NJ, 1976.
3. Bredin, H., Measuring shock and vibration, Mechanical Engineering, February: 30, 1983.
4. Measurement of Rotary Speed, ASME Performance Test Codes, ANSI/ASME PTC 19.131961, American Society of Mechanical Engineers, New York, 1961.
5. Gindy, S. S., Force and torque measurement, a technology overview, Experimental Techniques,
9: 28, 1985.
6. Measurement of Shaft Power, ASME Performance Test Codes, ASME PTC 19.7-1980,
(Reaffirmed Date: 1988), American Society of Mechanical Engineers, New York, 1980.
7. Palm, William J., Modeling Analysis and Control of Dynamic Systems, 2nd ed., John Wiley and
Sons, New York, 1999.
558 Chapter 12 Mechatronics: Sensors, Actuators, and Controls
13:54:20 Page 558
We have provided an introduction to block-diagram representation of dynamic systems based
on Laplace transforms, and have provided a review of the application of Laplace transforms to the
solution of ordinary, linear differential equations. A discussion of open- and closed-loop control
methods provided examples of proportional, proportional-integral, and proportional-integralderivative control.
NOMENCLATURE
a
acceleration (l t
À2 )
c
damping coefficient (m t
À1 )
c c
critical damping coefficient (m t
À1 )
g
acceleration of gravity (l t
À2 )
k
spring constant (m t
À2 )
m
mass (m)
p
pressure (m l
À1
t
À2 )
r
radius, vector (l )
t
time (t)
dt
time interval for data sampling (t)
u
uncertainty
v
linear velocity (l t
À1 )
y
displacement (l )
y hs displacement of housing, seismic instrument (l )
y m
displacement of seismic mass (l )
y r
relative displacement between seismic mass
and housing in a seismic instrument (l )
dy
deflection (l )
A
amplitude
B
magnetic field strength (m C
À1
t
À1 )
C v
discharge coefficient
D c
coil diameter for magnetic pickup (l )
E i
input voltage (V )
E o
output voltage (V )
F
force, vector (m l t
À2 )
J
polar moment of inertia (l
4 )
L
length (l )
M
magnitude ratio
M
moment, vector (m l
2
t
À2 )
P
power (m l
2
t)
Q
volumetric flow rate (l
3 t
À1 )
R o
outer radius (l )
T
temperature (
)
T
torque (m l
2
t
À2 )
8
volume (l
3 )
z
damping ratio
t
time constant (t)
t max maximum shearing stress (m t
2
l
À1 )
f
phase angle
k
controller gain
v
rotational speed (t
À1 )
v n
natural frequency (t
À1 )
REFERENCES
1. Coltman, J. W., The transformer, Scientific American, 86, January 1988.
2. Herceg, E. E., Schaevitz Handbook of Measurement and Control, Schaevitz Engineering,
Pennsauken, NJ, 1976.
3. Bredin, H., Measuring shock and vibration, Mechanical Engineering, February: 30, 1983.
4. Measurement of Rotary Speed, ASME Performance Test Codes, ANSI/ASME PTC 19.131961, American Society of Mechanical Engineers, New York, 1961.
5. Gindy, S. S., Force and torque measurement, a technology overview, Experimental Techniques,
9: 28, 1985.
6. Measurement of Shaft Power, ASME Performance Test Codes, ASME PTC 19.7-1980,
(Reaffirmed Date: 1988), American Society of Mechanical Engineers, New York, 1980.
7. Palm, William J., Modeling Analysis and Control of Dynamic Systems, 2nd ed., John Wiley and
Sons, New York, 1999.
558 Chapter 12 Mechatronics: Sensors, Actuators, and Controls