1. Sensors & Actuators for Automatic Systems (S&AAS)
Lecture-1
Introduction
Dr. Imtiaz Hussain
Associate Professor
URL :

2. Lecture Outline Recommended Books Introduction Sensor & Transducer
Classification of Sensors
Thermal Sensors

3. Recommended Readings
The Mechatronic Handbook, Editor in Chief Robert H. Bishop, The University of Texas at Austin.
Process Control Instrumentation Technology, Curtis D. Johnson.

4. Introduction
Sensors and actuators are two critical components of every closed loop control system.
Examples:

5. Introduction
A sensing unit can be as simple as a single sensor or can consist of additional components such as filters, amplifiers, modulators, and other signal conditioners.
The controller accepts the information from the sensing unit, makes decisions based on the control algorithm, and outputs commands to the actuating unit.
The actuating unit consists of an actuator and optionally a power supply and a coupling mechanism.

6. Sensors
Sensor is a device that when exposed to a physical phenomenon (temperature, displacement, force, etc.) produces a proportional output signal (electrical, mechanical, magnetic, etc.).
The term transducer is often used synonymously with sensors.
However, ideally, a sensor is a device that responds to a change in the physical phenomenon.
On the other hand, a transducer is a device that converts one form of energy into another form of energy.

7. What is the difference between a transducer and a sensor?
A Sensor can sense in any form(usually electronic) i.e due to some mechanical change, it can react in electrical form. Thus there is a conversion, similar to that of a transducer.
A classic example would be a thermocouple. Or a pressure sensor which might detect pressure and convert it into electric current (3-15psi to 4-20ma)
Therefore, a thermocouple can be called a sensor and or transducer.

8. What is the difference between a transducer and a sensor?
A Transducer is more than a sensor. It consists of a sensor/actuator along with signal conditioning circuits.

9. What is the difference between a transducer and a sensor?
So one way to define is that the output from a sensor may or may not be meaningful i.e most of the times it needs to be conditioned and converted into various other forms.
The transducer output is always meaningful.

10. What is the difference between a transducer and a sensor?
The output of a motor is meaningful. The output of a loudspeaker is meaningful. They are transducers.
A sensor is nothing but just a primary element which senses any physical phenomenon or it gives an indication in any  change of the physical phenomenon.
We can say that Every transducer is also (or has) a sensor but every sensor need not be a transducer. Sometimes it is. 

11. What is the difference between a transducer and a sensor?
Sometimes in a sensor, there is no conversion at all.
Ex. Thermometer, where the temperature is sensed and is directly measured.
In a transducer there is always a conversion i.e transduction.
Ex. RTD, Thermocouple etc where the temperature is sensed and the measurement is made in terms of voltage.
Thus you can say that a SENSOR may or may not have a conversion and it only senses. A TRANSDUCER always involves a conversion and also has signal conditioning involved.

12. Classification of Sensors
The sensors are classified into the following three major classes.
Thermal Sensors
Mechanical Sensors
Optical Sensors

13. Thermal Sensors
Temperature is probably most widely controlled physical quantity among all.
In our natural surroundings, some of the most remarkable techniques of temperature regulation are found in the bodily function of living creatures.
On the artificial side, humans have been vitally concerned with temperature control since the first fire were struck for warmth.
Industrial temperature regulation has always been paramount importance and becomes even more so with the advance of technology.

14. What is Temperature? Temperature is the measure of Thermal Energy.
If we are to measure thermal energy, we must have some sort of units by which to classify the measurement.
The original units used were “hot” and “cold”.
The proper unit for energy measurement is the joule in SI system.
Special sets of units are employed to define the average energy per molecule of a material.

15. Calibration
To define the temperature scales a set of calibration points is used.
Oxygen: liquid/gas equilibrium
Water: solid/liquid equilibrium
Water: liquid gas equilibrium
Gold: solid/liquid equilibrium
For each, the average thermal energy per molecule is well defined.
The SI definition of the Kelvin unit of temperature is in terms of the triple point of water.
This is the state at which an equilibrium exists between the liquid, solid and gaseous state of water in a closed vessel.

16. Calibration
To define the temperature scales a set of calibration points is used.
K (Kelvin) and oR (Rankine) are absolute temperature scales.
Calibration Point
Temperature K oR oF oC
Zero thermal Energy
-459.6
Oxygen: liquid/gas equilibrium
90.18
162.3
-297.3
Water: solid/liquid equilibrium
273.15
491.6 32
Water: liquid gas equilibrium
373.15
671.6
212
100
Gold: solid/liquid equilibrium
2405
1945.5
1063
𝐾=671.6 °𝑅
1 𝐾= °𝑅= 9 5 °𝑅
𝑇 (𝐾)= 9 5 𝑇(°𝑅) ⇒

17. Calibration
The relative temperature scales differ from the absolute scales only in a shift of the zero axis.
Calibration Point
Temperature K oR oF oC
Zero thermal Energy
-459.6
Oxygen: liquid/gas equilibrium
90.18
162.3
-297.3
Water: solid/liquid equilibrium
273.15
491.6 32
Water: liquid gas equilibrium
373.15
671.6
212
100
Gold: solid/liquid equilibrium
2405
1945.5
1063
𝑇 °𝐶 =𝑇 𝐾 −273.15
𝑇 °𝐹 =𝑇 °𝑅 −459.6
𝑇 °𝐹 = 9 5 𝑇 °𝐶 +32

18. Resistive devices
One of the primary methods for electrical measurement of temperature involves changes in the electrical resistance of certain material.
The principal measurement technique is to place the temperature sensing device in contact with the environment whose temperature is to be measured. .
Two basic devices used are
RTD (Resistance Temperature Detector)
Thermistor

19. Resistive Devices RTD (Resistance Temperature Detector) Thermistor
Based on Metal Resistance variation with Environment
Thermistor
Based on Semiconductor resistance variation with environment.

20. Metal Resistance vs Temperature
A metal is an assemblage of atoms in the solid state in which the individual atoms are in an equilibrium with superimposed vibration induced by thermal energy.
As electron moves through the material, they collide with stationary atoms.
When the thermal energy is present in the material and the atoms vibrate the conduction electron tend to collide even more with the vibrating atoms.
This impedes the free movement of electrons, i.e. material exhibits a resistance to electrical current flow.

21. Metal Resistance vs Temperature
Thus Metal resistance is a function of temperature.

22. Resistance vs Temperature Approximation
An examination of the Resistance vs Temperature curve shows that the curves are very nearly linear.
In fact, when only short temperature spans are considered, linearity is even more evident.
This fact is employed to develop approximate analytical equations for resistance vs. temperature of a particular metal.

23. Linear Approximation
A linear approximation means that we may develop an equation for a straight line that approximates the resistance versus temperature curve over some specified span.
The equation of straight line is
R T =R 𝑇 𝑜 1+ 𝛼 𝑜 ∆𝑇 𝑇 1 <𝑇< 𝑇 2

24. Linear Approximation R T =R 𝑇 𝑜 1+ 𝛼 𝑜 ∆𝑇 𝑇 1 <𝑇< 𝑇 2 𝑊ℎ𝑒𝑟𝑒,
𝑅 𝑇 =𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇
𝑅 𝑇 𝑜 =𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇 𝑜
∆𝑇=𝑇− 𝑇 𝑜
𝛼 𝑜 =𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑝𝑒𝑟 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑡 𝑇 𝑜
𝛼 𝑜 = 1 𝑅 𝑇 𝑜 𝑅 2 − 𝑅 1 𝑇 2 − 𝑇 1

25. Example-1
A Sample of metal resistance versus temperature has the following measured values:
Find the linear approximation of resistance vs temperature between 60oF and 90oF.

26. Example-1
Find the linear approximation of resistance vs temperature between 60oF and 90oF.
𝑅 2 =112.2Ω
𝑅 𝑇 𝑜 =110.2Ω
𝑇 𝑜
𝑅 1
𝑇 1
𝑇 2
𝛼 𝑜 = 1 𝑅 𝑇 𝑜 𝑅 2 − 𝑅 1 𝑇 2 − 𝑇 1
= −106 90−60 = /℉

27. Example-1 Thus the linear approximation is 𝛼 𝑜 =0.001875/℉
𝑇 1
𝑇 2
𝑅 1
𝑅 2 =112.2Ω
𝑇 𝑜
𝑅 𝑇 𝑜 =110.2Ω
R T =R 𝑇 𝑜 1+ 𝛼 𝑜 ∆𝑇 𝑇 1 <𝑇< 𝑇 2
R T = (𝑇−75)

28. Example-2
A Sample of metal resistance versus temperature has the following measured values:
Find the linear approximation of resistance vs temperature between 65oF and 85oF.

29. Quadratic Approximation
A quadratic approximation of R-T curve is more accurate approximation.
It includes both a linear term, as before, and a term that varies as the square of the temperature.
𝑅 𝑇 =𝑅 𝑇 𝑜 1+ 𝛼 1 ∆𝑇+ 𝛼 2 (∆𝑇) 2
𝑊ℎ𝑒𝑟𝑒,
𝑅 𝑇 =𝑄𝑢𝑎𝑑𝑟𝑎𝑡𝑖𝑐 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇
𝑅 𝑇 𝑜 =𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑎𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑇 𝑜
∆𝑇=𝑇− 𝑇 𝑜
𝛼 1 =𝑙𝑖𝑛𝑒𝑎𝑟 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑝𝑒𝑟 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑡 𝑇 𝑜
𝛼 2 =𝑄𝑢𝑎𝑑𝑟𝑎𝑡𝑖𝑐 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑝𝑒𝑟 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑡 𝑇 𝑜

30. Example-3
A Sample of metal resistance versus temperature has the following measured values:
Find the Quadratic approximation of resistance vs temperature between 60oF and 90oF.

31. Example-3 Again, since 75oF is the midpoint we will use this for To.
To find 𝛼 1 and 𝛼 2 two equations can be set up using the end points of the data, namely R(60oF) and R(90oF).
𝑅 𝑇 𝑜 =110.2 Ω
𝑅 60 = 𝛼 1 (60−75)+ 𝛼 2 (60−75) 2
Eq.1
𝑅 90 = 𝛼 1 (90−75)+ 𝛼 2 (90−75) 2
Eq.2

32. Example-3 Adding Eq.1 and Eq.2 yields
𝑅 60 = 𝛼 1 (60−75)+ 𝛼 2 (60−75) 2
Eq.1
Adding Eq.1 and Eq.2 yields
Substituting this value in any of the above equation yields
Thus the quadratic approximation is
𝑅 90 = 𝛼 1 (90−75)+ 𝛼 2 (90−75) 2
Eq.2
𝛼 2 =−44.36× 10 −6 /℉
𝛼 1 = /℉
𝑅 𝑇 = (𝑇−75)−44.36× 10 −6 (𝑇−75) 2

33. Example-4
By what percentage do the predictions of the linear and quadratic approximations vary from the actual values at 60oF and 85oF.
Linear and quadratic approximations of the given data are given as:
At 60oF
Solution
𝑅 𝐿 T = (𝑇−75)
𝑅 𝑄 𝑇 = (𝑇−75)−44.36× 10 −6 (𝑇−75) 2
𝑅 𝐿 60 = (60−75) =107.1 Ω
𝑅 𝑄 60 = (60−75)−44.36× 10 −6 (60−75) 2
𝑅 𝑄 60 =106 Ω

34. Quadratic Approximation
Example-4
At 85oF
𝑅 𝐿 85 = (85−75) =112.3 Ω
𝑅 𝑄 85 = (85−75)−44.36× 10 −6 (85−75) 2
𝑅 𝑄 85 =111.8 Ω
Temperature
(oF)
Resistance (Actual)
Linear Approximation
% Error
Quadratic Approximation 60
106.0
107.1 -1
106 65
107.6
108.13
-0.49
107.64 70
109.1
109.16
-0.06
109.04
0.0507 75
110.2 80
111.1
111.23
-0.11
111.11 85
111.7
112.3
-0.54
111.8 90
112.2
113.29
-0.9

35. Example-4

36. RTD
RTD is a temperature sensor whose resistance increases with rise in temperature.
Metals used in these devices vary from platinum, which is very repeatable, quite sensitive, and very expensive, to nickel, which is not quite as repeatable, more sensitive, and less expensive.

37. Sensitivity
An estimate of RTD sensitivity can be noted from typical values of 𝛼 𝑜 .
For platinum this number is typically on the order of /oC and for Nickel a typical value is 0.005/oC.
Thus, for platinum, for example, a change of 0.4Ω would be expected for a 100Ω RTD if the temperature is changed by 1oC.

38. Response Time
In general, RTD has a response time of 0.5 to 5sec or more.
The slowness of response is due to the slowness of thermal conductivity in bringing the device into thermal equilibrium with its environment.
Generally time constants are specified either for “Free Air” or and “Oil Bath” condition.

39. Construction
RTD is simply a length of wire whose resistances is to be mentioned as function of temperature.
The construction is typically such that the wire is wound on a coil to achieve small size and improve thermal conductivity to decrease response time.
In many cases wire is protected from environment by a sheath or protective tube that inevitably increase response time but may be necessary in hostile environment.

40. Signal Conditioning
In view of the very small fractional changes of resistance with temperature (0.4%), the RTD is generally used in bridge circuit.

41. Dissipation Constant
Because the RTD is resistance, there is an 𝑖 2 𝑅 power dissipated by the device itself that causes a slight heating effect.
Typically a dissipation constant is provided in RTD specifications.
Which relates the power required to raise the RTD temperature by one degree of temperature.
Thus a 25mW/oC dissipation constant shows that if 𝑖 2 𝑅 power loss in RTD is 25mW, then the RTD will be heated by 1oC.

42. Dissipation Constant
The self heating temperature rise can be found from the power dissipated by RTD and the dissipation constant from
Where,
∆𝑇= Temperature rise because of self heating
𝑃= Power disseated by RTD
𝑃 𝐷 = Dissipation constant of RTD
∆𝑇= 𝑃 𝑃 𝐷

43. Example-5
An TRD has 𝛼 𝑜 =0.005/℃, 𝑅=500Ω and a dissipation constant of 𝑃 𝐷 =30𝑚𝑊/℃ at 20℃. RTD is used in bridge circuit as shown below with 𝑅 1 = 𝑅 2 =500Ω and 𝑅 3 a variable resistor used to null the bridge. If the supply is 10𝑉 and the RTD is placed in a bath at 0℃ find the value of 𝑅 3 to null the voltage.

44. Example-5 First find out the value of RTD resistance at 0℃.
Let us now find out the power dissipated in RTD.
Current can be calculated as
Power dissipation in RTD is
R T =R 𝑇 𝑜 1+ 𝛼 𝑜 ∆𝑇
R 0℃ = (0−20)
R 0℃ =450Ω
P= 𝐼 2 𝑅
𝐼= 𝑉 𝑅 𝑇 = =0.011𝐴
P= (0.011) 2 ×450=0.054𝑊

45. Example-5 Temperature rise now can be calculated as
Thus the RTD is not at bath temperature but at temperature of 1.8℃.
Thus the bridge will null at 𝑅 3 =454.5Ω
∆𝑇= 𝑃 𝑃 𝐷
∆𝑇= =1.8℃
R 1.8℃ = (1.8−20)
R 1.8℃ =454.5Ω

46. Range of RTD
The effective range of RTD depends principally on the type of wire used as the active element.
Thus a typical platinum RTD may have range of −100℃ to 650℃.
Whereas, RTD constructed from nickel might typically have a specified range of −180℃ to 300℃.

47. Effects of lead-wire Resistance
Because the RTD is a resistive device, any resistance elsewhere in the circuit will cause errors in the readings for the sensor.
The most common source of additional resistance is in the lead-wires attached to the sensor, especially with assemblies that have long extension leads.
Fortunately, the use of a 3-wire or 4-wire system will reduce errors to negligible levels in most applications.

48. 2-Wire Construction
2-wire construction is the least accurate of the 3 types since there is no way of eliminating the lead wire resistance from the sensor measurement.
2-wire RTD’s are mostly used with short lead wires or where close accuracy is not required.
𝑅 𝑇 = 𝑅 𝐿1 + 𝑅 𝐿2 + 𝑅 𝑏

49. 3-Wire Construction
3-wire construction is most commonly used in industrial applications where the third wire provides a method for removing the average lead wire resistance from the sensor measurement.
The 3 wire circuit works by measuring the resistance between 𝑅 𝐿1 & 𝑅 𝐿2 and subtracting the resistance between 𝑅 𝐿2 & 𝑅 𝐿3 which leaves just the resistance of the RTD.
This method assumes that wires 1, 2 & 3 are all the same resistance

50. 3-Wire Construction
Resistance between 𝑅 𝐿1 & 𝑅 𝐿2 can be calculated as
𝑅 12 = 𝑅 𝐿1 + 𝑅 𝐿2 + 𝑅 𝑏
Resistance between 𝑅 𝐿2 & 𝑅 𝐿3 can be calculated as
𝑅 23 = 𝑅 𝐿2 + 𝑅 𝐿3
Subtracting the resistance 𝑅 23 from 𝑅 12 which leaves just the resistance of the RTD
𝑅 12 − 𝑅 23 = (𝑅 𝐿1 + 𝑅 𝐿2 + 𝑅 𝑏 )−( 𝑅 𝐿2 + 𝑅 𝐿3 )
𝑅 12 − 𝑅 23 = 𝑅 𝑏

51. 4-Wire Construction
4-wire construction is used primarily in the laboratory where close accuracy is required.
In a 4 wire RTD the actual resistance of the lead wires can be determined and removed from the sensor measurement.
The 4-wire circuit is a true 4-wire bridge, which works by using wires 1 & 4 to power the circuit and wires 2 & 3 to read.
This true bridge method will compensate for any differences in lead wire resistances.

52. 4-Wire Construction
The true 4-wire measurement uses the current-potential method.
A current of known value (I+) is passed through the sensor along the “current” lead wires.
The voltage generated across the sensor is measured using the “potential” lead wires (Vsensor) and the sensor’s resistance is calculated by dividing the measured voltage by the Known current.
𝑅 𝑠𝑒𝑛𝑠𝑜𝑟 = 𝑉 𝑠𝑒𝑛𝑠𝑜𝑟 𝐼

53. RTD Packages
Two basic packages
Thin Film
Wire Wound

54. RTD Packages
Probe Type

55. Thermistor
Thermistor represents another class of temperature sensor that measures temperature through change of material resistance.
The characteristics of these devices are very different from those of the RTDs and depend upon the peculiar behavior of semiconductor resistance versus temperature.

56. Sensitivity
The sensitivity of thermistor is a significant factor in their application.
Changes in resistance 10% per 0C are not uncommon.
Thus a thermistor with a normal resistance of 10KΩ at some temperature may change by 1K Ω for 1oC change in temperature.

57. Response Time
For smallest bead thermistor in an oil bath (good thermal contact) response time of 0.5s is typical.
Same thermistor in still air will respond in 10s.
When encapsulated, the time response is further increased due to poor thermal contact.

58. Example-6
A thermistor is to monitor room temperature. It has a resistance of 3.5𝐾Ω at 20℃ with a slope of −10%/℃. The dissipation constant is 𝑃 𝐷 =5𝑚𝑊/℃. It is proposed to use the thermistor in the divider, as shown below, to provide the voltage of 5𝑉 at 20℃. Evaluate the effect of self heating.

59. Example-6 At 20℃ thermistor resistance will be 3.5𝐾Ω
Let us now consider the effect of self heating
𝑉 𝐷 = 𝑅 𝑇𝐻 3.5𝐾+𝑅 𝑇𝐻 10𝑉
𝑉 𝐷 = 3.5𝐾 3.5𝐾+3.5𝐾 10𝑉=5𝑉
𝑃= 𝑉 2 𝑅 𝑇𝐻
𝑃= 𝐾 =7.1𝑚𝑊

60. Example-6 Temperature rise of thermistor can be calculated as
Actual resistance is given as
Sot he divider voltage is 𝑉 𝐷 =4.6𝑉.
Δ𝑇= 𝑃 𝑃 𝐷
Δ𝑇= 7.1𝑚𝑊 5𝑚𝑊/℃ =1.42℃
𝑅 𝑇𝐻 =3.5𝐾Ω−1.42℃(0.1/℃)(3.5𝐾Ω)
𝑅 𝑇𝐻 =3 𝐾Ω

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