Labsheet Liquid Level and Flow System b

UNIVERSITI TUN HUSSEIN ONN MALAYSIA Faculty of Mechanical and Manufacturing Engineering

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DEPARTMENT OF ENGINEERING MECHANICS

CONTROL LABORATORY

LAPORAN MAKMAL/LABORATORY REPORT

Kod M/Pelajaran/ Subject Code

ENGINEERING LABORATORY VI BDA 37101

Kod & Tajuk Ujikaji/ Code & Title of Experiment

Kod Kursus/ Course Code

Seksyen /Section

Kumpulan/Group No. K.P / I.C No. Nama Pelajar/Name of Student

No. Matrik

Lecturer/Instructor/Tutors Name

1. 2.

Nama Ahli Kumpulan/ Group Members

No. Matrik Penilaian / Assesment

1. Teori / Theory 10 %

2. Keputusan / Results 15 %

3. Pemerhatian /Observation 20 %

4. Pengiraan / Calculation 10 %

5. Perbincangan / Discussions 25 %

Tarikh Ujikaji / Date of Experiment

Kesimpulan / Conclusion 15 %

Tarikh Hantar / Date of Submission

Rujukan / References 5 %

JUMLAH / TOTAL 100%

COP DITERIMA/APPROVED STAMP

ULASAN PEMERIKSA/COMMENTS


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BDA37101-Edition III/2011

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COURSE INFORMATION

COURSE TITLE: ENGINEERING LABORATORY VI (BDA 37101) TOPIC 5: PROPORTIONAL CONTROL (LIQUID LEVEL AND FLOW SYSTEM) 1. OBJECTIVES In this activity you will accomplish the following:

i. Describe the action of the proportional control algorithm ii. Define offset iii. Describe the system using Laplace transformations iv. Run the system with the proportional controller

2. SKILLS In this activity you will develop the following skills:

i. Technology: apply technology. ii. System: understand systems. iii. Resources: manage time, manage materials/facilities. iv. Interpersonal: work as a member of a team. v. Information: use computers to process information. vi. Personal: responsibility, self-esteem, self-management.

3. MATERIALS In this activity you will need the following materials:

i. Process Line panel for Level Control ii. PC computer with Process Motion software.

4. THEORY 4.1 PROPORTIONAL CONTROL ALGORITHM The proportional control algorithm output m is defined as: m = Kc*e + mo Eq. 1-1 Where:

m proportional control algorithm output, which is expressed in terms of percent input to the pump.

Kc proportional control algorithm constant (gain) e error mo controller bias. This is a fixed value that will provide a constant

value to the control algorithm.


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When the error is 0, m will be equal to mo. When the error is positive, m will be greater than mo, and when the error is negative m will be less than mo. Using the automobile cruise control example, when the cruise control is set to 55 miles per hour and the car is travelling at 55 miles per hour, the error is zero. However, the controller needs to send a constant amount of gas to the engine to keep the car going 55 mph. This constant amount of gas is the m for the cruise controller. Suppose that the car starts climbing a hill. Its speed will decrease and an error will develop. The cruise controller will add an amount of gas equal to Kc*e to the constant amount mo. As the car speeds up and approaches 55 mph, the error will decrease, and the controller will decrease the amount of gas sent to the engine back to the mo value. This example illustrates an important principle of the proportional controller. When a load is presented to a system, or when the reference value changes, an error is created. The proportional control algorithm output m changes proportionally to the error e. The ratio between the changes in the control algorithm output m and the error e is determined by the controller gain Kc, as expressed in Kc = m e The block diagram that describes the level control system with a proportional control algorithm is as shown in Fig1-1:

Figure 1-1: Level control system block diagram. With the proportional control algorithm is used the output m is proportional to the error (e) thus for a small error the signal will be relatively small and for a larger error it will be bigger. 4.2 LAPLACE TRANSFORMATIONS To examine the effect of changes in Kc over the system, you will use Laplace transforms. The Laplace transform is a technique for translating certain complicated differential equations into simple algebraic equations. By substituting

- +

Controller Algorithm Tank

error

Level Sensor

Actual Level q in

Final Control Element (pump)

m Reference level


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a complex number S for t, we translate the equation from the real time plane into an imaginary plane called the Laplace space. After the Laplace transform, time t is removed from the system and is replaced with S. The system is now said to be in the Laplace space, also known as the Laplace plane or Laplace domain. 4.3 LEVEL CONTROL AND ITS LAPLACE TRANSFORM The following is a block diagram in Fig 1-2 describes the level control system and specifically for this case it is a first order system in the Laplace domain.

Figure 1-2 : Control system in Laplace space - block diagram 4.4 DERIVING THE SYSTEM GAIN The four blocks of the system shown in fig 1-2 and their functions are:

1. Controller block.The function in the controller block in time domain is m = Kc *e mo. The controller multiplies the error e by the controller gain Kc and then adds the constant mo to determine the proportional algorithm output m. In the Laplace domain the controller function is m = Kc.

e 2. The Final Control Element (controlled pump gain).The controlled pump

gain is Kp. The dynamic properties of the pump will be ignored. In the Laplace domain the controller function is qin = K p .

m 3. The tank is a first order system whose gain is K and whose time constant

is . The gain K and time constant need to be determined first. The

Laplace transform of the tank is qin

kh tan = 1S

K

4. The level sensor gain is Km. The level sensor gain in this system can be regarded as 1 and it will not affect the overall gain in the tank. However, the sensors inability to measure itself leads to a very significant difference between the actual system output and the reference output. This difference

Controller Algorithm Tank

error

Level Sensor

q in

Final Control Element (pump)

m Ref s Kp

Km

ms=F(e)s

+

-


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is called the offset error. The relation between the level in the tank and the reference value is ;-

You should note here, that the reference value is always going to be slightly larger than the tank pressure. This will cause a condition called an offset error. In actuality, this means that a proportional controller can never really direct the system all the way up to the true reference value, and the system output will always be slightly lower than the reference. You will observe the offset when you run the system.

Simplifying equation 1-2 using algebra yields equation 1-3:

Where;-

4.5 CONCLUSIONS From the analysis of the proportional control system, it can be concluded as follows;-

1. When a proportional control algorithm is used to control a first order system the entire system acts also like a first order system (as demonstrated in equation 1-3).

2. The entire system gain is

3. The system gain is always smaller than 1. Thus, for a step input, the system will always display an offset error where the actual output is slightly less than the reference value.

4. Increasing Kc (the controller gain) increases the system gain and decrease

the offset error.


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5. The system time constant is . The value of the systems time constant system is smaller then the tank time constant.

6. Increasing the controller gain, Kc decreases the systems time constant and the system response time.

4.6 ADDITIONAL THEORY


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5. TASK In this activity you will:

1. Run the system using the proportional control algorithm. 2. Introducing a step input in the reference value and monitor the resulting

system response (time constant and error). 3. Vary the controller gain to test the resultant system response (in both

dynamic and static systems). 5.1 TASK 1 ; INVENTORY AND SAFETY CHECKS1

1. Check whether all materials required for this activity are available at your lab station.

2. Check whether your lab station conforms to the Safety Guidelines. 3. Complete the Inventory and Safety Check List on the Worksheet for this

activity. 5.2 TASK 2 ; SETTING UP

1. Turn on the computer. 2. Run the ProcessMotion Software. 3. Activate the PressureLine panel, making sure that the panel is connected to

a COM port on your computer and that the Communications key is turned to PC.

4. Drain the tank so that it is at its minimum level. Then close valve A and keep valve B open. Valve C should remain closed throughout.

5. Click On-Line (at modes). 6. Click the Level Control / Proses button. 7. Select the PID Controller from the dialog box and enter the following

parameters: Setpoint : 110 Kc : 5 Ti : 100000

Td : 0 Mo : 0

In setting these parameters, you have created a system where the Ti, Td, and Mo parameters will not contribute to the final m. m will be equal to Kc * e. This is a strict proportional control algorithm with no bias.

8. Click Run. 9. Run the system until it reaches steady state.

Question: Is there an offset? 10. Record the system output H in column 1 of the chart on your worksheet.

This column is marked Initial reference value. Record this value in every row of this column.

11. Record the controller output m in column 5 of the chart on your worksheet.


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5.3 TASK 3 ; USING PROPORTIONAL CONTROL

1. Click the Level Control button and change the Kc setting to 10. 2. Now perform a step input. Increase the set point, by changing it to the

Initial reference value + 30% (e.g. if your initial reference was 100mm, change the set point to 130mm.)Record the new set point value in column 2 of your chart. Click Run.

3. Wait till the system reaches steady state. Record the error in column 4 of the graph on your worksheet. Record the controller output m in column 5 of your graph.

4. Record the total response time (Time at reaching steady state minus Time of step input) in column 6.

5. Record the percentage of the offset error (Error/Reference) in column7.

Question: Describe the system output response

6. Reset the setpoint back to the initial reference value and allow the system to return to the reference value. Repeat the experiment, for step inputs of +40%, +50%, -20%, -30%and 40%, respectively. Record your results in the chart.

Question: When is the offset percentage highest? Lowest?

Question: What is the cause of offset? 5.4 TASK 4 ; VARY THE Kc VALUE Change the Kc value will change the system response. You will now present the system with a step input, and vary the Kc setting to see how the proportional control affects the system response. You will also add system loads to see how the system responds.

1. Reset the Setpoint to the initial reference value in Task 1-3. Click Run and allow the system to come to steady state. You will now raise the Kc value and test the system with step inputs and various loads.

2. Change the Kc to a value of 100. Perform a step input by increasing the setpoint by 30%.

3. Now present the system with a load, by opening valve A and closing valve B. Valve A drains more quickly than valve B, thus putting an added load on the system and Click Run.

Q: Describe the general system response, the response time, and the percentage of offset.

4. Now open both valve A and valve B.

Q: How does the system respond?


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5. Change the Kc to a value of 1. Perform a step input by increasing the

setpoint by 30%. Click Run

Q: Describe the general system response, the response time, and the percentage of offset.

6. Change the Kc to a value of 10. Perform a step input by increasing the

setpoint by 30%. Click Run.

Q: Describe the general system response, the response time, and the percentage offset.

Q: How does the Kc affect the system response time? The offset? (Kc

100,Kc1 and Kc 10) 6. OBSERVATIONS


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7. CALCULATIONS


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8. GRAPH ANALYSIS .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................


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9. QUESTIONS

TASK 2 (REFERE TO TASK 2 PROCEDURES): Question: Is there an offset? .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... TASK 3 (REFER TO TASK 3 PROCEDURES): Question: Describe the system output response .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................


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Question: When is the offset percentage highest? Lowest? .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... Question: What is the cause of offset? .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................


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TASK 4 (REFER TO TASK 4 PROCEDURES): Q: Describe the general system response, the response time, and the percentage of offset. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... Q: How does the system respond? .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................


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Q: Describe the general system response, the response time, and the percentage of offset. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... Q: Describe the general system response, the response time, and the percentage of offset. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................


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Q: How does the Kc affect the system response time? The offset? (Kc 100,Kc1 and Kc 10) .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... 10. CONCLUSION Deduce conclusions from the experiment. Please comment on your experimental work in terms of achievement, problems faced throughout the experiment and suggest recommendation for improvements. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................


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11. REFERENCES .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... ....................................................................................................................................


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RESULTS WORKSHEET

Column 1

Column 2

Column 3

Column 4

Column 5

Column 6

Column 7

Initial reference

value (e=0)

Reference value

(after step input)

Percentage of step

Error Controller output

Total response

time

Error/ reference

value

Same 0%

30%

40%

50%

-20%

-30%

-40%


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Labsheet Liquid Level and Flow System b

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