Instrumentation & control handout

INDEX NO............................................... NAME................................................................ CODE.........
1
STRAIN MEASUREMENT
In recent times, measurement of stress on members is by electrical strain gauges. The most
important instrument the Extensiometer has a number of disadvantages. Mainly its relative
bulkiness which makes its use impossible in conditions of limited space. In 1856 Lord Kelvin
discovered that basic length and diameter the electrical resistance of metal wire changes with
stress and this is the basis of operation of electrical resistance gauges.
GUAGES EFFECT OF STRAIN
Extensiometer This include variety of method for measuring extension such as
Mechanical, Optical and Pneumatic
Bonded wire or Foiled or
Semiconductor
Change of electrical resistance
Photoelectric Works under the effect of fringe displaced
STRAIN
Direct strain: this is the ratio of the change in the length ie∇𝐿 to the unstressed lengh L of the
body under consideration.
𝜺 =
∆𝑳
𝑳
𝑤ℎ𝑒𝑟𝑒, 𝜺 𝑖𝑠 (Epsilon)
The unit as 𝜇 − 𝑠𝑡𝑟𝑎𝑖𝑛 𝑜𝑟 10−6
𝜇 (𝑀𝑈)
Lateral Strain: this strain is associated with increase and decrease in the dimension normal to
the applied force.
𝜺 =
∆𝑫
𝑫

2
For angular deformation we have shear strain
ɣ =
∆𝑳
𝑳
= 𝒕𝒂𝒏𝜽
ɣ(𝐺𝑎𝑚𝑚𝑎)
When tan 𝜃 is for small angle 𝛾approximetry equal to change in length.
STATIC – TRANSIENT AND DYNAMIC STRAIN
Static – transient and dynamic strains which remain constant value for relatively long period. It
can occur in by moving stationary members. Examples are
𝐿
∝
∆𝐿
Lateral strain
Directstrain
P
P P

3
Transient is a transition strain which changes from static to dynamic and vice versa
Dynamic Strain: This is a strain which is changing with time
STRAIN GUAGES
A strain gauge consist of a wire or a foil element mounted on a paper or some other low packing
material using adhesive to the surface being instrumented. These strain gauges are transducer
that exhibits a change in electrical resistance in response to mechanical strain. Basically there are
two (2) types of strain gauges.
1. The bonded electrical resistance strain guage
2. The unbounded electrical resistance strain guage
BONDED ELECTRICAL RESISTANCE STRAIN TYPE CONSTRUCTION
These guages are bonded directly or cemented directly on the surface of the body or structure
which is being examined. Hence any change in strain in the body is transmitted directly to the
gauge.
From the relation;
𝑅 =
𝜌𝑙
𝑎
Where;
𝑅 = 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝜌, 𝑙 = 𝑅𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 ( 𝑅ℎ𝑜) 𝑎𝑛𝑑 𝑙𝑒𝑛𝑔𝑡h
𝑎 = 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎

4
Thus to obtain a high resistance gauge the material should have
1. A high resistivity
2. Small area
3. Long length or large number of turns
The cement holds the wire rigidly unto backing so that it will not buckle under strain. Two
important features associated with the fill types are;
a) The thickening at the end of each loop introduced low transverse resistance that reduces
cross sensitivity to almost negligible proportion.
Wire type
Etched Foil Gauge
b) Easy soldering due to large tab into the grid.
Tab
Foil
Solderedtab
Fine thickening

5
Unbounded type
The wire is attached directly to the material under test. An unbounded strain gauge can form
parts of an accelerometer to determine the acceleration force applied to the transducer.
Classification is based on material are;
1. Material used
a) Wire
b) Foil
c) Semi-conductors
2. Base or Backing material
a) Paper
b) Bakelite
c) Polyester
d) Polyamide
3. Configuration
a) Single Axial
b) Multiple Axial
c) Rosette
d) Special pattern
Five Important Factors Which Influence Metallic Gauge and Application
a) Grid material and construction
b) Backing material
c) Bonding material and method
d) Guage protection
e) Gauge configuration

6
Grid
Selection of grid material is based on a compromise of the ff. desirable factors.
a) High gauge factor, G
b) High resistivity, 𝜌
c) Low temperature sensitivity
d) High electrical stability
e) High yield point
f) High endurance limit
g) Good workability
h) Good solderability or weldability
i) Low hysteresis
j) Low thermal emf, when joined with other material
k) Good corrosion resistance
Backing Materials
Desirable characteristic of backing material include;
a) Minimum thickness consistence with other factors
b) High mechanical strength
c) High dielectric strength
d) Minimum temperature restriction
e) Good adherence to cement used
f) Non hygroscopic characteristics
Bonding Material and Method
Strain gauge normally falls into the ff. categories
a) Cellulosic
b) Phenolic
c) Epoxy, cyanoacrylate
d) Ceramic

7
Generally desirable characteristic of strain gauges adhesive are;
a) High mechanical strength
b) High creep resistance
c) High dielectric strength
d) Minimum moisture attraction
e) Minimum temperature restriction
f) Good adherence
g) Ease of application
h) The capacity to set up fast
GAUGE PROTECTION
Gauge must be protected from mechanical abuse, moisture emersion in water, oil, dust and dirt,
liquid, gases, etc.
Protection material is:
Petroleum waxes, silicone resins, epoxy preparation and rubberized brushing compound.
Gauge Configuration
Larger gauge; Greater sensitivity, ease of installation
OTHER TYPES OF GAUGES
The wrapped Round Gauge
The wrapped round gauge can be made in short length, 2mm-6mm. it has low transverse
sensitivity.
Tensile
Guage wireV0

8
Woven Round Gauge
This is particularly useful for very large fabrics. The foil has the advantage that the gauge can
take almost any shape that can be drawn. They also have a low profile, very good linear cross
sensitivity and high rate of heat classification. (Since grid of rectangles form an extended
surface). For this reason the foil gauges are widely used over the wire gauges.
GAIN FACTOR OR STRAIN SENSITIVITY
Gain factor;
𝑲 =
𝑬𝒍𝒆𝒄𝒕𝒓𝒊𝒄𝒂𝒍 𝒔𝒕𝒓𝒂𝒊𝒏
𝑴𝒆𝒄𝒉𝒂𝒏𝒊𝒄𝒂𝒍 𝒔𝒕𝒓𝒂𝒊𝒏
The gain factor of a resistance strain gauge is defined as the fractional change in gauge resistance
(electrical strain) divided by the applied strain (mechanical strain).
The value is supported by the manufacturer and ranges between 1.7 – 4 for metal wire and for
foil. Usually k = 2 is adopted for metal wires and foils. For semi-conductors K ranges from -100
to+200.
Example
100Ω strain gauge is bonded to low carbon steel which is subjected to a tensile bar under tensile
load. If the bar has a pre-loaded uniform bar cross sectional area of 5x10-5m2 and E = 200GN/m2.
Determine the gain factor if a load of 50KN produces a change of 1Ω in the strain.
Guage wire
Tensile

9
Solution
R = 100Ω
Area = 5 × 10−5
m2
E = 200GN/m2
= 200 × 109
N/m2
k =?
∆R = 1
F = 50KN = 5× 104
N
E =
δ
ε
δ =
F
A
ε =
∆L
L
E =
F
A
∆L
L
Mechanical strain ε =
∆L
L
=
F
AE
But the gain factor k =
Electrical strain
Mechanical strain
k =
∆R
R
F
AE
k =
AE∆R
FR

10
k =
200 × 109
× 5 × 10−5
× 1
5 × 104 × 100
k = 2
AXIS OF SENSITIVITY
The direction of strain gauge in which the change of resistance for any given strain is greatest is
called the Principal or Active axis of the strain gauge.
The cross sensitivity or the transverse sensitivity of the strain gauge is defined as the ratio of
the resistance change ∆R1which occurs for a given strain along the cross sensitivity axis and the
resistance change ∆R2 occurring when the same strain occurs along the principal axis.
Cross sensitivity =
∆R1
∆R2
for the same applied strain is usually expressed as a %.
X X
CROSS SENSITIVITY AXIS (X): It is the direction in which the gauge is least sensitive
SIGNAL CONDITIONS
The small changes in resistance of the gauge which occurs due to the applied strain is converted
into a voltage by a Wheatstone Bridge arrangement as shown below.
PRINCIPALAXIS
XX
CROSSSENSITIVITY

11
V = IR
𝑉𝐴𝐵 = 𝐼1 𝑅1
𝑉𝐵𝐶 = 𝐼1 𝑅2
𝑉𝐴𝐷 = 𝐼2 𝑅4
𝑉𝐷𝐶 = 𝐼2 𝑅3
𝐵𝑢𝑡 𝑉𝐵𝐶 = 𝑉𝐷𝐶
𝐼1 𝑅2 = 𝐼2 𝑅3
𝐼1
𝐼2
=
𝑅3
𝑅2
…………………………… (1)
𝐴𝑙𝑠𝑜, 𝑉𝐴𝐵 = 𝑉𝐴𝐷
𝐼1 𝑅1 = 𝐼2 𝑅4
𝐼1
𝐼2
=
𝑅4
𝑅1
…………………………… (2)
Dividing equation (1) by equation (2)
∴
𝑅1
𝑅2
=
𝑅4
𝑅3
EXCITATION VOLTAGE
V0
R1
R
R2
I1
R3
I2
R4
A
C
D
B

12
Example
A single 100Ω resistance spring gauge having a gauge factor of 2 is mounted on a steel bar and
is connected into a symmetrical bridge circuit when the steel bar is subjected to a tensile forced,
the output voltage of the unloaded bar is 5mV. If the recommended operating current of the
gauge is 15mA, determine the value of the mechanical strain.
Solution
k = 2
𝑉𝑜 = 5 × 10−3
𝑉
R = 100Ω
I = 15 × 10−3
𝐴
For a single active gauge of resistance
𝑉𝑜 =
𝑉
4
×
∆𝑅
𝑅
……….. (1)
Where; V = the bridge excitation voltage
∆R = small change in resistance of one element
R = the resistance of the element before the change
Also;
∆𝑅
𝑅
= 𝑘
∆𝐿
𝐿
………… (2)
Substituting (2) into (1)
𝑉𝑜 =
𝑉
4
× 𝑘
∆𝐿
𝐿
V0
gauge 1
gauge 2

13
V = 2(IR)
𝑉𝑜 = 2 ×
𝑉
4
× 𝑘
∆𝐿
𝐿
∆𝐿
𝐿
=
4 × 𝑉𝑜
2 × 𝑘 × 𝐼 × 𝑅
=
4 × 5 × 10−3
2 × 2 × 15 × 10−3 × 100
= 3.33μ strain
APPLICATON OF STRAIN GAUGES
Strain gauges can be used to determine all types of strain that occur when a member is under
loading.
a) Bending strain
b) Direct strain
c) Shear strain and Torsional strain
d) Linear displacement
e) Linear position
f) Linear acceleration
g) Angular acceleration
h) Force
i) Torque
j) Torsional vibration
k) Pressure.
Definitions
Direct strain 𝑉𝑜 =
𝑉
4
×
∆𝑅 𝑑
𝑅
Where Rd = Resistance change due to direct strain
R = Unstrained resistance of gauge

14
For, Bending Strain 𝑉𝑜 =
𝑉
4
×
∆𝑅 𝑏
𝑅 𝑏
Where Rb is resistance strain due to bending
R is unstrained resistance
For, shear strain Vo =
Where Rs= resistance due to shear
R = unstrained resistance
SOURCES OF ERRORS
Temperature changes: it is not possible to have perfect temperature compensation. No two
gauges have identical electrical resistance coefficient or expansion or gauge factors and therefore
temperature compensation is not possibly complete.
Fatigue: this is associated with dynamic strain installations resulting from stress reversals at the
point which leads have to be made well secured in manufacturing.
Moisture &Humidity: moisture absorption by backing or fixing cement causes volume changes
and subsequently error in reading. Gauges should be guided against moisture. Inevitable,
manufacturers’ water proofing technique must be strictly adhered to.
Hysteresis: a graph of
𝛥𝑅
𝑅
(electrical strain) against
𝛥𝐿
𝐿
(mechanical strain for a higher value shows
non-linearity and therefore unrelieved stress, a hysteresis loop is formed.
∆R
R
∆L
L
NonLinearresponse

15
It is usual to cycle the gauge a number of times before use for a higher strain level to eliminate
this effect.
ADVANTAGES OF STRAIN GAUGES
1. Very accurate
2. Excited by both DC/AC current
3. Excellent static and dynamic response
4. Fast speed or response
5. Smallest possible size.
FORCE MEASUREMENT
Force is that which changes or tends to change the motion or shape of a body to which it is
applied.
Measurement of force systems use:
1. Mechanical
2. Hydraulic
3. Pneumatic
4. Electrical
Mechanical
1. Lever types system
2. Analytical types system
1. Lever type system: this determines the unknown force or weight by balancing it against
the gravitational force on a known standard mass. Quite often a system levers is used as
amplifiers.

16
2. Analytical balance type system:
Null balance is achieved by added standard masses to the pan to bring the deflection pointer back
to zero (0).
For small discrepancies from the standard mass the scale can be calibrated in fractions of grams
for direct reading.
Platform or Compound Lever
The system of levers allows the measurement of large forces by means of much smaller standard
masses. Coarse adjustment is achieved by adding one of several standard masses, fine adjustment
by the system of levers allows the measurement of large forces by means of much smaller
0
Scale
Unknown
Standards
0
Load Platform Standardmass
Slidingmass
Scale

17
standard masses along a calibrated scale until the Null balance is achieved. By the use of suitable
gearing direct reading scale can be produced.
Signal conditioning
Internal signal conditioning consists of levers for amplifications and for converting force
movement into angular displacement. No external signal conditioning is needed.
Example
A simple tensile testing machine is shown below. Calculate the force or Load L on the platform
Solution
Taking the moment about fulcrum, P
W × 2 = (2 ×
10
100
) + (1 × 4)
2w = 4.02
w =
4.02
2
w = 2.01N
2 2 2
10g
0.80.8
0.6 0.6
1kg
W
6 1m1m
P

18
Also, taking the moment about the point D
W × 6 = (
L
4
× 2) + (
L
2
× 1)
6w =
L
2
+
L
2
6w = L
But w = 2.01
∴ 6 × 2.01 = 𝐿
L = 12.06kg
Hence the force or load on the platform is 12.06kg
Range: Static loads of some few milligrams up to few hundreds of tones.
HYDRAULIC AND PNEUMATIC METHODS
Load
Connection of
bourdon guage
pipe / hose
Bourdon tube guage
Direct scale
L
4
L
2
1m 1m
W
A B
C D
6m

19
The hydraulic cell
This uses the hydraulic pressure to measure forces. A chamber with a diaphragm and containing
oil is connected to a bourdon tube. When a force is applied to the diaphragm a pressure is
developed in the chamber equal to the applied force divided by the effective diaphragm area.
Range: Some few kilograms to hundred of tones. Application is for static loads.
THE SPRING BALANCE
The spring balance is the simplest form of spring system and has the advantage of being cheap,
robust, and easy to use when very accurate measurement is not prime importance. The load is
suspended from a hook attached to a spring which extends proportional to the magnitude of the
load. A calibrated scale indicates the load applied.
Signal Conditioning: No signal conditioning necessary for the simple spring balance but scales
with circular calibrated dials requires gears and lever system to convert linear motion to angular
motion.
Range: Course measurement of static loads up to few kilograms.
THE PIEZO-ELECTRIC FORCE TRANSDUCER
The piezo-electric force transducer is used for the measurement of high frequency dynamic
forces in test applications such as safety belt tests, shock and fatigue testing machine, automatic
stamping, pressing and welding machine.
Signal Conditioning – And Principle of Operation
Some materials such as quartz synthetic crystals (such as lithium sulphate), when under the
action of applied force produce opposite polarity (charges) on the surface of the material by
piezo-electric effect. The output charges are proportional to the applied force. They measure
dynamic and impact tensile and compressive forces. For tensile forces up to 40% full load
deflection.

20
Question
Test equipment for measuring the maximum shock load in a car seat belt incorporate a piezo
electric force link, a charge amplifier and recorder. For a certain test carried out at 50km/hr a
maximum deflection of 90mm was obtained on the recorder, determine the maximum value of
the shock load if the equipment has the following sensitivity.
Solution
System sensitivity = Force link x charge amplifier x recorder sensitivity
= 4pc/N x 10−3
v/pc x 1mm/v
= 40 x 10−3
mm/N
𝐵𝑢𝑡𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦𝑘 =
∆𝑜𝑢𝑡𝑝𝑢𝑡
∆𝑖𝑛𝑝𝑢𝑡
⇒ ∆𝑖𝑛𝑝𝑢𝑡 =
∆𝑜𝑢𝑡𝑝𝑢𝑡
𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦( 𝑘)
∴ 𝑀𝑎𝑥𝐹𝑜𝑟𝑐𝑒 =
90
40 × 10−3 𝑚𝑚
= 2.25KN
INTELLIGENT WEIGNING MACHINE
This is the name given to a system incorporating a microprocessor along with the load cell. The
microprocessor itself does not improve anyway the accuracy of the force measurement but adds
to the system complexity control function such as modern weighing scale used in various
shops/department. This weighing scale provides digital displaying the weight of the goods, the
cost per unit weight and the total cost.
The display is retained for a period time, long enough for the shopper to display the information.

21
PRESSURE MEASUREMENT
Pressure is defined as force per unit area. Its units in SI is Pascal or N/m2 or bar (Newton per unit
square) bar, other units are mmHg, bar gauge absolute
Pa
1
=
Bar
1 × 105
=
N/m3
1
𝑃 𝑅 = 𝑥𝛿 𝑔 + 𝑃1
𝑃 𝑄 = 𝑥𝛿 𝑚𝑔 + ( 𝑥 − ℎ) 𝛿 𝑔 + 𝑃2
GAUGE ABSOLUTE AND DIFFERENTIAL PRESSURE
Gauge pressure: it is the measurement of pressure with reference to the atmosphere that is
gauge pressure 𝜌𝑔ℎ
Atmospheric pressure: it is the measurement of pressure with reference to vacuum.
𝑃1 𝑃2
x
h
PR PQ𝑃1 𝑃2
x
h
PR PQ

22
Method of Pressure measurement
1. Manometer as shown below.
𝑃1 + ℎ𝛿𝑔 = 𝑃2 + ℎ2 𝛿𝑔
𝑃1 − 𝑃2 = (ℎ1 − ℎ2) 𝛿𝑔
𝐿𝑒𝑡ℎ1 − ℎ2 = ℎ
ℎ2 = ℎ1 − ℎ2 = ℎ
∴ P1 − P2 = δgh
Sensitive Manometer
1. Inclined manometer
2. Well type or U-tube manometer with enlarged ends.
Inclined Manometer
The sensitivity of the manometer can be increased by using the inclined manometer with water
as manometric fluid where ϴ is the angle of inclination of the manometer.
h = vertical increase head
d = the movement of column along limb.
ℎ2
ℎ1
h
𝑃2
𝑃1

23
Methods of Pressure measurement
Signal conditioning: The pressures are converted to movement of liquids in a column. The
column is calibrated and usually read by the operator.
Range: Used for static pressure measurements for the following;
For U-tube = 1mm bar to 1.5 bar
For inclined = 1mm bar to 30 bar.
𝜃P
d
h

24
ELASTIC PRESSURE TRANSDUCER
This includes the bourdon tube pressure gauge diaphragm pressure transducer and bellows.
A bourdon pressure guage
A bourdon tube is a long thin walled cylinder of non-circular cross section sealed at one end
made from materials such as phosphorous, steel or beryllium, copper.
A pressure applied to the inside of the tube covers a deflection of the force and proportional to
the applied pressure. That is a pressure gauge where an elastic deformation is produced when an
amount of pressure released. The sensitivity of the bourdon depends on the length of the tube, the
thickness of the tube walls and the form of the cross section of the tube. Increase sensitivity can
be achieved by using a spherical and a helical shaped tube.

25
Signal Conditioning: In the simplest form of mechanical pressure gauge, the displacement is
converted into a pointer rotation over sealed by means of gear and lever often (rack and pinion).
Range for static and load frequency pressure up to 500mm/m2. The frequency range is limited by
the inertia of the bourdon tube.
Diaphragm Pressure Transducer
Elastic Pressure Transducer
Flat diaphragm is very widely employed as primary sensing element in pressure transducers
using;
1. The centre deflection of a diaphragm
2. The strain induced in the diaphragm
They can be conveniently fabricated as flush mounting sensing element providing a clean,
smooth fair ideal for use in dirty environment and for surface pressure sensing. For high pressure
transducer, very stiff diaphragm must be used to limit the centre deflection up to less than 1/3 of
the diaphragm thickness otherwise non-linearity results occur.
They are used for lower pressure range up to few bars. Beryllium copper diaphragm and bellows
are used to give higher sensitivity.
AC exitedcoils
Half – bridge output
ExcitedVoltage
Flexible diaphragm
Pressure source

26
Signal Conditioning: This depends upon the type of transducer being used.
APPLICATION OF PRESSURE TRANSDUCER
1. Measurement of airflow in the inlet manifold of an IC engines. The flow of air is
converted into a differential pressure by means of an orifix to it. This small pressure
difference is measured using an inclined manometer.
Orifice
Air inlet to engine
Inclined manometer

27
2. A Leak Testing Of a Pressure Container under Test.
The arrangement shown above is used to detect pressure difference or pressure leakages in
containers, and same pressure is applied to both containers which are in turn connected to
opposite side of a differential pressure transducer operating on the strain guage diaphragm
principles any leak in the container under test will be sensed as a pressure difference by the
transducer.
DISPLACEMENT – MEASUREMENT
Displacement is the difference between two positions a body occupies at different times. It is a
vector quantity.
(a) Mechanical Displacement Devices
This include the use of steel rules, slip gauges, micrometer screw gauge, Venier calipers, dial test
indicators. All these are mechanical displacement devices.
Reference container
Container under test
Pen Recorder
Amplifier
Common

28
The Dial Test Indicator (DTI)
The displacement of the test body is transmitted by means of a plunger kept in contact with a
body surface by a spring. A mechanical amplification of gear and rack and pinion converts the
displacement to angular displacement over a scale.
A second pointer recorder scale records a number of revolutions of the same pointer. The main
pointer scale can be rotated to obtain a zero reading corresponding to some reference
displacement. Thus, enabling displacement from the reference to be measured
APPLICATION
1. For calibration of electrical displacement transducer
2. In force measurement
Factors to note when using dial indicator
Pressure Scale
Pointer
Guide
SpringReturn
Plunger

29
1. The indicator axis should lie along the axis of rotation otherwise a component of
displacement not the actual displacement will measured (do not tilt it). It should be
perpendicular to the Axis for being measured.
2. The indicator is initially set up so that it does reach its limit of travel before the body thus
(set it to zero(0))
Range: Dial test indicators are available from 5mm to 50mm travel.
Typical specification
Travel = 25mm
Graduation = 0.01mm
Diameter =57mm
Anvil = Ball
RECORDING UNIT AND DISPLACEMENT UNIT
The recorder of display unit is the final element for measuring system and it is the component
that provides the results of measurement. Recorders usually provide a permanent record of the
signal. Display units are not associated with permanent recording or reading.
Example of recorders
1. Pen recorder
2. X – Y plotters
3. Tape recorder
4. Ultra violet recorder
Examples of display units
1. Speedometer
2. Oscilloscope
3. Thermometer scale

30
Mechanical recording pointer
This consists of a pointer and a scale connected to a number of transducing element for the
measurement of a measurant.
1) Eg. The bourdon tube pressure gauge
2) The pressure chart recorder
3) The bi-metallic temperature measuring device.
The Bi-metallic Temperature Measuring Device
ELECTRICAL RECORDING-THE MOVING COIL MECHANISM
POINTER
BIMETALLIC
FIXED
END

31
The moving coil mechanism
As the current moves through the coil, electronic field is produced which tries to align itself with
the field of the magnetic coils. The electromagnetic torque causes a rotation of the pointer which
opposed by the torsion in the spiral spring. When the spring torque and the electromagnetic
torque balances, the rotation ceases, then angular deflection of the mechanism is produced. This
is usually employed in the moving coil mechanism such as the moving Ammeter and Multi-
meter or Multiple Ammeter.
Comparison of Mechanical and Electrical Recorder
Mechanical Recorder
1. Records slowly changing signal
2. Response time is relatively long.
Electrical Recorders
1. They have better frequency response characteristics
2. They are flexible in handling a wide range of transducers.

32
INTRODUCTION TO CONTROL ENGINEERING
Most mechanical means of work have relieved man of the laborious work of improving his
environment and with the advent of more complex and sophisticated processes. The problem of
human operators in controlling the process becomes more difficult hence man has to rely on
some sort of control system which may be completely automatic or may include human
operators. This brings out the subject of control systems in various engineering sectors.
One facet of control system is the industrial control process typically involving either liquids or
gases. One example of this process control application is the control of liquid level in a tank
shown below.
CONTROLLER
LIGUID LEVEL SENSOR
FLOW OUT
ACTUAL
LEVEL
Pv = 10
FLOW IN
VALVE
10
9
8
7
6
5
4
3
2
1
0
Level in the Tank is Process Variable control

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To maintain a constant liquid level the liquid flow out of the tank is controlled by opening and
closing of a valve. The control system for this application consists of liquid level sensor, valve
and a controller.
Common applications are in the
 Pharmaceutical Production
 Fuel Refinement
 Chemical Manufacturing.
In control system there are three basic terms that are used to describe their operation.
 Process variable
 Set point
 Error.
Process Variable: This is the aspect being controlled. It is described as numerical value and is
often abbreviated as “PV”
Set Point: This is the desired value of the process abbreviated “SP”. SP refers to the value at
which the PV is to be maintained. For instance if you want the level in the tank to be 10cm, the
set point is10cmof water (SP=10cm). However the actual level in the tank (the PV) may be more
or less than the desired SP as shown in below.

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Actual level not equal to SP
Error: The difference between SP and PV at any given point in time is called the error as shown
in the following formula.
Error = SP- PV
Where;
 SP = Set point
 PV= Process value

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Error in a process
The error is important because it is the value the controller uses to determine what the output
needs to be to cause the process variable (PV) to become equal to the Set point (SP).
Process control system can be designed to control many types of process variables. The five
common process variables are:
 Flow
 Level
 Pressure
 Temperature
 Chemical/Analysis
A typical example of a chemical process system has it diagram shown bellow and its typical
application include waste water treatment, pharmaceutical production and proper manufacturing.

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Chemical process systems, also known as Analysis Control systems, measures and control the
chemical properties of a process fluid. Properties that are commonly measured include humidity,
specific gravity, Ph, conductivity, and density. The figure above shows a process measuring pH.
In this process, controlling the flow of two chemicals into the tank allows control over the pH of
the resulting mixture.
DEFINE TWO TYPES OF PROCESS VARIABLES CONTROLLED AND
MANIPULATED
The controlled variable is the facet of the process that the system is designed to control.
However, the variable that actually changes to alter the control variable is often a different
variable, which is called the manipulated variable.
For example, in a liquid level loop like the one in the figure below, the control variable is liquid
level. However, the variable that actually changes to control level is the flow rate out of the tank.
Flow is therefore the manipulated variable in this process.

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DETERMINING THE MANIPULATED AND CONTROL VARIABLES GIVEN
PROCESS DESCRIPTION
Procedure overview:
In this procedure, you will be given various scenarios that describe a control loop. With this
information, you will determine the control and manipulated variable of that loop. This will
allow you to practice identifying the relationships within a process.
1. Determine the manipulated variable and the controlled variable for the following
scenarios.
Scenario: You are adjusting the flow into a vessel to prevent the vessel from
overflowing. The control system uses a valve that is opened and closed by pneumatic
pressure.
Controlled variable flow rate_______________________
Manipulated variable pressure_________________________
In this case, the controlled variable is flow and the manipulated variable is pressure.

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2. Determining the manipulated variable and the controlled variable for the following
scenarios.
Scenario: You are adjusting the flow out of a water tower in order to keep the water level
in the tower at the constant level.
Controlled variable flow rate___water level____________________
Manipulated variable water_level___Flow rate_____________________
scenarios.
Scenario: To develop a pressure in a vessel, you are heating the vessel.
Controlled variable Pressure_______________________
Manipulated variable Temperature_________________________
scenarios.
Scenario: To heat a process fluid, you are adjusting the amount of electrical current that
is flowing to a heating element.
Controlled variable Temperature_______________________
Manipulated variable Current_________________________
scenarios.
Scenario: To maintain a neutral process pH, you are controlling the flow of an alkali into
the process fluid.
Controlled variable Flow rate_______________________
Manipulated variable Acidity_________________________
6. Examine the control loop in the figure below. Determine the manipulated and the
controlled variables.
Controlled variable Pressure_______________________
Manipulated variable Flow rate_________________________

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Types of control systems
1) Open loop
2) Close loop
Closed Loop
Open Loop
𝜃1 𝜃2𝐺2
𝐺1
Desired Input Error Output Actual
Comparator
𝜃2𝐺2
𝐺1
Input Output

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Open Loop System
This is a control system where no comparison between the desired and the actual value is made.
Example
STEAM GENERATING TURBINE
OR
Desired
Temperature
Switch
Heating
element
Room Actual temperature
Controller
Electrical supply
Input Turbine
Generatin
g
OutputControl
Steam supply
Controller
G
OutputInput

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Important Features of Open Loop System
1. No comparison between the actual and the desired
2. Each input setting determine a fixed operating position for the controller
3. Change in external condition results in an output change unless the controller setting is
altered manually.
Closed Loop System
Supposing for the same room heating system, a thermostat is used to regulate the heat flowed in
connection with the room condition, then the thermostat compares the actual room temperature
with the desired value and any deviation (error) occurs appropriate control action to be taken.
Room Heating System
𝜃1 𝜃2
Desired temperature
Actual temperature
Comparator
on
of
Heating
element
Feed Back
Thermostat controller
Desired
Output
Comparator
Heating
element
Feed Back
Controller Turbine
generator

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Important Features of Closed Loop System
1. A comparator to produce error signal for amplification
2. Self regulating property since any external distortion will change the output resulting in
an error signal and consequently reaction to maintain output.

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