ANALOG SENSORS FOR
MOTION MEASUREMENT
TOPICS
 Introduction
 Motion transducers
 Potentiometers
 Variable inductance transducers
 Permanent magnet transducers
 Eddy current transducers
 Variable capacitance transducers
 Piezoelectric transducers
 Design criterion for control systems
INTRODUCTION
•
Measurement of plant outputs and feedback signals are very important.
•
The measurement subsystem in a control system contains sensors and
transducers that detect measurands and convert them into acceptable signalstypically voltages
Sensor: A device for measuring some quantity. The sensor usually converts
the measurement space to an electrical signal.
Transducer: It is a device, that converts one type of energy to another.
Transducers are used for compensation in different plants and systems.
Help in reducing the sensitivity of a system to parameter change.
Several analog sensor-transducer devices are commonly used in control system
instrumentation
We will deal with several analog motion transducers.
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•
•
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MOTION TRANSDUCERS
• Motion here means the four kinematics variables
 Displacement
 Velocity
 Acceleration
 Jerk
• Each variable is a time derivation of the preceding
one.
• Motion measurement is extremely important for
system’s or plant proper functioning.
Examples:
• Proximity sensors (to measure displacement) and
accelerometers are the two most common types of
measuring devices used in machine protection
systems for condition monitoring, fault detection,
control of large machinery.
• Strain gages are used in measuring strains, they can
be adopted to measure displacement by using
auxiliary sensor element i.e. cantilever (spring),
Resolver provides angular displacement.
• Pulse generating transducers like digital tachometers
can serve as both displacement and velocity
transducer depending on absolute number of pulses
generated is counted or the pulse rate is measured.
Motion Transducers
Motion transducers will be limited mainly to
following types of devices:
 Potentiometers
 Variable inductance transducers
 Eddy current transducers
 Variable capacitance transducers
 Piezoelectric transducers
Potentiometers
•Uniform coil of wire or a film of high resistive material – carbon, platinum or
conductive plastic
•Resistance is proportional to its length.
Resistive
Element
Wiper
Arm
vref
(Supply)
+
i
vo
(Measurement)
x
(Measurand)
No Current
FIG 1
vref
Load
Z v%o Impedance
i
Nonzero
Current
FIG 2
• Slider displacement x is proportional to the output voltage
vo  kx
+
 This relationship is valid only if the output terminals are open circuit (no
current) as shown in FIG 1.
 The output voltage drops when a load with a finite impedance is
connected which is shown in FIG 2.
 Because of this loading effect the linear relationship will no longer be
valid
 Loading can also affect the supply (reference) voltage
 To minimize loading effects


Use a stabilized power supply with low output impedance
Signal conditioning circuitry with high input impedance
 An element with high resistance will have reduced power dissipation
and less thermal effects
 However, increased resistance increases the output impedance
resulting in loading non-linearity error
 FIG 3 shows the linear motion of the translatory potentiometer whereas
the FIG 4 shows the angular motion of Rotatory potentiometer.
Translatory and Rotatory potentiometers
Resistive
Element
(Measurand)
Wiper
vo
(output)
x
(Measurand)
Wiper
vref
vo
(output)
FIG 3
Translatory for
Rectilinear Motions
vref
FIG 4
Rotatory for Angular
Motions
VARIABLE-INDUCTANCE TRANSDUCERS

These motion transducers employ the principle of
electromagnetic induction

Types of variable inductance transducers include



Mutual induction transducers
Self-induction transducers
Permanent magnet transducers

An AC excitation in the primary winding induces an AC voltage
in the secondary winding as indicated in FIG 5.

The amplitude of the induced voltage depends on the flux
linkage between the two coils

In mutual induction transducers change in the flux is effected by
either


Moving a ferromagnetic material on the flux path – LVDT,
RVDT, mutual induction proximity probe
Moving one coil with respect to the other – resolver, synchrotransformer
vo
Secondary
Coil
Core
Primary
Coil
FIG 5
MUTUAL INDUCTANCE TRANSDUCER
(Linear variable differential transformer (LVDT))
 An LVDT transducer shown
in FIG 6 comprises a coil
former on to which three
coils are wound.
 The primary coil is excited
with an AC current, the
secondary coils are wound
such that when a ferrite core
is in the central linear
position, an equal voltage is
induced in to each coil.
 The secondary are connected
in opposite so that in the
central position the outputs of
the secondary cancels each
other out.
vo
(Measurement)
Primary
Coil
Insulating
Form
Core
Ferromagnetic Core
Secondary
Coil Segment
vref
FIG 6
x
Secondary
Coil Segment
LINEAR VARIABLE DIFFERENTIAL
TRANSFORMER
 When the armature is in the
central position there is an
equal voltage induced in to
both secondary coils. The sum
of secondary outputs cancels
each other out resulting in a
zero output.
 As the armature moves in to
sec1,the result is that sum of
sec1 and sec2 favors sec1.
 As the armature moves in to
sec2,the sum favors sec2.
 The output is an AC waveform
which is indicated in FIG 7
FIG 7
LINEAR VARIABLE DIFFERENTIAL
TRANSFORMER
•
Signal conditioning
associated with differential
transformers includes
rectification and
demodulation.
•
•
FIG 8 shows Rectification.
FIG 9 shows Demodulation.
FIG 8
FIG 9
Self Induction Transducers
 Based on the principle
of self induction.
 Only a single coil is
employed as shown in
FIG 10.
 Self Induction
transducers are
usually variablereluctance devices.
 This can be used as a
displacement sensor
FIG 10
Permanent Magnet Transducers
 A permanent magnet is used to generate a uniform
and steady magnetic field.
 Permanent magnet transducers are used in
measuring speed.
 Two types of speed are measured.
 Rectilinear speed
 Rectilinear velocity transducer shown in FIG 11 is
used to measure rectilinear speed
 Angular speed.
 DC tachometer-generator in FIG 12 and AC
tachometer-generator are used in measuring angular
speed.
Rectilinear velocity transducer
FIG 11
DC Tachometer-generator
FIG 12
Eddy Current Transducers
Principle of Eddy current:

An eddy current is caused by a
moving magnetic field intersecting a
conductor or vice-versa.

The relative motion causes a
circulating flow of electrons, or
current, within the conductor.

These circulating eddies of current
create electromagnets with magnetic
fields that oppose the change in the
external magnetic field.

The stronger the magnetic field, or
greater the electrical conductivity of
the conductor, the greater the currents
developed and the greater the
opposing force.

This principle is used in eddy current
proximity sensor

FIG 13 illustrates concept of Eddy
current
FIG 13
Eddy current proximity sensor

The Eddy Current Transducer
uses the effect of eddy (circular)
currents to sense the proximity of
non-magnetic but conductive
materials.

A typical eddy current transducer
contains two coils: an active coil
(main coil) and a balance coil as
shown in FIG 14.

The active coil senses the presence
of a nearby conductive object, and
balance coil is used to balance the
output bridge circuit and for
temperature compensation.
FIG 14
Schematic diagram of eddy current
proximity sensor
FIG 15
•Active coil and compensating coil forms arms of inductance bridge.
•When a measurand brought to near to active coil, due to eddy current which produces eddy current magnetic
field that opposes active coil field causes change in inductance and thus creates imbalance in inductance
bridge.
•This change is noted in calibrated unit.
Variable capacitance transducers

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A variable capacitor is a capacitor whose capacitance may be
intentionally and repeatedly changed mechanically or
electronically.
Capacitance of two plate capacitor is given by
C=KA / x
A change in anyone of K,A,x may be used in sensing process.
Variable capacitance is used to convert physical phenomena
into electrical signals
Types of capacitor sensors



capacitive rotation sensor
capacitive displacement sensor
capacitive liquid level sensor
Variable capacitance transducers
Capacitive rotation sensor
Angular displacement of one of the plates causes the
a change in A (area of plate) which is shown in FIG
16.
FIG 16
Variable capacitance transducers
Capacitive Displacement sensor
Transverse displacement of one of the plates
changes x (distance between plates) as shown in FIG
17.
FIG 17
Variable capacitance transducers
Capacitive liquid level sensor
A change in K (depends on
dielectric properties of
medium between two plates)
is produced as the fluid level
between the capacitor plate
changes
 The advantage of capacitance
transducer is negligible loading
effects.
 FIG 18 shows change in K
value used to measure the
displacement
FIG 18
Piezoelectric transducers
• Piezoelectric materials: Barium titanate, single crystal
quartz.
• Piezoelectric Effect:
When mechanical stress or strain is applied to the
piezoelectric material, generates an electric charge and
associated potential difference.
• The direct application of piezoelectric effect is used in
pressure and strain measuring devices
The Piezoelectric Effect
Crystal material at rest: No forces applied (as shown in FIG 19),
so net current flow is 0
Crystal
+-+-+-
Current Meter
=0
Charges cancel
each other, so
no current flow
+-+-+-
FIG 19
The Piezoelectric Effect
Crystal material with forces applied in direction of arrows (FIG 20).
Crystal
--Force
+++
Due to properties of symmetry,
charges are net + on one side &
net - on the opposite side: crystal gets
thinner and longer
Current Meter
deflects in +
direction
FIG 20
The Piezoelectric Effect
Changing the direction of the
applied force………..(FIG 21)
Crystal
++++
Force
----…. Changes the direction of
current flow, and the crystal gets
shorter and fatter.
Current Meter
deflects in direction
FIG 21
Piezoelectric accelerometer

Piezoelectric velocity transducer:
 It uses piezoelectric accelerometer and an integrating amplifier
along with impedance matching amplifier which is show in FIG 22.

FIG 22
Piezoelectric displacement transducer:
 It is obtained by using a double integration of piezoelectric
accelerometer.
Piezoelectric Sensor
 It may be represented as a charge source with a series
capacitive impedance Z as shown in FIG 23
Z = 1/jwc
Fig 23
 Piezoelectric sensors have a limitation on the useful
lower frequency.
Piezoelectric accelerometer




Accelerometers are acceleration measuring devices.
The piezoelectric accelerometer is a piezoelectric motion transducer.
It is based on d’ Alembert’s principle which states that
“ If a force of magnitude Ma were applied to the accelerating mass in the
direction opposing the acceleration, then the system could be analyzed using static
equilibrium considerations.”
FIG 24
DESIGN CRITERION FOR CONTROL
SYSTEM
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
Accuracy is affected by parameter
changes in the control system
components and by the influence of
external disturbances
Consider general feedback control as
shown in FIG 25 system to parameter
changes and to external disturbances.
GP(s) = Transfer function of the plant (
Of the system to be controlled)
Gc(s) = Transfer function of the
controller ( Including Compensators)
H(s) = Transfer function of the output
feedback system ( Including the
measurement system)
u = System input command
ud = External disturbance input
y= system output
FIG 25



After analyzing the feedback back control system we can
stipulate the following design criterion for the system.
Make the measurement system (H) very accurate and
stable
Increase the loop gain to reduce the sensitivity of the
control system to changes in the plant and controller .
Increase the gain of GcH to reduce the influence of
external disturbances
Conclusion
 Analog Transducers play a very important part in
insuring proper functioning of the systems.
 They are simple, user friendly and reliable.
 But with increase in complexity and need for accuracy
in modern day plants use of analog transducers is very
limited. Newly developed Digital and Optical
Transducers are more apt for use in these plants.
References:
 Sensors and Actuators by C W Desilva.
 http://en.wikipedia.org/wiki/Sensor
 http://en.wikipedia.org/wiki/Eddy_current
 http://www.infoplease.com/ce6/sci/A0839004.
html
 http://www.encyclopedia.com/doc/1E1piezoele.html
Discussions
 Discuss briefly Eddy current Proximity
sensor.
 How does linear displacement is measured
using potentiometer ?
 Explain how different motions are measured
using Variable capacitance transducers ?
Questions and comments…