PROCESS INSTRUMENTATION AND CONTROL LAB

(CCB3072)

EXPERIMENT 5:

FREQUENCY RESPONSE OF COUPLE TANK

GROUP 5

GROUP MEMBERS:

1. YOONG KAI BIN 18491

2. NUR AININA BINTI YUSOH 18130

3. KISHORTHAREN A/L VIJAYA CHANDRAN 20010

4. NURUL ASYIQIN BINTI IBRAHIM 18044

5. SARAVANAN A/L ELANGOVAN 15003

LAB INSTRUCTOR: SYED NASIR

LECTURER: NASSER MOHAMED RAMLI

DATE OF EXPERIMENT: 1ST OCTOBER 2015

DATE OF SUBMISSION: 8TH OCTOBER 2015

2

TABLE OF CONTENT

NO ITEM PAGE

1 Summary 3

2 Introduction 4

3 Theory 5

4 Procedure 7

5 Results 10

6 Discussion 16

7 Conclusion 18

8 References 19

9 Appendices 20

3

1.1 SUMMARY

The main objective of this experiment are

i. To demonstrate the amplitude frequency and amplitude phase characteristics (frequency

response characteristics) of single pneumatic tank, and

ii. To demonstrate the amplitude frequency and amplitude phase characteristics (frequency

response characteristics) of two pneumatic tanks connected in series.

We used a Coupled tank system to measure frequency of a coupled system, and a system using

either small tank or big tank, please refer to a figure below; this shows a coupled tank system.

Tank A or Tank B may be tested single or both Tank A and Tank B can be connected

together to give a series connected system. The air supply to the system comes from a

pneumatic sine wave generator. The pressure in Tank A and Tank B can be measured using

the digital manometers provided and recorded in the Oscillographic Recorder.

From the frequency response data of tank A and tank B, it was found that the log AR

decreases as the frequency increases. It was also obtained that the phase angle decreases as the

frequency increases.

From the frequency response data of tank in series, it was found that the amplitude ratio

fluctuates as the frequency increases. The phase angle also fluctuates up and down as the

frequency increases from 0.01 to 0.1 Hz.

4

2.0 INTRODUCTION

A measure of the ability of a system to respond or transmit input signals of various

frequencies that are applied to it is called Frequency response. Frequency response measures

the ability of the device to respond to changes in the input that are changing with respect to

time. Therefore it measures the dynamic characteristics of the system as against the first four

experiments in this series that measures the static characteristics like accuracy and resolution of

the device. Frequency response can also be used as a technique for parameter estimation of

unknown system. By determining the frequency response of unknown system we can determine

the order of the system as well as its dynamic parameters like time constant, gain and delay

time.

5

3.0 THEORY

When the transfer function of a system is known; consider a first order system represented by

the transfer function,

G(s) Y

X K

s 1

Where;

X, Y = input and output variables respectively, in the Laplace domain

K = system gain

= time constant

s = Laplace operator

If the input in the time domain x is a sinusoidal signal such that,

X Asint

then, the corresponding Laplace domain input is given by

X A

s2 2

We can determine its frequency response by substituting jfor s and then after rationalizing the

complex function convert it to the polar form and determine the magnitude and argument

(angle) of the complex number in the polar form.

G( j) 1

1 j

On rationalizing by multiplying the numerator and denominator by (1-j) and separating the

real and imaginary factors we get

6

a2 b2

122 1

G( j) 1

1 22 j

1 22

The complex numbers in the rectangular form a+jb can be converted to polar form by the

relationships,

z and angle z tan1 b

a

Converting into polar form using, we get

Amplitue ratio AR

Phase angle tan1 ()

The frequency response of a system is presented in the form of the Bode diagrams.

7

4.0 PROCEDURE

Figure 1: Equipment connections

Before the experiment

1. Please read Instruction Manual of FG120 Function Generator, IM706011-01E for the

operation

2. Please read also Instruction Manual of OR100E/OR300E Handy Oscillographic Recorder,

IM OR100E-01E for the operation

3. Please confirm input setting range of JH12 is set to 0 to 4 V.

4. Please confirm air supply to PK200 I/P Converter is set to 240 kPa before connection

Connect the equipment as shown in Figure 1. For recording device we can use the LR recorder, X-

Y-t plotter or the 2 channel Oscillograph. In the present experiment we will be using the 2

channel Oscillograph.

8

Open the appropriate valves such that the Tank A is in the circuit. Close valve MV-02 and MV-03.

Open Valve MV-01 and RV-01.Set the FG120 Function generator high amplitude to 4VDC and low

amplitude to 0 VDC.

1. Set the OR142 Oscillographic Recorder Channel 1 to 0.2 V/div and Channel 2 to 0.5V/div.

For chart speed please select suitable measurement range to record the input of the two

channels.

2. Set the input frequency as 0.01 Hz. Measure the amplitude of the input signal from

Channel 1 and the output signal from channel 2. A typical trace in the recorder is shown

in Figure 10.5.

3. Record all the relevant amplitude data.

4. Determine the horizontal displacement of the two sine wave in mm. Convert this

displacement to the phase angle in degrees.

5. Increase the frequency to 0.02 Hz and repeat the experiment. Maintain the input

amplitude constant at if necessary by adjusting the function generator output knob.

6. Continue the experiment for at least 3 decades of frequency that is up 1 Hz. As the

frequency increases the chart speed also must be increases to get good recording.

Similarly as the frequency increases the output amplitude decreases. Increase the

sensitivity of channel 2 as the output sinusoid becomes smaller and smaller.

7. Repeat the experiment using the tank B. Close valve RV-01, MV-03 and MV-04. Open

valve MV-01, MV-02 and RV-02. Record all the relevant data.

8. Connect the two tanks in series and repeat the experiment. Close valve MV-02 and MV-

04. Open valve MV-01, RV-01, MV-03 and RV-02. Record all the relevant data.

9

Figure 2: Recording of input and output sinusoids in the oscillograph recorder

5.0 RESULTS

F (Hz)

Amplitude V1 Amplitude V2

Tc Td Phase Angle AR Log F Log ARMax V1 Min V1

V1 = V1max –

V1min

Max V2 Min V2V2=V2max-

V2min

0.01 0.55 0.22 0.33 5.33 3.44 1.91 102 6 -9.80 5.79 -2.000 0.7626

0.02 0.57 0.24 0.33 5.16 3.46 1.60 51 8 -11.65 4.85 -1.699 0.6857

0.03 0.57 0.24 0.33 5.01 3.64 1.35 33 6 -11.74 4.09 -1.523 0.6117

0.04 0.57 0.24 0.33 4.91 3.73 1.17 24 4 -15.75 3.55 -1.398 0.5502

0.05 0.56 0.24 0.32 4.79 3.79 1.00 19 3 -17.74 3.13 -1.301 0.4955

0.06 0.57 0.24 0.33 4.76 3.85 0.90 17 2 -20.14 2.73 -1.222 0.4361

0.07 0.57 0.24 0.33 4.73 3.89 0.82 14 2 -21.92 2.49 -1.155 0.3962

0.08 0.57 0.24 0.33 4.66 3.94 0.71 12 2 -24.93 2.15 -1.097 0.3324

0.09 0.56 0.24 0.32 4.56 3.96 0.60 11 1 -28.07 1.88 -1.046 0.2741

0.10 0.56 0.25 0.31 4.56 4.00 0.57 11 2 -28.54 1.84 -1.000 0.2648

Table 1: Frequency response data for Experiment A (Tank A)

10

Graph of log AR vs log F0.90.80.70.60.50.40.30.20.10

-2.5 -2 -1.5 -1 -0.5 0log F (Hz)

Graph of φ vs log F0

-2.5 -2 -1.5 -1 -0.5 0-5

-10

-15

-20

-25

-30log F (Hz)

Diagram 1: Bode Diagram (Tank A only)

11

Phas

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Am

plitu

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log

Table 2: Frequency response data for Experiment B (Tank B)

F (Hz)

Amplitude V1 Amplitude V2

Tc Td Phase Angle AR Log F Log AMax V1 Min V1

V1 = V1max –

V1min

Max V2 Min V2V2 = V2max –

V2min

0.01 0.59 0.25 0.34 4.85 3.66 1.19 99 18 -15.95 3.50 -2.000 0.5441

0.02 0.59 0.24 0.35 4.69 3.94 0.75 50 10 -25.02 2.14 -1.699 0.3304

0.03 0.59 0.24 0.35 4.37 3.91 0.46 33 8 -37.27 1.31 -1.523 0.1173

0.04 0.59 0.25 0.34 4.31 3.96 0.35 25 6 -44.17 1.03 -1.398 0.0123

0.05 0.59 0.24 0.35 4.21 3.94 0.27 20 4 -52.35 0.77 -1.301 -0.1135

0.06 0.58 0.25 0.33 4.21 3.98 0.23 17 3 -55.12 0.70 -1.222 -0.1549

0.07 0.58 0.25 0.33 4.29 4.07 0.22 15 3 -56.31 0.67 -1.155 -0.1739

0.08 0.57 0.24 0.33 4.19 4.01 0.18 12 2 -61.39 0.55 -1.097 -0.2596

0.09 0.57 0.24 0.33 4.19 4.04 0.15 9 2 -65.56 0.46 -1.046 -0.3372

0.10 0.57 0.26 0.31 4.16 4.02 0.14 9 1 -65.70 0.45 -1.000 -0.3467

12

Graph of log AR vs log F

-2.5 -2 -1.5 -1 -0.5

0.60.50.40.30.20.10

-0.1 0-0.2-0.3-0.4

log F (Hz)

Graph of φ vs log F0

-2.5 -2 -1.5 -1 -0.5-10

0

-20-30-40-50-60-70

log F (Hz)

Diagram 2: Bode Diagram (Tank B only)

13

Phas

e an

gle,

Am

plitu

de R

atio,

log

Table 3: Frequency response data for Experiment C (Tank A and Tank B in series)

F (Hz)

Amplitude V1 Amplitude V2

Tc Td Phase Angle AR Log F Log ARMax V1 Min V1

V1 = V1max –

V1min

Max V2 Min V2V2 = V2max –

V2min

0.010.50 0.25 0.25 0.90 0.70 0.20 100 29 -51.34 0.80

-2.000-0.10

0.020.52 0.30 0.22 1.00 0.80 0.20 50 22 -48.37 0.88

-1.699-0.06

0.030.60 0.50 0.10 1.00 0.80 0.20 33 15 -26.57 2.00

-1.5230.30

0.040.62 0.37 0.25 1.10 0.80 0.30 25 8 -39.81 1.20

-1.3980.08

0.050.62 0.50 0.12 1.20 0.90 0.30 21 7 -22.62 0.24

-1.301-0.62

0.060.67 0.50 0.17 1.10 0.90 0.20 16 7 -41.19 1.14

-1.2220.06

0.070.52 0.25 0.27 1.20 0.80 0.40 14 5 -34.51 1.45

-1.1550.16

0.080.75 0.52 0.22 1.20 0.70 0.50 15 6 -24.23 2.22

-1.0970.35

0.090.60 0.25 0.35 1.00 0.90 0.10 11 3 -74.05 0.29

-1.046-0.54

0.100.75 0.52 0.22 0.90 0.80 0.10 12 4 -66.04 0.44

-1.000-0.36

14

1

Graph of log AR vs log F0.60.40.20

-2.5 -2 -1.5 -1 -0.5 0-0.2-0.4-0.6-0.8

log F (Hz)

Graph of φ vs log F

-2.5 -2 -1.5 -1 -0.50

-10 0-20-30-40-50-60-70-80

log F (Hz)

Diagram 3: Bode Diagram (Tank A and B in series)

Phas

e an

gle,

Am

plitu

de R

atio,

log

1

6.1 DISCUSSION

6.2 1 Frequency Response Data of Tank A

From the experiment, we can see in the methodology use the range of frequency from 0.01Hz until

0.1Hz. However, in this part we only used it for the Tank A. This tank size is smaller than the Tank B. The

frequency response that we get from the oscillograph consists of Channel 1 (input) and Channel

2(output). For the Channel 1, the highest peak that we get is 0.57 and the lowest one is 0.22. As for the

Channel 2, the highest peak is 5.33 and the lowest one is 0.57. From the above result, we can calculate

what is the Amplitude Ratio and as for this part, the AR is decreasing due to the increasing the input

frequency. Other than the Amplitude Ratio, the time delay and time between 2 peak also decrease

when the increase the input frequency. Therefore, this phenomenon is known as attenuation. For your

information, this phenomenon will happen when the signal strength is reducing during transmission

from input to output point. That is why we using the repeater or a coupled tank system so that we can

avoid this phenomena. However, we were using the small tank and the frequency response for this tank

is smooth. As the frequency increases the phase angle decreases.

6.3 2 Frequency Response Data of Tank B

Now for the experiment 2, which is using the Tank B and it is longer than the Tank A. As for this

experiment, we will using the same procedure from the lab manual which is need to put the

frequency input from 0.01Hz to 0.1Hz. For the Channel 1 (input), the highest peak is 0.59 and the lowest

is 0.24. For the Channel 2 (output) the highest peak is 4.85 and the lowest one is 3.66. We calculated

the Amplitude Ratio and observed that the attenuation still occur in the Tank B. The different is only

the time delay and time between two peaks. Therefore, we can say that the bigger the tank, the

longer the time between two peaks and the time delay between the output and input. As the

frequency increases the phase angle decreases.

6.4 3 Frequency Response Data of Tank A and Tank B in Series

As for the experiment 3, we will conduct the same procedure, which is the frequency input from 0.01Hz

until 0.1Hz. However, in this experiment we will combine the 2 tank in series. For the Channel 1 (input)

the highest peak is 0.75 and the lowest is 0.25. For the Channel 2 (output) the highest peak is 1.2 and the

lowest is 0.70. The Amplitude Ratio from this experiment is still show the same result that is attenuation.

1

However, start from input frequency of 0.04; we can see that the output frequency is starting to become

constant. For the time also, if we combine both of the tank, it will make the time longer. As for the

frequency increases the phase angle decreases. There is a point of inflexion in the -curve.

1

7.0 CONCLUSION

By conducting the experiment, we managed to fulfil all of the objective stated earlier. For tank A,

the highest peak that we get is 0.57 and the lowest one is 0.22 for Channel 1 and the highest peak is 5.33

and the lowest one is 0.57 for Channel 2. After doing some calculations, it shows that AR, time delay and

time between 2 peaks is decreasing due to the increasing in the input frequency. For tank B which was

bigger than Tank A, the highest peak is 0.59 and the lowest is 0.24 for Channel 1 and for Channel 2, the

highest peak is 4.85 and the lowest one is 3.66. We observed that the attenuation still occur in the Tank

B. The different is only the time delay and time between two peaks. Therefore, we can say that the

bigger the tank, the longer the time between two peaks and the time delay. For tank C (two tank

connected in series), for the Channel 1, the highest peak is 0.75 and the lowest is 0.25. For the Channel

2, the highest peak is 1.2 and the lowest is 0.70. The Amplitude Ratio from this experiment is still show

the same result that is attenuation. However, start from input frequency of 0.04; we can see that the

output frequency is starting to become constant and the time also become longer. For all three type of

tank, we can conclude that as the frequency increases the phase angle decreases.

1

8.0 REFERENCES

Seborg, D., & Edgar, T. (2011). Process Dynamics and Control (Third ed.). New York: Wiley.

Lab manual, Frequency response of couple tank, 2015.

2

9.0 APPENDICES

Raw data

Min V2

Table 4: Frequency response data for Experiment A (Tank A)

F (Hz)Amplitude V1 Amplitude V2

Max V1 Min V1 Max V2 Min V2

0.01 0.59 0.25 4.85 3.66

0.02 0.59 0.24 4.69 3.94

0.03 0.59 0.24 4.37 3.91

0.04 0.59 0.25 4.31 3.96

0.05 0.59 0.24 4.21 3.94

0.06 0.58 0.25 4.21 3.98

0.07 0.58 0.25 4.29 4.07

0.08 0.57 0.24 4.19 4.01

0.09 0.57 0.24 4.19 4.04

0.10 0.57 0.26 4.16 4.02

Table 5: Frequency response data for Experiment B (Tank B)

F (Hz) Amplitude V1 Amplitude V2

Max V1 Min V1 Max V2

0.01 0.55 0.22 5.33 3.44

0.02 0.57 0.24 5.16 3.46

0.03 0.57 0.24 5.01 3.64

0.04 0.57 0.24 4.91 3.73

0.05 0.56 0.24 4.79 3.79

0.06 0.57 0.24 4.76 3.85

0.07 0.57 0.24 4.73 3.89

0.08 0.57 0.24 4.66 3.94

0.09 0.56 0.24 4.56 3.96

0.10 0.56 0.25 4.56 4.00

2

F (Hz)Amplitude V1 Amplitude V2

Max V1 Min V1 Max V2 Min V2

0.01 0.59 0.25 4.85 3.66

0.02 0.59 0.24 4.69 3.94

0.03 0.59 0.24 4.37 3.91

0.04 0.59 0.25 4.31 3.96

0.05 0.59 0.24 4.21 3.94

0.06 0.58 0.25 4.21 3.98

0.07 0.58 0.25 4.29 4.07

0.08 0.57 0.24 4.19 4.01

0.09 0.57 0.24 4.19 4.04

0.10 0.57 0.26 4.16 4.02

Table 6: Frequency response data for Experiment C (Tank A and Tank B in series)