Experiment 1

The time constant of Thermocouple & Its calibration

 Experiment 1
The time constant of Thermocouple & Its calibration

Aim: To calibrate a thermocouple, determine its time constant and to compare it with that of an
ordinary thermometer.

Set-up: It consists of an electric heater on which a beaker containing water is placed. The water is
made to boil. One junction point of thermocouple is dipped into hot water while the other is kept at
the room temperature. The free end of thermocouple is connected to the storage oscilloscope (fig. 2.1)
to record output voltage variation.

Calculations:
• Temperature of hot junction of thermocouple: 100∘ C
Time constant for thermocouple 150 ms

• The temp. of hot junction boiling water 𝜃1 = 100∘ C

Time taken for temp. rise to 0.95𝜃1 , of thermometr 𝑇2 : 17sec
Time constant of thermometer: 17/3 = 5.67sec

Observations:

Observation for voltage vs. Time graph for thermocouple Temperature vs. Voltage Readings
Temperature (C) Voltage (mv)
20 2.4
25 4.5
30 10.8
35 14.6
40 19.1
45 24.2
50 27.8
55 32.2
60 37.0
65 40.6
70 46.6
75 51.1
80 55.1
85 59.2
90 65.5
95 70.0
100 75.3
Results/Conclusion:
• The plot between the voltage and temp for the thermocouple is linear.

• Time constant of thermocouple is 150 ms

• Time constant of thermometer is 5.67 s

• The plot between voltage and time for thermocouple is exponential.

Discussion:
• Performance comparison of thermocouple vs. ordinary thermometer:
The time constant of thermocouple is much smaller than that of ordinary thermometer. Hence
performance of thermocouple is much better. The reason behind this difference in time
constant is because in ordinary thermometer, sensitivity depends on the rate at which mercury
rises in column. This rate is much smaller than Seeback effect which depends on the flow of
electrons.

• Sensitivity of Iron-constantan and Copper-constantan:

Iron constantan thermocouple is more sensitive (sensitivity ∼ 50 − 60μV/ ∘ C ). The reason is
that copper is less sensitive as it has quite uniform thermal properties whereas Iron is in
generally impure and hence it has higher sensitivity.

• Factors on which time constant of thermocouple depends

1. Surface area of wire in thermocouple
2. Metals used in thermocouple
3. Convective heat transfer coefficient of medium
4. Type of junction
• To reduce time constant of thermocouple.

1. Reduce the surface area, i.e., diameter of wire used.

2. By using high conducting materials
Sources of error:
• The parallax error introduced while noting down the temperature from the thermometer.
• Inefficiencies introduced during noting down the voltage, 𝑖. 𝑒, time lag.
• The boiling temperature may not be constant due to presence of impurities.
• The tip of wire may not be dipped properly in water.
Voltage vs. temperature graph
EXPERIMENT 2
 EXPERIMENT 2
OP-AMP CIRCUIT

Aim: To study integrated circuit operational amplifier and their use in various applications.

Theory: Operational amplifiers are directly coupled devices such that the input signal may be either
A.C or D.C. or combination of the two. All op-amps have two inputs connected in a differential mode,
so that output voltage is 𝑉0 = 𝐴(𝑉+ − 𝑉− ) where 𝑉+is voltage of non-inverting input and 𝑉− is the
voltage of inverting input.
For basis inverting amplifier, the output and gain be defined as:
𝑅𝑓
𝑉0 = (− )𝑣
𝑅| 𝑠
𝑅𝑓
𝐺𝑎𝑖𝑛 =−
𝑅|

Observations & Calculations:

1 Basic inverting circuit:
𝑅| = 9.9 KΩ Vin = 552mv
𝑅𝑓 = 270 ⋅ 2kΩ Vout (observed) = 14.4v
𝜔 = 1kH2
𝑅 270⋅2
𝑉𝑜𝑢𝑡 (As expected,) = 𝑉𝑖𝑛 ( 𝑅𝑓) = 552 × 9.9
= 15.06 of V
|
The expected output voltage, i.e., 15 V is in range of observed output voltage 152 V.
We even observe an inverted output waveform.
2. Integrating Circuit:
𝑉𝑖𝑛 = 5.76 V
𝜔 = 1kHz (Triangular input)
𝐶 = 470𝑝𝐹
𝑅𝑓 = 9.9kΩ

For a triangular input, a parabolic waveform is observed. For a sinusoidal input, a sinusoidal
waveform is observed as output with a phase shift of nearly (𝜋/2) radians, which is in
accordanre with an expected cosine wave.
Vout (observed) = 120 V
Gain = 20.84
Result and Discussion:
1. In case of inverting amplifying circuit, we obtain an inverted waveform. The amplified
voltage has differed as, the expected voltage is 15.06 where as the observed volthge is 14.4
This error can be attributed to inaccuracy in measuring the resistance values.
𝑅𝑓
𝐴𝑚𝑝 = ( )
𝑅|
 Error in 𝑅| and 𝑅𝑓 significantly hampers amplifications.
2. In case of integrating circuit, when the input is sine wave, observed output waveform is
shifted from original waveform by 90∘ . Thi is however not perfectly as expected.

Observations for summing Circuit

𝑉1 = 𝑉2 = 𝑉3 = 0.2 V
3.
𝑅1 = 𝑅2 = 𝑅3 = 9.9 kΩ

Vout (observed) = 17.8 V

𝑅𝑓 𝑅𝑓 𝑅𝑓
𝑉out (observed) = − Vin ( + + )
𝑅1 𝑅2 𝑃3
1 1 1
= − Vin (10 + 10
+ 10) × 270

Vout (observed) = −16.2 V

 EXPERIMENT -03

DIGITAL TANK LEVEL CONTROL SYSTEM

Fig. Hardware system overview (digital tank level control system)

 EXPERIMENT 03

DIGITAL TANK LEVEL CONTROL SYSTEM

Experimental Set-up:

Components:

Component Type

Tank Rectangular

Floater-Potentiometer Height sensor

DC Supply 0.32 V

DAQ NI 6221-68 pin

Relay Switch 12 V, 200 Ω

Solenoid Valve Oriface-16mm, V=220 v AC

Transistor CL-10

Hardware System Overview:

The resistance of potentiometer is connected in series with 55Ω resistor on one end and to a 10 ∨ 𝐷𝐶
supply on another end.
10𝑥
𝑉= 𝑉 = 𝑂𝑢𝑡𝑝𝑢𝑡 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑐𝑟𝑜𝑠𝑠 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟
(𝑥 + 55)
55 𝑉
𝑥= 𝑥 = 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟
(10 − 𝑉)
𝐻1 = 𝐻0 + 𝑠 𝑥 𝐻1 = 𝐻𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 𝑎𝑛𝑦 𝑡𝑖𝑚𝑒 𝑡 𝑖𝑛 𝑡ℎ𝑒 𝑡𝑎𝑛𝑘

The above equation is used to convert 𝑉 into 𝐻 inside the lab view program. The voltage across the
resistance in potentiometer is fed as input in the DAQ Card which is connected to computer. DAQ
card converts the analog-signal to digital signal which is received by computer. The input voltage
received by the computer is fed into the LABVIEW software automatically. The software converts
this digital voltage signal into the corresponding water level in the tank through a program already
described above. The water level is detected by the controller in the program. Now, when the voltage
corresponding to lowest level of the tank is achieved the software sends a digital signal to DAQ card.
Current flowing through the coil of the relay creates a magnetic field which attracts a lever and
changes the switch contacts.

Fig. Experimental setup

Observations:
Height of water in tank (cm) Voltage (V) x (cm)
37.0 4.38 42.857
41.0 5.09 57.143

Calculations:
𝐻1 = 𝐻0 + 𝑠𝑋
37 = 𝐻0 + s × 42.857 -----(1)
41 = 𝐻0 + s × 57.143 -----(2)
𝑠 = 0.28 𝐻0 = 25

Discussion:
1. Hysteresis is present in the system.
2. On-off control system requires less sophistication and less cost, but has problem due to errors.
 Experiment04
TRANSIENT AND FREQUENCY RESPONSE OF FIRST ORDER SYSTEM

AIM: To determine the time constant of the system and study its frequency
response to a sinusoidal input.

APPARATUS REQUIRED: Breadboard, Function generator, C.R.O., Resistors,

Capacitor.

EXPERIMENTAL SET UP: The first order system setup consists of a resistance R
and a capacitance C in series which connection is made in a breadboard as
shown in fig.2. The input signal of desired frequency and amplitude is supplied
through a function generator. Fig.1. shows the connection diagram where the
input signal is connected to the channel 1 and output signal to channel 2 of the
C.R.O. Both the input and output waveform are displayed in a C.R.O.

Fig.1. Experimental Set-up for First order RC Circuit

 Fig.2: Circuit diagram for transient and frequency response of first order system

THEORY:

• For transient response the circuit is either connected to a battery through

a key or a square wave input is generated by the function generator. The
output voltage is measured across the circuit; the transient response is
given as

• For frequency response, the circuit is connected to an oscillator, which

supplies sinusoidal voltage Eisin(wt) of any desired frequency. The
response is given as
PROCEDURE:

• For transient response make the connections as shown in fig. 2, and

choose a suitable value for R.

• Supply a square wave input using the function generator and obtain the
response on the oscilloscope.

• Using the oscilloscope determine the time for the voltage to reach
0.632E as in fig.3. This is the time constant of the system.

• Change R and repeat steps 2 and 3.

• For frequency response make connections as shown in fig.2.

• For frequency response, feed a harmonic input at different frequencies.

Determine by quick measurement the amplitude of Eo and Ei and their
phase difference.

• Make theoretical plots of Eo / Ei and  against frequency  as per the

observations made above for the values of  chosen in the experiment
and show experimental points on these plots.

OBSERVATIONS:
Table01
 Time
Sr.no Frequency (𝛚) Resistance(kΩ) Capacitance(μF) Constant (𝜏 in
ms)
1 10 24.2 2 48.2

2 10 263 2 526
3 10 4.7 2 9.4

Table02

Sr.no frequency Ei (V) Eo Eo /Ei 𝛟(

(hz) input (V) deg)

1 10 18 16.6 0.92 0.452

2 20 18 14.8 0.82 0.603

3 30 18 13 0.72 0.829

4 40 18 10.8 0.6 0.955

5 50 18 9.6 0.53 1.068

6 60 18 8.6 0.47 0.98

7 70 18 7.4 0.41 1.143

8 80 18 6.6 0.36 1.206

Oscilloscope output when given sin input to function generator

Oscilloscope output when given square wave input to function generator

CALCULATIONS
DISCUSSIONS
• We observed the time constant for RC circuit and verified with its
theoretical values.
• We will be able to observe the relation between frequency and phase
difference also between frequency and ratio of output voltage.
• Sources of error, included in accuracy in measurements, loose
connections etc.

EXPERIMENT 05
TRANSIENT AND FREQUENCY RESPONSE OF SECOND ORDER SYSTEM
AIM: To study the frequency and damping characteristics and frequency
response of second order system.
APPARATUS REQUIRED: Capacitor, Inductor, Resistor, C.R.O., Function
Generator, Multimeter.

EXPERIMENTAL SET UP:

The first order system setup consists of a resistance R and a capacitance C in
series which connection is made in a breadboard as shown in fig.2. The input
signal of desired frequency and amplitude is supplied through a function
generator. Fig.1. shows the connection diagram where the input signal is
connected to the channel 1 and output signal to channel 2 of the C.R.O. Both
the input and output waveform are displayed in a C.R.O.

Fig.1. Experimental Set-up for First order RC Circuit

Fig.2: Circuit diagram for transient and frequency response of first order
system

THEORY:

Fig.3.
PROCEDURE:
 • For transient response study connect the circuit as shown in fig.2 (ckt
fig)
• For different values of R and L, feed low frequency square wave to
obtain a damped response on the oscilloscope as shown in fig 3.
• From the response curve, determine damping ratio and natural
frequency values with the use of following equation.

• For frequency response study, choose suitable value of R and L, feed a

harmonic input, measure amplitudes Eo and Ei and their phase
difference (𝛟) by using the quick measurements on the two signals as in
fig4 .

Fig.4.
• Repeat above step for different values of r.

OBSERVATIONS:
TABLE I: Transient Response.
Capacitance (µF)= 0.01
R (tot) L(H) V1 V2 ξ Time ωn
period(ms)
Natural
frequency
2.516 2.40 14.8 4.8 0.176 1.2 5316.30

2.616 3.00 14.4 4.8 0.172 1.340 4757.46

3.870 6.00 14 6.0 0.133 1.90 3334.90

TABLE II: Frequency Response

Capacitance: 0.01µF; Inductance: 6H; Resistance:3.875 kΩ;

F(khz) Eo(v1) Ei (v2) E0/ Ei 𝛟

1 0.92 2.18 0.422 2.72
2 0.192 2.16 0.088 2.80
3 0.098 2.22 0.044 2.89

SOURCES OF ERROR:
• Connections should not be loose.
• Error may take place while measuring using cursor.

Experiment06
Servo Position Control System
AIM: Study of servo position control system
METHODOLOGY
 • To develop circuit for position control of DC motor.
• Study of position control of DC motor using Proportional Controller.
• Study of position control of DC motor using Proportional and Integral
Controller.

THEORY:

• Proportional controller (P controller) is mostly used in first order

processes with single energy storage to stabilize the unstable process.
The main usage of the P controller is to decrease the steady state error
of the system. As the proportional gain factor K increases, the steady
state error of the system decreases. However, despite the reduction, P
control can never manage to eliminate the steady state error of the
system. As we increase the proportional gain, it provides smaller
amplitude and phase margin, faster dynamics satisfying wider frequency
band and larger sensitivity to the noise. We can use this controller only
when our system is tolerable to a constant steady state error. In
addition, it can be easily concluded that applying P controller decreases
the rise time and after a certain. value of reduction on the steady state
error, increasing K only leads to overshoot of the system response. P
control also causes oscillation if sufficiently aggressive in the presence of
lags and/or dead time. The more lags (higher order), the more problem
it leads. Plus, it directly amplifies process noise.

• Proportional and Integral Controller: Proportional and Integral (P-I)

controller is mainly used to eliminate the steady state error resulting
from P controller. However, in terms of the speed of the response and
overall stability of the system, it has a negative impact. This controller is
mostly used in areas where speed of the system is not an issue. Since P-I
controller has no ability to predict the future errors of the system it
cannot decrease the rise time and eliminate the oscillations. If applied,
any amount of I guarantees set point overshoot.

EXPERIMENTAL SETUP:
 • The experimental setup of the servo position control system is DYNA-
1750, Transducer and Instrumentation Trainer, DYNALOG (India) Ltd. The
figure of the setup is shown in fig.1.

Fig.1: Experimental setup for servo position control system

PROCEDURE :
PART 1

• Connect the circuit as shown in fig.2.

• Set Amplifier #1 GAIN COARSE Control to 10 and GAIN FINE to 1.0 to
give an overall gain of 10.0.
• Transfer the volt meter to terminal B of the wire wound resistor. Adjust
the setting of the resistor control to its central position to give zero volt
output.
• Adjust Amplifier #1 OFFSET to give 0 Volt.
• Rotate the input control slowly and observe the servo position control
system achieved.
 Fig.2

PART 2

• Connect the circuit as shown in fig.3.

• Set Amplifier #1 GAIN COARSE Control to 10 and GAIN FINE to 0.1 to give
an overall gain of 1.0.
• Switch ON the power supply.
• Connect the Volt Meter temporarily to terminal B of the wire wound
resistor and adjust the setting of the resistor control to its central
position to give zero volt output.
• Transfer the Volt Meter back to the output of the Power Amplifier and
Check the adjustment of Amplifier #1 OFFSET to give 0V.
• Transfer the Volt Meter back to the output of Amplifier #2, set the GAIN
COARSE control to 100 and GAIN FINE to 1.0 and check the adjustment
of the OFFSET control for an output of +3 V. Return the GAIN COARSE
control to 1. This control will again be used to introduce a step input.
• Rotate the input control slowly and observe the servo position control
system achieved.
• How do you obtain the response when a step input is given? Trace the
response curve with the help of an oscilloscope.
 Instrumentati
Amplifie
Integrat

Differential
Amplifie Summin
Amplifie
Powe
Amplifie
Variable Amplifier
resistanc
Amplifier

Fig.3

DISCUSSION:

• What are the various components used in the experiment and state
their functions.
• Observe the stability of the system when gain changes.
• Study how the servo potentiometer and rotary encoder works