Mechatronics Systems : Sensors used in Mechatronics integration

A strain gauge and bridge circuit are used to measure the tension force in a
steel bar.
The steel bar has a cross-sectional area of 13 cm2.
The strain gauge has a nominal resistance of 120 Ω and a GF of 2.
The bridge is supplied with 10 V.
When the bar is unloaded, the bridge is balanced so the output is 0 V.
Then force is applied to the bar, and the bridge voltage goes to 0.0005 V. Find
the force on the bar.
calculate the change in strain-gauge resistance due to the applied force:

calculate the elongation (strain) of the strain gauge (how much it
was stretched):
to calculate the force on the bar. This will require looking
up the value of Young’s modulus.
E= 2.07 × 107 N/cm for steel.

A strain gauge and bridge circuit are used to measure the tension
force in a steel bar.
The steel bar has a cross-sectional area of 50 cm2.
The strain gauge has a nominal resistance of 120 Ω and a GF of
2.15. The bridge is supplied with 5 V. When the bar is unloaded,
the bridge is balanced so the output is 0 V.
Then force is applied to the bar, and the bridge voltage goes to
0.005 V.
Find the force on the bar.

A strain gauge and bridge circuit are used to measure the tension
force in a steel bar. Force Applied to Bar is 30000 N
The strain gauge has a nominal resistance of 120 Ω and a GF of
2.15. The bridge is supplied with 10 V. When the bar is unloaded,
the bridge is balanced so the output is 0 V.
Then force is applied to the bar, and the bridge voltage goes to
0.005 V.
Find the cross section of bar ?

Thermal Sensors
• Temperature sensors give an output proportional to
temperature.
• Most temperature sensors have a positive
temperature coefficient (desirable), which means
that the sensor output goes up as the temperature
goes up,
• but some sensors have a negative temperature
coefficient, which means that the output goes down
as the temperature goes up.

Temperature Sensors
Absolute Scales
Rankine (°R)
Kelvin (K)
Relative Scales
Fahrenheit (°F)
Celsius (°C)

Temperature Sensors
100:C 373:K
273:K
255:K
0:C
-18:C
-273:C 0:K
-460:F 0:R
0:
F
32:F
460:R
492:R
672:R
212:F
Fahrenheit
[°F] = [°C] · 9/5 + 32
Celsius
[°C] = ([°F] − 32) · 5/9
Kelvin
[K] = [°C] + 273.15
Rankine
[°R] = [°F] + 459.67
Imperial
Fahrenheit (⁰F) / Rankine (⁰R) +/- 460
Metric
Celsius (⁰C) / Kelvin (⁰K) +/- 273

Methods of Measurement of Temperature
1. Mechanical Methods
1. Expansion of materials
2. Electrical Methods
1. Bimetallic Temperature Sensors
2. Thermocouples
3. Thermistors
4. Electrical resistance change (RTD)
5. Pyrometers

Bimetallic Temperature Sensor
• The bimetallic strip is a laminate of two metals with different
coefficients of thermal expansion.
• As the temperature rises, the metal on the inside expands more
than the metal on the outside, and the spiral tends to straighten
out.
• These sensors are typically used for on-off control as household
thermostat where a mercury switch is rocked from on to off.

Thermocouples
The thermocouple is based on the
See-beck effect, a phenomenon
whereby a voltage that is proportional
to temperature can be produced from
a circuit consisting of two dissimilar
metal wires.

Seebeck Effect
emf generated can be given by integration over the temperature

Thermocouples
Maintaining Cold Junction Temperature
• One method is to maintain the cold junction at
constant temperature with a control system.
– This can be useful if there are many thermocouples in a
system they can all be referenced to the same temperature
• Another method (used by a computer controller) is to
simply look up in a table the value of Vcold for the
ambient temperature and add this value to Vnet to
yield Vhot.

Thermocouples
Maintaining Cold Junction Temperature
• Use a temperature-sensitive diode (in an interface circuit) that
makes the thermocouple output behave as if the cold junction
were still at freezing, even though it’s not.
• The cold junctions are maintained at the same temperature as
the diode by mounting them all on an isothermal block.
• As the ambient temperature increases, the diode forward-
voltage drop (about 0.6 V) decreases at a rate of about 1.1
mV/°F. This voltage is scaled down (with R2 and R3) to 28 µV/°F,
which is the same rate that the real cold-junction voltage
increases with ambient temperature.

Classification
• Type J (iron-constantan) has the highest sensitivity but the
lowest temperature range,
• Type K (chromel-alumel) has a higher temperature range but a
lower sensitivity, and
• Type R (platinum-rhodium) has an even lower sensitivity but can
work at higher temperatures.

Type Composition Temperature Range
B Platinum 30% Rhodium (+) 2500-3100 degrees F
Platinum 6% Rhodium (-) 1370-1700 degrees C
C W5Re Tungsten 5% Rhenium (+) 3000-4200 degrees F
W26Re Tungsten 26% Rhenium (-) 1650-2315 degrees C
E Chromel (+) 200-1650 degrees F
Constantan (-) 95-900 degrees C
J Iron (+) 200-1400 degrees F
Constantan (-) 95-760 degrees C
K Chromel (+) 200-2300 degrees F
Alumel (-) 95-1260 degrees C
M Nickel (+) 32-2250 degrees F
Nickel (-) 0-1287 degrees C
N Nicrosil (+) 1200-2300 degrees F
Nisil (-) 650 -1260 degrees C
R Platinum 13% Rhodium (+) 1600-2640 degrees F
Platinum (-) 870-1450 degrees C
S Platinum 10% Rhodium (+) 1800-2640 degrees F
Platinum (-) 980-1450 degrees C
T Copper (+) negative 330-660 degrees F
Constantan (-) negative 200-350 degrees C

9/18/2015 Dr. Suhas Deshmukh 119
First, put the thermocouple in the oven and connect the thermocouple leads to the voltmeter.
Try to make the cold-junction connections to the meter probes be at ambient temperature,
which is about 90°F (as reported by a thermometer on the wall).

The graph of (for type J) is based on the cold junction being at freezing (32°F), which
it certainly is not in this case. From the graph, we can see that the 90°F would create
about 2.0 mV by itself.
You can see from that if Vcold increases, it will reduce Vnet, so if we are going to use
the graph, we must compensate by increasing our reading of 17 mV to 19 mV.
Now using the graph of
Figure for 19 mV, we read the
temperature is 660°.
This temperature is much
lower than the desired
1000°F, so clearly there is
something wrong with the
temperature-control system.
19 mv
6600F

An iron-constantan thermocouple is referenced at 32°F and has
an output voltage of 45 mV. What is the temperature at the hot
junction?
45 mv
1500 0F

Resistance Temperature Detector (RTD)
Metal resistance increases linearly with temperature with
smaller slope value
Change in the resistance is due to change in the resistivity (𝜌) of
the material

Resistance Vs Temperature Approximation
Linear Approximation
Straight line is drawn between two
points of the curve (i.e. T1 and T2) .
T0 represents midpoint
temperature equation of straight
line is linear approximation of
curve between T1 & T2

Resistance Vs Temperature Approximation
Quadratic Approximation
It includes both linear term and
term that veries as square of the
temperature, such approximation
is quadratic

Resistance Temperature Detectors (RTD)
• These are made up of
semiconductor materials
• Temperature Range:
– About -45°C - 150°C
The resistance temperature detector (RTD) is a temperature sensor based on the
fact that metals increase in resistance as temperature rises.
Platinum wire has a temperature
coefficient of 0.0039 Ω/Ω/°C,
which means that the resistance goes up
0.0039 Ω for each ohm of wire for each
Celsius degree of temperature rise.
RTDs are available in different
resistances, a common value being 100
Ω.
Thus, a 100-Ωplatinum RTD has a
resistance of 100 Ω at 0°C, and it has a
positive temperature coefficient of 0.39
Ω/°C.

RTD
• Sensitivity :
– for platinum is
0.004/0C, nickel
0.005/0C. i.e. 0.4 Ω
would be expected for
100-Ω RTD if
temperature is changed
by 10C
Response Time:
0.5 to 5 sec or more
Signal Conditioning:
High sensitive Wheatstone Bridge circuit is used which can
detect 0.4% change in the temperature
Repeatable, more sensitive and less expensive

Thermistors
 Thermistor, a word formed by combining thermal with
resistor, is a temperature-sensitive resistor fabricated from
semiconducting materials.
 The resistance of thermistors decreases proportionally with
increases in temperature.
 The operating range can be -200°C to + 1000°C

Thermistors
• The thermistors can be in the shape of a rod, bead or
disc.
• Manufactured from oxides of nickel, manganese,
iron, cobalt, magnesium, titanium and other metals.

9/18/2015 134
• Thermistors are nonlinear;
therefore, they are not usually
used to get an accurate
temperature reading
• Also, most thermistors have a
negative temperature coefficient,
which means the resistance
decreases as temperature
increases, as illustrated with the
solid line in the graph of Figure.
• A very desirable feature of these
devices is their high sensitivity. A
relatively small change in
temperature can produce a large
change in resistance.
Interface Circuit

Thermistor Characteristics
• Sensitivity:
– Change in resistance of 10% per 0C is common.
Thermistor with nominal resistance of 10kΩ at
some temperature may change 1kΩ for a 10C
change temperature
• Range:
– Lower limit is -800C i.e. -50 to -1000C
– Upper limit is 3000C
• Response Time:
– ½ sec typically with oil bath
– 10 sec with air contact

Thermistors
 The word that best describes the thermistors is
“sensitive”

Elements of Mechatronics System
Mechanical
System
Sensors
Actuators
Amplifying
Electronics
Amplifying
Electronics
Control System
Micro-controller or
Computer
Data Acquisition
System
Data Acquisition
System

Why Signal Conditioning ?
To measure signals from transducers, you must convert
them into a form a measurement device can accept.
Common types of signal conditioning include amplification,
linearization, transducer excitation, and isolation.

DAQ (Construction)
Transducer Filter ADC Computer DAC Amplification Actuator

Steps in DAQ
1. The input transducers measure some property of the
environment.
2. The output from the transducers is conditioned (amplified,
filtered, etc.).
3. The conditioned analog signal is digitized using an analog-to-
digital converter (ADC).
4. The digital information is acquired, processed and recorded by
the computer.
5. The computer may then modify the environment by outputting
control signals. The digital control signals are converted to
analog signals using a digital-to-analog converter (DAC).
6. The analog signals are conditioned (e.g. amplified and filtered)
appropriately for an output transducer.
7. The output transducer interacts with the environment.

Example : Components of PCM encoder
(Pulse Code Modulation)
PCM consists of three steps to digitize an analog signal:
1. Sampling
2. Quantization
3. Binary encoding

What is Analog / Digital Signal ?
Digital Control
System
Analog Control System

What is DSP (Digital Signal Processing) ?
• Converting a continuously changing waveform (analog)
into a series of discrete levels (digital)

What is DSP ?
• The analog waveform is sliced into equal segments and the
waveform amplitude is measured in the middle of each segment
• The collection of measurements make up the digital
representation of the waveform
0
0
.
2
2
0
.
4
4
0
.
6
4
0
.
8
2
0
.
9
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1
.
1
1
1
.
2
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.
2
4
1
.
2
7
1
.
2
4
1
.
2
1
.
1
1
0
.
9
8
0
.
8
2
0
.
6
4
0
.
4
4
0
.
2
2
0
-
0
.2
2
-
0
.4
4
-
0
.6
4
-
0
.8
2
-
0
.9
8
-
1
.1
1
-
1
.2
-
1
.2
6
-
1
.2
8
-
1
.2
6
-
1
.2
-
1
.1
1
-
0
.9
8
-
0
.8
2
-
0
.6
4
-
0
.4
4
-
0
.2
2
0
-2
-1 .5
-1
-0 .5
0
0 .5
1
1 .5
2
1
3
5
7
9
1
1
1
3
1
5
1
7
1
9
2
1
2
3
2
5
2
7
2
9
3
1
3
3
3
5
3
7

Resolution in DAQ ?
• Resolution (bits) & Code Width
• Sampling rate (samples/second)
• Number of channels, and data transfer rate (usually
limited by “bus” type: USB, PCI, PXI, etc.)).
• Precision of ANALOG to DIGITAL conversion process
is dependent upon the number (n) of bits the ADC of
DAQ is used.
• The higher the resolution, the higher the number of
division the voltage range is broken into (2n), and
therefore, the smaller detectable voltage changes.

Sampling Rate
• The data is acquired by an ADC using a process called
sampling.
• Sampling an analog signal occurs at discrete time
intervals.
• The rate at which the signal is sampled is known as the
sampling frequency.
Sampling

Sampling of analog signal
Continuous Signal
Sampled Signal
It is usual to specify a sampling rate
or frequency fs rather than the
sampling period. The frequency is
given by
fs= 1/Ts, where fs is in Hertz.
If the sampling rate is high enough,
then the signal x(t) can be
constructed from x[n] by simply
joining the points by small linear
portions, thus approximating to the
analog signal.

Sampling Theorem
The sampling theorem, or more correctly Shannon's
sampling theorem, states that we need to sample a
signal at a rate at least twice the maximum frequency
component in order to retain all frequency components in
the signal.
fs > 2 fmax
where fs is the sampling rate (frequency),
fmax is the highest frequency in the input signal,
and the minimum required rate (2/fmax) is called the
Nyquist frequency.

Effect of Sampling Frequency in signal reconstruction
Sampling the waveform cos(60t)
1000 Hz
20 Hz 10 Hz
100 Hz

A/D Converter: Sampling Rate
• Aliasing
– Acquired signal gets distorted if sampling rate is too small.

159
Aliasing (Time Domain)
Actual Signal
Reconstructed
Signal

160
Methods of avoiding Aliasing
To avoid aliasing, there are two approaches:
One is to raise the sampling frequency to satisfy the
sampling theorem.
The other is to filter off the unnecessary high-
frequency components from the continuous-time
signal.
We limit the signal frequency by an effective low-
pass filter, called anti-aliasing prefilter, so that the
highest frequency left in the signal is less than half
of the intended sampling rate.

Quantization theory
• Analog to digital conversion is a two-step process, which changes
a sampled analog voltage into digital form.
– Quantization (Quantization is the transformation of a
continuous analog input into a set of data represented by
discrete output states.)
– Coding (Coding is the assignment of a digital code word or
number to each output state)

Quantization theory
• The analog quantization size (or resolution) Q is defined as the
full scale range of the ADC divided by the number of output
states:
• (Vmax – Vmin) is range of ADC
• n is bit of ADC
m ax m in
2 1
n
V V
Q




Examples

Examples
• Knowing the resolution, Q, and range, R, of an ADC,
we can determine the number of bits required as
follows:

• In case of laser scanning machine, laser spot position
is measured using LVDT which is mounted on
positioning stage. And further processed using DAQ
system having a maximum sampling frequency of 500
KCycles/s. Determine the possible maximum scanning
speed using proposed system?

• Temperature values from –20°F to 120°F are input
data for a microprocessor computer.
• Are 8 bits sufficient measure the minimum
temperature change of less than 0.50F? If so, what is
the resolution?

• A data acquisition board has a 12-bit analogue-to-
digital converter and is set for input signals in the
range 0 to 10 V with the amplifier gain at 10. What is
the resolution in volts?

• The binary output of an ADC should have the range
00000000-11111111 corresponding to an input of 0-6
V. Find the necessary reference voltage.

Examples

DAQ Properties
• DAQ devices have four standard elements:
– Analog input (AI)
– Analog output (AO)
– Digital I/O (DIO)
– Counter/Timers
• A counter is a digital timing device used
for event counting, frequency
measurement, period measurement and
pulse generation.

DAC & ADC
Physical System
(may be mechanical System, chemical system, etc)
Micro-controller, DAQ System
Variable
to sense
Actuator
Signal
ADC
Analog
Signal
Digital
Signal Digital
Signal
DAC
Current
Amplifier
Analog
Signal
Analog
Signal

Digital to Analog Convertor
• When data is in binary form, the 0's and 1's may be of several
forms such as the TTL form where the logic zero may be a value
up to 0.8 volts and the 1 may be a voltage from 2 to 5 volts.
• The data can be converted to clean digital form using gates
which are designed to be on or off depending on the value of the
incoming signal.
• Data in clean binary digital form can be converted to an analog
form by using a summing amplifier.
• For example, a simple 4-bit D/A converter can be made with a
four-input summing amplifier. More practical is the R-2R
Network DAC.

Four-Bit D/A Converter
This approach is not satisfactory for a large number of bits because
it requires too much precision in the summing resistors.
This problem is overcome in the R-2R network DAC

Weighted sum DAC
• One way to achieve D/A conversion is to use a
summing amplifier.
• This approach is not satisfactory for a large number
of bits because it requires too much precision in the
summing resistors.
• This problem is overcome in the R-2R network DAC.

DAC Parallel Interface
The parallel interface is ideal for inputting or outputting data from
devices that are either on or off.
A single limit switch uses only one input bit, and an on-off signal to a
motor requires only one output bit. These 1-bit signals are called
logic variables, and eight such signals can be provided from a single
(8-bit) port.
The parallel interface
transfers data 8 bits
(or more) at the same
time, using eight
separate wires. It is
essentially an extension
of the data bus into the
outside world.

DAC (Digital to Analog Conversion)
• Properly weighted voltages
are summed together to
yield the analog output.
• Three weighted voltages are
summed. The three-bit
binary code is represented
by the switches.
Thus, if the binary number is 1102,
the center and bottom switches
are on, and the analog output is 6
volts. In actual use, the switches
are electronic and are set by the
input binary code.

Example
An 8-bit DAC has a Vref of 10 V. The binary input is
10011011. Find the analog output voltage.
The binary input of 10011011 has a decimal value of 155.

DAC ?
0 1 2 1
0 1 2 1
ou t
2 2 2 2
2
n
n
n
x x x x
V k


 
   
  
 
reference voltage in “multiplying” DAC
i.e., 00...0 => 0 volts; 11....1 => k volts (slightly less)
k / 2n = “step size”

R/nR DAC
The simplest form of ADC uses a
resistance ladder to switch in the
appropriate number of resistors in
series to create the desired voltage
that is compared to the input
(unknown) voltage
Resistor values span a wide range
– n-bit DAC ==> resistors from 2R to
2n
R
– 8-bit DAC ==> 2R to 512R, e.g., 2K
to 512K
– Difficult to fabricate wide ranges
of resistance in semiconductor
processes.
V -7
V -6
V -lo w
V -1
V -2
V -3
V -4
V -5
V -h ig h
S W -8
S W -7
S W -6
S W -5
S W -4
S W -3
S W -2
S W -1
O u tp u t

R/nR DAC
classic inverting summer circuit
is an operational amplifier using
negative feedback for controlled
gain, with several voltage inputs
and one voltage output. The
output voltage is the inverted
(opposite polarity) sum of all
input voltages:
ALL RESISTORS HAVE SAME VALUE

R/nR DAC
Starting from V1 and going through V3, this would give each input voltage
exactly half the effect on the output as the voltage before it. In other
words, input voltage V1 has a 1:1 effect on the output voltage (gain of 1),
while input voltage V2 has half that much effect on the output (a gain of
1/2), and V3 half of that (a gain of 1/4).
Intentionally setting the input resistors at different values. Suppose
we were to set the input resistor values at multiple powers of two: R,
2R, and 4R, instead of all the same value R

R/nR DAC
• If we wish to expand the resolution of this DAC (add
more bits to the input), all we need to do is add more
input resistors, holding to the same power-of-two
sequence of values:

R/nR DAC
• Different resistors in the network have different accuracy
requirements.
– 5% resistance change at MSB has 2.5% effect
– 5% resistance change at LSB (8-bit) has .02% effect
– MSB of 16-bit DAC (as in CD player) would require accuracy of one
part in 215
(.003%) to have less than one step-size error

DAC Resolution
• The resolution of a DAC is the worst case error that is
introduced when converting between digital and analog.
• This error occurs because digital words can only represent
discrete values, as indicated by the stair-step diagram.
• The maximum value of an 8-bit number is 255 decimal,
which means there are 255 possible “steps” of the output
voltage
• The difference between steps is least significant bit
(LSB).
• Smallest increment is one step, the resolution (for 8-bit
data) is 1 part in 255, or 0.39%.

Example
A computer uses a DAC to create a voltage that represents
the position of an antenna. The antenna can rotate 180° and
must be positioned to within 1°. Can an 8-bit port be used?
The resolution required is 1 part in 180. Because 8 bits provide a
resolution of 1 part in 255, an 8-bit port is certainly adequate.
We could have the LSB = 1°, in which case the input values would
range from 0 to 180, or we could equate 180° with 255, which makes
the LSB = 0.706°.

A data acquisition system uses a DAC with a range of ±15 V and a
resolution of 0.02 V. Determine the number of bits the DAC must
have.
A data acquisition system uses a DAC with a range of ±10 V and a
resolution of 0.05 V. Determine the number of bits the DAC must
have.
A data acquisition system uses a DAC with a range of —10 V to 4-
15 V and a resolution of 0.005 V. Determine the number of bits
the DAC must have.

A DAC is used to deliver velocity commands to the motor of a
drilling machine whose maximum velocity is to be 2000
revolutions per minute, and the minimum non-zero velocity is to
be 1 revolution per minute.
Determine:
(a)the number of bits required in the DAC;
(b)(b) the resolution required.
The voltage range of feedback signal from a mechatronic process
is —3 V to +12 V, and a resolution of 0.05% of the voltage range
is required. Determine the number of bits required for the DAC.
What is the minimum number of bits required to digitize an
analog signal with a resolution of: (a) 2.5%; (b) 5%; (c) 10%?

The output voltage of an aeroplane altimeter is to be sampled
using an ADC. The sensor outputs 0 V at 0 m altitude and
outputs 10 V at 50 km altitude. The altimeter datasheet shows
that the allowable error in sensing (± ½ LSB) is 5 m.
Determine the minimum number of bits required for the ADC.
An 8-bit ADC with a 0V to 10V range is used for the purpose of
sampling the voltage of an analog sensor. Determine the digital
output code that would correspond to the following: (a) 2.5 V;
(b) 5 V; (c) 7.5 V.

Sensor Signal
Sampling
Quantizing
Digitization
Digital to Analog Conversion
Output

ADC (Analog to Digital Conversion)
• The basic principle of operation is to use the
comparator principle to determine whether or not to
turn on a particular bit of the binary number output.
• It is typical for an ADC to use a digital-to-analog
converter (DAC) to determine one of the inputs to
the comparator.
3 Basic Types
• Digital-Ramp ADC
• Successive Approximation ADC
• Flash ADC

ADC Analog-to-Digital Conversion
• To start the conversion process, a start-conversion pulse is sent to
the ADC. The ADC then samples the analog input and converts it to
binary.
• When completed, the ADC activates the data-ready output. This
signal can be used to alert the computer to read in the binary data.

ADC
The purpose of the ADC is to digitize the input signal from the
sample and hold circuit to 2B discrete levels, where B is the number
of bits of the ADC.
The input voltage can range from 0 V to Vref (or — Vref to +Vref for
a bipolar ADC).
voltage reference of the ADC is used to set the range of conversion
of the ADC.
For inputs between these two voltage levels, the ADC will
output binary numbers corresponding to the signal level.
For ADC, a 0 V input will cause the converter to output all zeros
If the input to the ADC is equal to or larger than Vref then the
converter will output all ones.

ADC Conversion
Buffer amplifier (chosen to
provide a signal in a range close to
but not exceeding the full input
voltage range of the ADC).
Low-pass filter (to remove undesirable
high-frequency components in the signal
that could produce aliasing).
Sample and hold amplifier (to
maintain a fixed input value during the
short conversion time).
Analog to digital converter (ADC)
Computer

ADC (Analog to Digital Conversion)
At the input end of the system, we have the analog-to-digital
converter, or ADC. The ADC may include both the quantizer and
the sample-and-hold, or it may consist of the quantizer only, with
an external sample-and-hold.
Sample
And
Hold
N-bit
quantizer
V(t) Vq(n)
Analog-to-Digital Converter (ADC)

1-bit analog to
digital conversion
2-bit analog to
digital conversion
3-bit analog to
digital conversion

Mechatronics Systems : Sensors used in Mechatronics integration

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