Elec 471 Embedded Computer Systems
Chapter 1, Basic Concepts
By Prof. Tim Johnson, PE
Wentworth Institute of Technology
Boston, MA
Theory and Design for Mechanical Measurement
by Richard Figliola
Content
• Basic Concept of Measurement Methods
• General Measurement System
• Experimental Test Plan
– Variable, Parameters, Noise & Interference, Random Tests, Replication and
Repetition, Concomitant Methods
• Calibration
– Static & Dynamic Calibration, Static Sensitivity, Range, resolution,
Accuracy/Error, Types of Errors/Uncertainty, Sequential and Random Tests
• Standards
–
–
–
–
Base Dimensions and their Units
Derived Units
Hierarchy of Standards
Test Standards and Codes
• Presenting Data
– Coordinated Formats
– Significant digits
Basic Concepts of Measurement
Methods
• General familiarity with ordinary measurements
• Specifics and modern needs demand greater
attention to the methods of measurement
• Measurement methods seek to answer the
questions:
– How does one establish the relationship between the
real value of a variable and the value actually
measured?
– Can a measurement be devised so that the
measurement system provides unambiguous
information?
General Measurement System
The MSP430 16-bit analog to digital converter (ADC) contains signal conditioning
and output stages which along with a C-program will provide a control stage.
Quick Definitions
A. Sensor—a physical device that is sensitive to the process
being measured. Changes within the sensor can be
detected because they are connected to the transducer.
B. Transducer—converts the sensed information into a signal
(electrical, mechanical, optical or other).
C. Signal Conditioning—amplifies the transducer signal so it
can be read and minimizes the noise by filtering. If
digitized this stages writes a data value to memory.
D. Output—converts the conditioned signal into a format
useful for display.
E. Control—evaluates the conditioned signal (the data value)
to control the process either manually or automatically via
computer program.
Complete Measurement System Example
Experimental Test Plan
• Answers a question such as what is the optimum speed to
minimize fuel consumption?
• Here are the steps once the question is formulated:
– Parameter Design Plan
• Identify process variables and limits (parameters allowed range)
• Identify a means for control
– System and Tolerance Design Plan
• Selection of a measurement technique
• Identification of equipment and test procedure
• Tolerance desired
– Data Reduction Design Plan
• Analysis of data
– Data collection
– Sample frequency
– Frequency response
• Information display
• System and data evaluation
Process Variables
• Variable are entities that influence the test.
• The measured variable is the targeted variable.
• If a change in one variable doesn’t affect another
variable then the variables are independent.
• A variable that is affected by changes in one or
more other variables is a dependent variable.
• A variable may be continuous meaning it changes
all the time or it may be quantized where it
changes between discrete values.
Variables continued
• A variable is controlled if it can be held at a
constant value during a measurement.
• The relationship (mathematical model/equation)
between independent variables and a dependent
variable can be determined by taking
measurement while stepping the independent
variable value.
• Variable that affect the value of the target
variable but can not be controlled are called
extraneous variable. These variables can
introduce difference in repeated tests.
Example of an Extraneous Variable
Parameter Defined
• A parameter is a functional grouping of variables.
• Examples
– Moment of Inertia—object’s resistance to a change of
its rotation, scalar formula ½mv2
– Volume—formula V = length*width*height
• Control parameter has an effect on the behavior
of the measured variable. A parameter is
controlled if its value can be maintained during a
set of measurement.
How to develop a parameter
• Fan flow rate, Q, is a function of the rotational
speed, n in rpm, and diameter, d, formula: Q =
nd3 (text formula)
• Fan flow coefficient, C, is a parameter that
indicates efficiency, formula C = Q/nd3.
• The variables, d and n, can then be held constant
one at a time to observe their effects on C.
• Lesson: by having a formula, a parameter is
developed by dividing the outcome of an
equation by its inputs.
Noise and Interference
• Noise is a random variation in the measured
signal as a consequence of extraneous variables.
• Noise increases data scatter about a data plot;
variance of data reading from average value.
Noise has a short time duration and affects only a
few data points.
• Interference is an undesired trend of data point
derived from the measure signal from the ideal
value.
• Interference has a longer time duration than
noise and observes a deterministic trend.
Random Tests
• A random test is a form of randomization.
• Needed to detect when a target variable dependent on
several independent variable that may be effect by
other extraneous variables unknown to the system
designers.
• Examples are the use of different instruments, test
operators, and test operating conditions.
• A random test is defined as measurement matrix that
sets a random order to the change in the value of the
independent variable applied.
• Additionally, organizing a test matrix in random blocks
where a data set of developed with a controlled
variable varied but extraneous variable is fixed then
repeated with the extraneous variable stepped through
a range.
Replication and Repetition
• Rule: the estimated value of a measured variable
improves with the number of measurements.
• Repeated measurements during a test run are
called repetition.
• Repetition helps to quantify the variation in a
measured variable while the operating conditions
are held under nominal control.
• Repetition will not permit an assessment of how
exact the operating conditions can be set.
• Changing the operating conditions, such as,
machines, and/or operators is called Replication.
Concomitant Methods
• Are the results good?
• Using different measurement methodologies that
can provide an estimate of the target variable
which can be compared will show the degree of
agreement in the final estimate.
• Analysis of the difference can reveal hidden
extraneous variables in one or the other
measurement test.
• This methodology employs a double-check policy
by using different equipment.
Calibration
• Is the application of a known input value to a
measurement system for the purpose of
observing the system output value.
• Calibration establishes the relationship between
the input and output values.
• Calibration using an acknowledged known value
(called a standard) can verify a system output.
• In a calibration the input value is usually a
controlled independent variable.
• The output would be the dependent variable of
the calibration.
Static Calibration
• Is when the value of the input variable
involved in a calibration remain constant: not
varying in time or space.
• Only the input and output magnitudes are
considered in the evaluation.
• During a measurement test set by varying the
input values you can develop a calibration
curve.
Calibration Curve
• A calibration curve describes the static input-output
relationship for a measurement systems.
• A formal equation can be developed from a calibration
curve modeling the input-output relationship.
• Error measurements of data sets points plotted vs. a
calibration curve can be developed using Excel
statistical functions.
• The correlation can be used to ascertain an unknown
input value based on an output value using the
calibration curve or mathematical model.
• The slope of the curve is Static Sensitivity K= dy/dx
Dynamic Calibration
• This type of calibration uses an input variable
that varies with time or space.
• The input will vary in magnitude and/or
frequency content.
• A dynamic calibration determines the
relationship between a dynamic input and the
measurement system output.
• This topic is covered in Chapter 3.
Range and Resolution
• A calibration range is inputs of known minimum
to maximum values for which a measurement
system is to be used.
• These values define the operating range which is
the span of ri = xmax - xmin.
• The output span, aka, full-scale-operating range
(FSO) is ro = ymax - ymin.
• Resolution is the smallest increment in the
measured value that can be discerned. It is
quantified by the smallest scale increment of the
output readout indicator.
Accuracy and Error
• The exact value of a variable is called the true value.
• The value of a variable as indicated by a measurement
system is called the measured value.
• The accuracy of a measurement refers to the closeness
of agreement between these two values.
• The error, e, is the difference between the measured
value and the true value: e = measured value – true
value
• You can tell a person is an engineer because they will
always ask “What’s the error?” at some point in a
conversation. If the person answering this question
provides an answer you can be certain that they are an
engineer also.
Random error
• Random error is a measure of the random variation
found during repeated measurements of a variable.
• The repeatability of a measurement system refers to its
ability to indicate the same value on repeated
measurements for a specific value of input. This is also
referred to as precision.
• The portion of the absolute error, |e|, that remains
constant on repeated measurements is called the
systematic error. This error is a bias that can not be
discerned from repeated measurements.
• However, an offset between the apparent average of
the readings and the true value is a measure of the
systematic error.
Linearity error
• A linear system has a relationship between the
input and output that can be expressed
mathematically as: yLinear = mx + b
• Actually systems y(x) measurement data sets are
often close to a linear fit so the linear error is
eL(x) = y(x) – yLinear
• The linear equation, yLinear, is a
result of a best fit for a linear
equation on calibration data.
Sequential Test & Hysteresis error
• A sequential test applies an incremental change to the
input value over a desired range by incrementing or
decrementing the input by an incremental value (which is
usually small when compared to the input value).
• This test can determine hysteresis error, eh, which is a
result of retention by the system of a portion of the
output value from the previous input.
• eh= (y)upscale –(y)downscale
Uncertainty
• There is an uncertainty in the error for a measurement
because the true value is not known exactly and a
reference value is used instead during the instrument’s
calibration.
• Uncertainty refers to the estimate of the sum of all the
errors present in the measurement system, its
calibration, and the measurement technique. It is a
property of the test results.
• After calibration, an error can be estimated to be
bounded by a ± range of the indicated reading with a
certain confidence. This quantifies the uncertainty.
Sensitivity error
• This is an error, eK, in the slope of the calibration
curve. This could be caused by temperature changes
in the ambient temperature.
• The “thermal” sensitivity error can be found by
calibration at different temperatures.
• Other source could cause a change
in the slope and their error
estimation is dependent on
determining the source.
(Sensitivity error graph shown with fixed zero intercept)
Zero error
• If the zero intercept (y = 0 when x is zero) drifts
meaning the variable b changes in the linear
equation y = mx + b, this is called a zero error, ez.
• This results in a vertical shift of the calibration curve
as seen here:
• This error is detected by
repeated random tests.
Repeatability
• Instrument repeatability, %eRmax, is the ability of a
measurement system to indicate the same value
upon retesting using the same input.
• Specific claims of repeatability are based on multiple
calibration tests: replication.
• A standard deviation, Sx, is developed.
• The formula uses Full
Scale Output, ro, to
calculate the percentage:
%eRmax = 2Sx/ro x 100
Overall instrument error
• An estimate of the overall instrument error, uc
is made by combining all known errors.
• This results in a number that is an uncertainty.
• An estimate is computed from the square root
of the sum of the squares of all known errors.
• For m known errors:
Uc = [ (e1)2 + (e2)2 + … +(em)2 ]½
Standards
• When a measurement system is calibrated its indicated value is
compared directly with a reference value.
• This reference value forms the basis of the comparison and is
known as the standard.
• This standard is based on long standing observations of instruments
and published values from standard organizations such as the ISO,
the International Organization for Standardization, the National
Institute of Standards and Technology (NIST), American Society of
Testing and materials (ASTM), and others.
• These organizations published values for physical phenomenon
such as conversion values and procedures for quality assurance ISO
2000, ISO 2001 and many others.
• Section 1.5 in the text covers numerous details about these
standards but a visit online to the original sources is encouraged.
• Note that there are original measurements, secondary sources,
transfer standards, and working standards used by calibration
laboratories.
Metrology
•
•
•
•
•
Metrology is the science of measurement. It deals with physical measurement standards
(not documentary standards). Measurements play a key role in modern life; in industry as
well as in trade and in society in general, in assuring quality and safety. There is a growing
need in science and technology for increasingly accurate and more complex measurements.
There are seven base units of measurement, which form the base of the International System
of Measurement (SI). These include:
– Meter (length)
– Kilogram (mass)
– Second (time)
– Ampere (electric current)
– Kelvin (temperature)
– Mole (amount of substance)
– Candela (luminous intensity)
Many derived units, such as force, pressure, watt, and volt can be formed by combining the
base units.
Signed in 1875, the Treaty (or Convention) of the Meter remains the basis of all International
agreement on units of measurement. Countries are represented in the treaty by their
National Measurement Institutes (NMI) that have the responsibility for maintaining national
measurement standards. In the United States, Congress gave this responsibility to NIST in
1901.
http://gsi.nist.gov/global/index.cfm/L1-5/L2-47
Research (aka Homework)
• Suppose you were to develop a product…that had
a power cord attached to it so the product could
be turned on.
• Find out what organization would be responsible
for publishing the documentation for the cord.
• Find out the standard number(s) that would
apply to the power cord.
• What is the procedure to obtain a UL or EU
certification listing.