Page 226 - Mechanical Engineers' Handbook (Volume 2)

4 Data Conditioning 215

sors change. A parametric model (equation) can be used to convert between types of units
or to correct for changes in the parameters of the model. The parameters for this equation
may be derived through a process known as calibration (Chapter 1 covers much of the process
of calibration and sampling). This involves determining the parameters of some equation by
placing the sensor in known environmental conditions (such as freezing or boiling water)
and recording the voltage or other measurable quantity it produces. Some (normally simple)
calculations will then produce the parameters desired. (See the following discussion of simple
linear fit for the procedure for a simple, two-parameter equation.) The complexity of the
model increases when the measured value is not directly proportional to the desired units
(nonlinear). Additionally, as sensors get dirty or age, the parameters might need adjusting.
There are a variety of control techniques to assist with compensating for changes in the
environment around the sensor, including adaptive control.

4.1 Simple Linear Fit
The simplest formula for converting a measured value to the desired units is a simple linear
equation. The form of the equation is y ax b, where x is the measured value, y represents
the value in the units desired, and a and b are parameters to adjust the slope and offset,
respectively. The procedure for finding a and b is as follows:
1. Create a known state for the sensor in the low range. An example would be to put
a temperature sensor in ice water.
2. Determine the value obtained from the sensor.
3. Create a known state for the sensor in the high range. An example would be to
immerse the sensor in boiling water.
4. Determine the value obtained from the sensor
5. Calculate the values of a and b from these values using the equations
actual high value actual low value
a (1)
measured high value measured low value
b actual low value (a measured low value) (2)
Figure 3 demonstrates example relationships between measured values and engineering units.

4.2 Nonlinear Relationships
Often, there is not a simple linear relationship between the engineering units and the mea-
sured units (Fig. 4). Instead, for a constantly rising pressure or temperature, the measured
value would form some curve. If possible, we use a portion of the sensor’s range where it
is linear, and we can use Eqs. (1) and (2). When this is not possible, we have to characterize
the sensor by a different equation, which could be a polynomial, a transcendental, or a
combination of a series of functions.
One can imagine several sensors which are linear in different ranges to be used in
conjunction to create a larger range of operational data. This variety of formulas should
make one point clear: Without an understanding of the basic model of the sensor, one cannot
know what type of conversion to use. Many sensors have known differences in output de-
pending on the range of sensed data. Be aware of the effect environmental conditions have
on the sensor readings. If the characteristics of a sensor are unknown, then the sensor must
be measured under a variety of conditions to determine the basic relationship between the