
664 31. PROCESS CONTROL
the form of a current. One standard specifies that
the signal from a sensor be conditioned such that
a signal in the range of 4—20 mA be reported for
the range of the variable. The controller usually
converts this to a voltage by taking the signal
across a resistor (i.e., the IR drop). In pneumatic
systems, one common standard calls for a signal
output of 3—15 psi (20-100 kPa).
Response times of sensors
The time
response
of a sensor is a measure of
how the sensor responds to an actual change as a
function of
time.
For example, all thermocouples
have mass. This mass takes a certain period of
time to change temperature. Thus, when the
thermocouple at one temperature is immersed in a
liquid of a different temperature, the output of the
thermocouple will change with time until it finally
gives a reading that is within its normal error.
This might take a fraction of a second to many
seconds depending on the geometry of
the
thermo-
couple. The time constant of the sensor is usually
much lower than that of the system, so it should
not be a factor. The time constant, however, may
depend upon how the sensor is used; for example,
temperature measuring devices respond much
more quickly in a water bath (where heat transfer
is high) than in air (where heat transfer is low).
A first—order time response (such as the
charging of a capacitor, or, approximately, most
temperature sensing devices) follows the equation:
when
b^
= 0, then: b{t) = bf[l - e-'"]
where b is the output value as a function of time,
r, initially, /, or finally, /. The symbol r is called
the time constant. If the initial output is zero then
after one time constant of time has passed the
sensor reaches only 63.2% of its final output.
After 2, 3, 4, 5, and 6 time constants, the sensor
reaches
86.5%,
95.0%, 98.2%,
99.3%,
and
99.75%
of its final value, respectively.
Second—order responses will cause an oscil-
lation in the output (as will be shown in Fig. 31-
4),
that is impossible to solve precisely, but can be
characterized mathematically.
Optical sensors
The principles of light have been presented in
Chapter 24, which (implicitly) provides some
details for measurement of
light.
Photoconductors
use a thin band (in a serpentine pattern to increase
the effective length) of a material that becomes
conductive when exposed to light of a minimum
frequency (energy level). Two common materials
are CdS (which requires light of wavelength 515
nm or less and has a time constant of about 100
ms) and CdSe (which requires light of wavelength
716 nm or less and has a time constant of about 10
ms).
Photovoltaic cells produce a voltage and
current that are a fimction of the light level inci-
dent to them. These have time constants on the
order of
1
to 100 /xs. For very low levels of light
(used in liquid scintillation counters to determine
radioactivity) photomultiplier tubes are used.
31.3 TEMPERATURE SENSORS
Resistance—temperature detectors
(RTDs)
The resistance of metals is a fimction of
temperature and increases with increasing tempera-
ture.
The relationship is fairly linear over a wide
temperature range, although second—order trans-
fer functions are often used. Resistance—temper-
ature detectors (RTDs) often use platinum or
nickel. The sensitivity of platinum is a function of
temperature, but is about 0.00385 QIWC (cali-
brated to the internationally accepted DIN 43760
standard.) (One common U.S. practice is to
configure RTDs at 0.00392 0/0/°C.) Nickel is
0.005/°C at room temperature. Thus, a 100.00
platinum RTD at 0°C will have a resistance of
100.385
12
at rC.
This small signal difference is conditioned by
using a Wheatstone bridge circuit which may
contain a
compensating
line to nullify the effect of
long leads to the RTD. The current used in RTD
devices must be low enough so that the RTD does
not alter the environment through self—heating.
RTD time constants are about 0.2 to 0.5 seconds
in flowing water to more than 10 times that time
in air. RTD devices can be used from —100 to
600°C (or 900°C with ceramic materials).
Thermistors
The resistance of semiconductors is also a
function of temperature, but semiconductor materi-
als (oxides of Ni, Mn, Fe, Co, Cu, Ti, etc.) can
be made whose resistance increases drastically
with increasing temperature. This fact is used to