ENG-7858: Industrial Control and
Instrumentation
Laboratory Experiments
Credit 4 × 5%
1
Linear Variable Differential Transformer
1.1
OBJECTIVES
In this lab, you will learn how to build
A) a simple LVDT capable to measure position accurately, and
B) an oscillator capable of driving the primary winding of the LVDT.
In particular, you will get familiar with these aspects of instrumentation:
• Coil winding.
• Impedance measurement.
• Analog circuit simulation.
• Oscillator analysis.
1.2
BACKGROUND
The letters LVDT are an acronym for Linear Variable Differential Transformer, a
common type of electromechanical transducer that can convert the rectilinear motion
of an object to which it is coupled mechanically into a corresponding electrical signal.
The transformer’s internal structure consists of a primary winding centered between a pair of identically wound secondary windings, symmetrically spaced about
the primary. The coils are wound on a one-piece hollow spool. This coil assembly
is the stationary element of the position sensor.
The moving element of an LVDT is a separate tubular armature of magnetically
permeable material called the core, which is free to move axially within the coil’s
1
hollow bore, and mechanically coupled to the object whose position is being measured. This bore is typically large enough to provide substantial radial clearance
between the core and bore, with no physical contact between it and the coil.
In operation, the LVDT’s primary winding is energized by alternating current of
appropriate amplitude and frequency, known as the primary excitation. The LVDT’s
electrical output signal is the differential AC voltage between the two secondary
windings, which varies with the axial position of the core within the LVDT coil.
This AC output voltage is converted by an electronic circuitry to high level DC
voltage or current.
Below is a list of features that make LVDT an ideal candidate for our electronic
weight scale/balance project; for more information see
http://www.macrosensors.com/lvdt macro sensors/lvdt tutorial/ or
“Handbook of Measurement and Control: An Authoritative Treatise on the Theory
and Application of the LVDT” (Paperback) by Edward E. Herceg, Schaevitz
Engineering (1980), ASIN: B000I76D0Q.
• Friction-Free Operation
• Infinite Resolution
• Unlimited Mechanical Life
• Overtravel Damage Resistance
• Zero Cross-Axis Sensitivity
• Environmentally Robust
• Null Point Repeatability
• Fast Dynamic Response
• Absolute Position Output
• (Separable Coil And Core)]
1.3
EQUIPMENT
2
Equipment
Digital LCR Meter
Function generator with GND isolation plug
Variable DC power supply
Prototyping breadboard with jump wires
Multimeter and Storage oscilloscope
Part A
Acrylic/glass tube 1/4” / 1/8” - 4”
Two 2.7m long enamel wire #30
One 8.0m long enamel wire #30
Lacing cord
Scotch tape & scissors
Paraffin/candle & heat gun
Marker & ruler
Utility knife or fine sand paper
Part B
Two NPN transistors (2N2219A or equivalent)
Resistors
Capacitors
1.4
LVDT Construction & Analysis
1.4.1
Steps for winding LVDT:
1. Watch the practical demonstration !!!
2. Make the PRIMARY winding first:
(a) Use a pen to mark off the piece of acrylic tube as follows (Figure 1):
i. Mark 1, the center of tube
ii. Mark 2&3, 16mm from mark 1 on both sides
(b) Mark one end of the lacing cord, bend it to create a loop, and tape it to
the tube as shown in Figure 2.
(c) Pass 20cm of the 8.0m long wire through the loop as shown in Figure 3
and tape the short end.
(d) Wind 50 turns of the primary winding over the lacing cord. Wind the
coil so that all turns are nicely packed together (Figure 4). This will not
cause a short circuit because the wire is coated with an insulating enamel.
3
The easiest way of doing this is to make 10 turns quickly at one time with
spaces between individual turns, and then pack the turns tightly together
by sliding them back. Always keep the wire pretensioned at any time.
NOTE: Don’t wind the coil by holding the long end of wire still and
moving your hand around and around the tube. When you do this every
turn puts a twist in the wire. After a while the wire will start to kink
and then get into a hopeless tangle.
(e) Remove the tape and pull gently the marked end of the cord until the
first turn of the primary winding is tightly held in place (Figure 5).
(f) Complete the the first layer of winding by making another 55 turns.
(g) Tape over the first coil layer to make a smooth surface without grooves
for the second layer, and crossover the lacing cord to the other side.
(h) Wind 100 turns over the lacing cord the same way as in the first layer.
The second layer should not exceed the end of the first layer as there are
five turns less in the second layer.
(i) Tape over the second layer and crossover the lacing cord again. Wind 50
turns the same way as before. Now, before we finish the coil, we need to
do some preparation for fixing the last turn a similar way we did for the
very first one.
Crossover the lacing cord at the other end of the coil and tape the small
loop just created near the coil’s end. Wind the remaining 45 turns and
here again, the third layer should not exceed the end of the second/first
layer as there are five turns less in the third layer.
The last turn passes through the end loop on the cord. Pull the cord to
tightly fix the last turn in place (Figure 6).
(j) Congratulations, you just created the PRIMARY coil. Trim the cord
ends as well as any tape left on both sides of the coil.
3. Make the two SECONDARY windings using the 2.7m long wire, each having
two layers of 50 turns each, i.e. 100 turns in total. Always start from the
PRIMARY side first so there is no gap left between the windings.
4. When all three LVDT windings are done, use the heat gun to put a layer of
paraffin coat over the coils for extra protection.
5. Trim the wire leads to length between 15 to 20cm and use a utility knife or a
sand paper to remove the insulating enamel on all six wire leads!
4
Figure 1
Figure 2
Figure 3
5
Figure 4
Figure 5
Figure 6
6
1.4.2
LVDT inductance measurement
LCR Meter is used to measure the impedance of the primary coil for two core
materials. Note the LCR meter can not measure a sample which has one lead
connected to earth (grounded)! Measure in Series Inductance (Ls) Mode using
1V at 10kHz.
Determine the series inductance Ls[µH] and the quality Q of the primary coil
without a core and with a soft-iron ferromagnetic core. Calculate the respective
Impedances Z[Ω] and the phase angles Φ at 10KHz.
1.5
Oscillator Design
Install the circuit simulator from http://qucs.sourceforge.net/download.html
for your platform (Win32, MacOS, Linux or FreeBSD).
In your course folder you will find two oscillator models:
7858/Labs/Qucs/LVDT Colpitts.sch
7858/Labs/Qucs/LVDT Peltz.sch
Perform the transient simulation for each model using the inductance value for
the PRIMARY coil measured with the iron core. Find the capacitances to obtain the
frequency between 10kHz and 100kHz. Print out the schematics and the waveforms
generated.
1.6
Oscillator Construction & Analysis
1.6.1
Colpitts oscillator
Implement the Colpitts oscillator shown in Figure 1 and perform the following
measurements:
1. Using 5VDC supply, record the voltage across the PRIMARY winding with
and without the core using an oscilloscope.
2. Record the frequency and the peak-to-peak voltage.
3. Repeat the previous steps using 10VDC supply.
7
Measurement with core without core
5VDC SUPPLY
Frequency
Vpp
10VDC SUPPLY
Frequency
Vpp
1.6.2
Peltz oscillator
Implement the Peltz oscillator shown in Figure 2 and perform the following
measurements:
1. Using 5VDC supply, record the voltage across the PRIMARY winding with
and without the core using an oscilloscope.
2. Record the frequency and the peak-to-peak voltage.
3. Repeat the previous steps using 10VDC supply.
Measurement with core without core
5VDC SUPPLY
Frequency
Vpp
10VDC SUPPLY
Frequency
Vpp
1.7
CONCLUSION
Draw a conclusion on the performance of each oscillator using the data collected
above. Select the oscillator having better performance in terms of the frequency, the
quality of the generated sinusoid and the voltage/power level. Justify your decision.
8
Output1
C2
C=15nF
T1
Type=npn
R1
R=220
transient
simulation
L1
L=10u
C1
C=15nF
R2
R=5.1k
R3
R=5.1k
TR1
Type=lin
Start=0 us
Stop=50 us
Output2
Equation
Eqn1
Vout=Output1.Vt-Output2.Vt
V1
U=10 V
15
10
Vout
5
0
-5
-10
-15
0
5e-6
1e-5
1.5e-5
2e-5
2.5e-5
3e-5
3.5e-5
time
Figure 1: Colpitts Oscillator
9
4e-5
4.5e-5
5e-5
Output1
L1
L=10u
V1
U=5 V
C1
C=100nF
T1
T2
Output2
transient
simulation
R1
R=560
TR1
Type=lin
Start=0
Stop=0.1 ms
Equation
Eqn1
Vout=Output1.Vt-Output2.Vt
1
Vout
0.5
0
-0.5
-1
0
1e-5
2e-5
3e-5
4e-5
5e-5
6e-5
time
Figure 2: Peltz Oscillator
10
7e-5
8e-5
9e-5
1e-4
2
2.1
LVDT Detector
OBJECTIVES
In this lab, you will learn how to build an LVDT signal detector. In particular,
you will get familiar with these aspects of instrumentation:
• Analog circuit simulation.
• Precision half/full wave rectifiers.
• Performance analysis.
2.2
BACKGROUND
In the last Lab you built an oscillator to drive LVDT primary coil. Today,
you will build an OP AMP based LVDT signal detector in the frequency range of
100kHz-1MHz. The high frequency impacts our design in terms of the component
selection. Each secondary winding will pick up the primary signal through the
mutual inductance coupling that is proportional to the ferromagnetic core position.
Their relative amplitudes are then the measure of the core position.
2.3
EQUIPMENT
11
Equipment
HP 4261A Digital LCR Meter
Dual variable DC power supply
Function Generator
Prototyping breadboard with jump wires
Multimeter and Storage oscilloscope
Parts
Eight LM318 OP AMPs or equivalent
Resistors
Capacitors
Four fast (signal) diodes
Miscellaneous
Permanent markers of three colors (fine)
Scissors
Double sided Scotch tape
Oscilloscope screen overlays (3x)
12
2.4
SIMULATION
Use QUCS circuit simulator installed in the senior computer lab or you can install it home from
http://qucs.sourceforge.net/download.html for your platform (Win32, MacOS, Linux or FreeBSD).
In your course folder you will find three half/full way rectifier models:
7858/Qucs/Half Way OP AMP Rectifier.sch
7858/Qucs/Half Way OP AMP Rectifier 2.sch
7858/Qucs/Full Way OP AMP Rectifier.sch
Perform a transient simulation for these models. Print out the waveforms for
each case.
R1
R=10k
R3
R=10k
Output
D1
OP1
D2
12V
_12V
V1
U=1 V
f=100kHz
C1
C=100nF
C2
C=100nF
13
transient
simulation
TR1
Type=lin
Start=0
Stop=0.1 ms
Output
OP1
_12V
V1
U=1 V
f=100kHz
transient
simulation
D1
12V
C1
C=100nF
TR1
Type=lin
Start=0
Stop=0.1 ms
R1
R=10k
C2
C=100nF
D1
12V
R3
R=10k
_12V
V1
U=1 V
f=100kHz
2.5
Output
R5
R=10k
OP1
C1
C=100nF
C2
C=100nF
transient
simulation
TR1
Type=lin
Start=0
Stop=0.1 ms
ANALYSIS
Verify analytically, that:
Half Way Rectifier uout = uin for uin > 0 and uout = 0 for uin < 0
Full Way Rectifier uout = |uin |
14
2.6
EXPERIMENT
2.6.1
Half Way Rectifier ’A’
Implement the half way rectifier ’A’ and record the waveforms for three frequencies, 1kHz, 10kHz, 100kHz.
Half Way Rectifier ’A’ Waveforms
2.6.2
Half Way Rectifier ’B’
Implement the half way rectifier ’B’ and record the waveforms for three frequencies, 1kHz, 10kHz, 100kHz.
15
Half Way Rectifier ’B’ Waveforms
2.6.3
Full Way Rectifier
Implement the full way rectifier and record the waveforms for three frequencies,
1kHz, 10kHz, 100kHz.
Full Way Rectifier Waveforms
2.7
LVDT SIGNAL DETECTOR DESIGN
16
Based on the analysis, simulation and experiments above, select the rectifier of
the best performance and implement the LVDT signal detector as shown in the
block diagram below. Justify your selection.
17
SEC#1 --> Buffer --> Rectifier --> Buffer --|
|
|--> Summer & LP Filter
|
SEC#2 --> Buffer --> Rectifier --> Buffer --|
(180deg phase)
Using a mm scale, measure the LVDT output voltage versus the core displacement within ±10mm of the null position in 0.5mm steps. Comment on the measured
characteristic.
18
3
3.1
Spring Loaded Weight Scale
OBJECTIVES
In this lab, you will learn how to analyze and calibrate a spring loaded weight
scale.
3.2
BACKGROUND
Spring is a mechanical transducer that converts force into displacement. We
have already developed an electro-mechanical transducer, the LVDT, that converts
reliably displacement (rectilinear motion) into voltage with no mechanical friction.
Combining the two transducers, we can measure a force electronically.
Weight measurement is then conducted through gravity that converts the measured weight into force using Newton’s law: F = m × g
[N ].
We use a helical spring that becomes longer under load. This characteristic is
linear, i.e. obeys Hooke’s law, only when stretched slightly. If a spring is overloaded,
plastic deformations may occur making the spring non-linear with a consequent
damage to the device.
A mechanical system will be constructed to exert a tensional force at the spring
element. This can be done by simply hanging the weight on a spring, or using a
balancing arm. The later method will be utilized in our application since it provides
a much greater versatility in terms of used component parameters, system analysis
and system implementation.
3.3
EQUIPMENT
19
Equipment
Dual variable DC power supply
Prototyping breadboard with jump wires
Multimeter
Function Generator
Oscilloscope
Parts
Helical spring
Cord to attach components
LM318 OP AMPs or equivalent
Resistors
Capacitors
Miscellaneous
paper mm scale
glue stick
soft wire
weight reference (3x lock washer 39g)
3.4
LVDT Calibration & Linear Range
1. Use the function generator to drive the primary coil by 10kHz sine wave (50Ω
impedance output). Turn up the amplitude to maximum, and measure the
primary coil voltage using the oscilloscope (peak-to-peak).
2. Using the oscilloscope, measure the secondary coil voltages (waveforms) in
open-circuit configuration. Expect these results based on the LVDT core position x:
Pri
amplitude
Sec 2
Sec 1
20
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Secondary 1
Secondary 2
0
0.2
0.4
time
0.6
0.8
1
amplitude
Sec 2
Pri
Sec 1
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Secondary 1
Secondary 2
0
0.2
0.4
time
0.6
0.8
1
3. Measure the rectified outputs:
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Secondary 1
amplitude
amplitude
The waveforms below assume using half-wave rectifiers; the rectifier attached
to the secondary coil 1 passes only positive polarity portion of the signal while
the rectifier attached to the secondary coil 2 passes only negative polarity
portion of the signal.
Secondary 2
0
0.2
0.4
time
0.6
0.8
1
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Secondary 1
Secondary 2
0
0.2
0.4
time
0.6
0.8
1
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Secondary 1
amplitude
amplitude
The above waveforms are obtained when the secondary coil 1 and the secondary
coil 2 signals are in phase.
Secondary 2
0
0.2
0.4
time
0.6
0.8
1
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
Secondary 1
Secondary 2
0
0.2
0.4
time
0.6
0.8
1
The above waveforms are obtained when the secondary coil 1 and the secondary
coil 2 signals are 180◦ out of phase.
4. Measure DC voltage at the low-pass filter output in terms of the LVDT core
position. Sketch the characteristic below:
21
5. Determine a linear range YLlin of your LVDT from the measured characteristic.
3.5
Spring Calibration & Linear Range
1. Measure the helical spring prolongation YS in terms of the applied loading
force FS .
22
2. Determine the spring constant k (FS = k × YS ) from the measured characteristic above.
3. Determine the modulus of elasticity G of the spring material1 :
G =
where:
G
YS
n
F
D
d
=
=
=
=
=
=
8nkD3
8nF D3
=
YS d4
d4
(1)
modulus of elasticity [N/m2 ]
spring deflection [m]
number of coil turns [1]
applied force [N ]
mean coil diameter [m]
wire diameter [m]
4. Determine the loading range FSlin and the deflection range YSlin obeying Hooke’s
law by assuming the maximum allowable tensile stress σt = G/103 :
1
Ref: The New American Machinist’s Handbook, McGraw-Hill (1955)
23
πd3 σt
8D
(2)
8nFSlin D3
Gd4
(3)
FSlin =
YSlin =
3.6
Balance Arm Ratio
Determine the balance arm ratio assuming the maximum measured weight 0.5kg
and the maximum spring loading FSlin :
Xm
FSlin
=
XS
Fmax
(4)
L
Xm
Xs
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11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000
11111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
Fmax
00000000
11111111
FSlin
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000
11111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
3.7
LVDT Arm Ratio
Determine the LVDT arm ratio assuming the maximum spring extension YSlin
and the LVDT linear range YLlin :
XL
YL
= lin
XS
YSlin
24
(5)
YL_lin
YS_lin
Xs
Xm
XL
11111111111111111111111111111111111111
00000000000000000000000000000000000000
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000
11111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
FS_lin
Fm
00000000
11111111
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
000000000
111111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000
11111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000
11111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
00000000000000000000000000000000000000
11111111111111111111111111111111111111
3.8
Implementation
Determine the arm lengths Xm , XS and XL using the following constraints:
Case A: Pivot in Center In this case, the balancing arm is supported in the arm
center as shown in the above figures:
L/2 = M AX(Xm , XS , XL )
(6)
Case B: Eccentric Pivot In this case, the balancing arm is not supported in the
arm center:
L = Xm + M AX(XS , XL )
(7)
Using Eq. 4, Eq. 5, and Eq.6 or Eq.7, determine Xm and XL .
Attach a hand drawn sketch or digital picture of your weight scale configuration
that includes all the dimensions.
25
4
4.1
Offset and Span Adjustment
OBJECTIVES
In this lab, you will learn how to scale the LVDT output voltage to make it
closely correspond to the measured weight.
4.2
BACKGROUND
Offset and Span (Zero and Gain) adjustment offers the functionality to control
an output characteristic of a linear measurement system to meet specific parameters
such as passing through two given reference points. For example, in our particular
application, we want a zero voltage output to represent a zero weight, and ±5V or
±0.5V output to represent 0.5kg weight limit. This way, we can simply connect
an analog or digital voltmeter to the weight scale output and read the voltage as
weight.
The OFFSET adjustment sets the value of output when the input is zero, i.e.
translates the input-output characteristic along the vertical axis; while SPAN adjustment changes the slope of this input-output relationship.
A typical calibration procedure consists of these iterative steps:
1. The first calibration point should be selected close to the bottom of the input
range. The offset adjustment is then used to give the required output signal
for the input signal.
2. Because alteration of the span results in a higher output deviation at the top
end of the input range it follows that the second calibration point should be
at this top end. Thus the calibration at this point is achieved by imposing an
input signal of suitable magnitude and adjusting the span potentiometer to
give the correct output.
3. In practice it is sometimes difficult to eliminate the interaction effects between
offset and span so it is recommended that the procedure for setting these two
points be repeated until both points are obtained without the need for further
adjustments.
One objective of this lab will also be the development of a faster algorithm that
removes the repetitive nature of the calibration method.
4.3
EQUIPMENT
26
Equipment
Dual variable DC power supply
Prototyping breadboard with jump wires
Multimeter
Spring Loaded Weight Scale
Parts
LM741 OP AMPs or equivalent
Resistors
Capacitors
Potentiometers
Miscellaneous
Weight references (washers, etc.)
4.4
Analysis
Three different circuits for Offset&Span adjustment are shown below.
1. Derive a static transfer function for each of them, i.e. Vout = Vout (VR , Vin , Ri , k),
where k indicates the position of the pot’s wiper and ranges from -1 to 1.
2. Extract the offset and the gain.
3. What is the range of offset adjustment?
4.4.1
Example: Inverting Amplifier #2
R
R3
3
Vout = −
Vin +
kVR
R4
R1
R3
Vof =
kVR
R1
R3
G =
R4
R3
Vof ∈ ± VR
R1
10k
Vof ∈ ±
15V
1M
∈ ±150mV
27
(8)
(9)
(10)
(11)
(12)
(13)
4.5
Experiment
1. Implement the three circuits shown below allowing for 0.5 ∼ 2 gain and
±100mV offset. Note you will need another potentiometer in the op amp
feedback loop for the gain adjustment.
2. Implement a forth circuit by modifying the Inverting Amplifier #2 such that
the gain controlling potentiometer is placed in the forward path R4 .
3. Using only a multimeter, perform the offset and span adjustment to meet the
following mapping:
Input Signal Level
0.00V
5.00V
4.6
Output Signal Level
-0.05V
6.00V
Process Development & Selection
1. For each of the above circuits, using the analytical model and your experimental insight, develop a non-repetitive algorithm to adjust the circuit for the
Offset&Span.
2. Compare the results and discuss the advantages and disadvantages.
3. Select one circuit that features the best performance for your LVDT based
weight scale.
4. Implement this circuit to measure max 0.5kg weight using a multimeter.
5. Demonstrate your system to the instructor.
4.7
References
• National Semiconductor: Application Note 31: Op Amp Circuit Collection
(2002)
• Maxim: Application Note 803: EPOT Applications: Offset Adjustment in
Op-Amp Circuits (2001)
28
Figure 3: Inverting amplifier #1
Figure 4: Inverting amplifier #2
R1 ∼ 1000 × R3 //R4
Figure 5: Non-Inverting amplifier
29
R3 //R4 ≤ 10kΩ