Performance Comparison of Level Control with the Three, Five & Nine Fuzzy Rules based method

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Performance Comparison of Level Control with the

Three, Five & Nine Fuzzy Rules based method

*Ashok Kumar ^ Rajbir # Kuldeepak

Lecturer in ECE Deptt. Lecturer in ECE Deptt. Lecturer in ECE Deptt.

Amity University Haryana, Gurgaon Amity University Haryana Kurukshetra University, Kurukshetra

ABSTRACT:

In the previous paper we have discussed about the water level control in the ‘Three Non- Interacting Tank System’ with help of the Intelligent Fuzzy Controller over the classical method, in which we noticed that the performance of Classical method was very poor, system was slow i.e. response was slow and less accurate than that of Fuzzy Control system[1]. This paper discusses about comparing the performance of Intelligent Fuzzy Control system based on Three, Five and Nine Fuzzy rules. In that either comparing response of a single or interacting tank system with three rule based method, which gives better response, more accuracy than classical method. On the other hand, five rule based method is more complex and more accurate but system becomes slow than three rule based, because as increase in rule base makes system bulky more and more, but accuracy increase. Thus, nine rule based method makes system too bulky due to which system becomes very slow as compared to five and three rule based method but this system is more accurate than others.

This paper provides information about complexity of system, performance and accuracy with different rule bases. The system’s overall performance will be optimum but it requires more practice, skill or experience. So, out of Three, Five and Nine rule method, the five rule system shows optimum behaviour.

Keywords: Interacting Pair tank, MATLAB/ Simulink diagram, Conventional Controller.

1. INTRODUCTION: The control of liquid

level in tanks and flow between tanks is a fundamental and most important problem in the process industries. Liquid level control is a typical representation of process control which is widely used in iron and steel, petroleum based industries and others.

Many times the liquids are processed by chemicals or mixing treatment in the tanks, but the level of fluid in the tanks must be controlled, and the flow between tanks must be regulated. Often the tanks are so coupled together that the levels interact which must needed to be controlled[2].

Level and flow control in tanks are at the heart of all chemical engineering systems and

consequently, these systems are contributing a significant part to Indian economy.

The water closet toilet in house is also a liquid level control system. In this, a swinging arm attached to the input valve of the water closet, water tank allows water to flow into the tank until the float rises to a point that closes the valve. This is a simple and effective level control system for water tanks. It was a thing of great wonder in its early stages. Visitors will admire the automatic refilling of the water closet tank much more than the beauty of the house and our beautiful countryside. Thus, we can say that there is a great need of tank level control systems in every field.

There are many alternative controller design theories that can be used to control the level of liquid in tanks. Proportional integral derivative control is one of such kind of control strategies which is used to control the level and flow of liquid. Proportional control, PI control, PD control and PID control will be investigated to determine which controller is the best for liquid level control[3].

Even though the PID controller is widely used in industrial process, the tuning of PID parameter is a crucial issue in particular for the system’s characteristic which has large time delay and high order system. Commonly in industrial process, only experts or experience workers are able to monitor and tune the PID parameters based on their experience in that field.

There are significant chances for deficiency of experience in certain cases. So in that case, it is not possible to achieve a satisfactory performance. Hence, it is desirable to introduce other types of controller such as artificial conventional fuzzy logic controller.

Firstly, we would focus on comparing performance behaviour of Conventional Controller with three rule based method and select better one. Similarly, comparing behaviour of three rule based fuzzy controller with five and nine rule based fuzzy method; and chose the controller which shows optimum performance or behaviour.

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Simulink model of Interacting tank system; third section describe a little bit and briefly about fuzzy control system with their base rules in various case; fourth section describe observations and results; and the last section talks about conclusion and future scope.

2. INTERACTING TANK SYSTEM:

a)

Mathematical Modelling:

Similar to the single tank system, it is a split coupled tank i.e. nonlinear system, the equations of flows in the coupled tank can be determined where the system states, here and are the liquid levels in corresponding tanks[4].

Fig.1: Interacting Tank System

Fig.1 shows that height of liquid in tank1 is H1

which is greater than the height of liquid in tank2 i.e. H2. In that case we have to control the level

of liquid of tank2 w.r.t. tank1. This can be completed by the mass balance equations of both system.

Thus, mass balance for the first and second tank is respectively:

For Tank 1

For Tank 2

The flow out of the second tank is determined by the liquid head in that tank, i.e.

However, due to the coupling between the two tanks, the flow out of the first tank is determined by the difference in levels of the two tanks, i.e. H1 ˃ H2.

Thus the final set of ODE that describe given system behaviour is given by:

After rearranging the equations, these can be written as:

b) Simulink Model:

This model is designed by the use of non-linear differential equations which describe behaviour of given model mentioned in equation (5) & (6). Here, previous system input given to tank1, output of tank1 becomes the input of tank2 and output of tank2 respectively which is required to control with respect to inputs.

Fig.2: Simulink Model of Interacting System

Fig.2 represents the Simulink model of interacting tank system, designed by given non- linear differential equations[5,6].

3. FUZZY CONTROL SYSTEM:

This system works on the fuzzy rules and implemented system called ‘Fuzzy Logic Controller’ is used to obtain desired response. Fuzzy rules are the various combination of defined membership function of level with position of control valve[7]. These rules are described under different cases below:

Case I: Three rule based Fuzzy Logic Controller:

The Membership Functions are:

a) For Liquid level [cm]:

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b) For Valve control signal [%/s]:

Fig.4: Membership Functions for Valve Control Signal

Fuzzy Rules are:

Rule 1: IF level is okay, THEN valve is no change.

Rule 2: IF level is low, THEN valve is open fast.

Rule 3: IF level is high, THEN valve is close fast.

Since there is only one input [level] & one output [valve] for SISO system, so two membership have been defined in terms of low, high & okay for LEVEL and open fast, close fast & no change for valve control signal correspondingly.

Case II: Five rule based Fuzzy Logic Control:

Similar to implementation in the previous case, we can easily implement it with the help of five rules for tank system.

The Membership Functions are:

a) For Liquid level [cm]:

Fig.5: Membership Functions for Liquid level

b) For Valve control signal [%/s]:

Fig.6: Valve Control Signal

c) For rate of liquid [cm/s]:

Fig.7: Rate of Liquid

Rules are:

Rule 1: IF level is okay, THEN valve is no change.

Rule 2: IF level is low, THEN valve is open fast.

Rule 3: IF level is high,THEN valve is close fast.

Rule 4: IF level is okay AND rate is negative, THEN valve is open slow.

Rule 5: IF level is okay AND rate is positive, THEN valve is close slow.

Hence, in this case there is an implementation of 3 membership functions (Level, Rate & Valve) in the single tank system to smoothen the system’s response.

Case III: Nine rule based Fuzzy Logic Control:

To obtain maximum optimum value or desired value, we have to make more rules by implementing on five rule based method using same membership functions.

Rules are:

Rule 1: If Level is okay and rate is falling then valve is open slowly.

Rule 2: If Level is okay and rate is rising then valve is close slowly.

Rule 3: If Level is okay and rate is steady then valve is no change.

Rule 4: If Level is high and rate is falling then valve is close slowly.

Rule 5: If Level is high and rate is rising then valve is close fast.

Rule 6: If Level is high and rate is steady then valve is close fast.

Rule 7: If Level is low and rate is falling then valve is open fast.

Rule 8: If Level is low and rate is rising then valve is open slowly.

Rule 9: If Level is low and rate is steady then valve is open fast.

The membership function defines how fast system can response to maintain its certainty or to maintain its original position. By using these function we have defined the fuzzy rules i.e. three, five and nine rules mentioned respectively. Three rule based method is general method to control liquid level. Thus, it is called simplest method among the others. As go on, rules are increased up to five and nine. That makes system bulky because more and more rules makes system more and more complex. That affect the performance of system i.e. response time, setting time etc. but accuracy increased[8,9].

However, the rule base is directly proportional to accuracy and inversely proportional to the response of system. To remove this contradictory between the various cases by chosen of the efficient method, that is five rule based method which satisfies all condition and provide desired performance.[10,11]

4. PERFORMANCE:

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Fig.8: Responses Comparison between Liquid Levels in Coupled Tank System

Fig.8 shows the comparison between the liquid level of tank1 and tank2 of Interacting Tank System without controller.

Fig.9: Comparison Between for Tank1 Input & Tank2 Output

Fig.9 shows the comparison of the liquid input of tank1 and output of tank2 of coupled tank system without controller.

b) With controller:

From the base rules, we have designed fuzzy control system for three, five and nine rules in the simulink model using MATLAB software shown below in the given figure:

Fig.10: Rule Based Simulink Control System

a) Three rule based Simulink response

Fig.11: Response for Level Control

Fig.12: Response for Valve Position

Fig.11 and 12 show the level control and their corresponding change in the valve position of coupled tank system using three rule fuzzy method respectively. It takes 12ns to control the liquid level of tank as shown in fig.11 and corresponding very sharp change in valve position as in fig.12. That means system is very fast.

b) Five rule based Simulink response

Fig.13: Response for Level Control

Fig.14: Response for Valve Position

Fig.13 and 14 shows responses of liquid level control and their corresponding change in the valve position of coupled tank system using five rule fuzzy method respectively. It takes 15ns to control the liquid level of tank as shown in fig.13 and corresponding valve shows curve type behaviour as in fig.14. That means system take more time to settle down. Thus, system is slower and have slightly more accuracy than the above system.

c) Nine rule based Simulink response

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Fig.15 shows the responses of liquid level control and their corresponding changing in the valve position of tank system using nine rule fuzzy method respectively. Due to more rules system complexity increase so, it behaves like oscillatory system as shown in last section of given figure and corresponding valve also behaves oscillatory. Thus, complexity make system slow and it takes more time to settle down i.e. 31ns, which is greatest time taken by this system and response is much smoother with high degree of accuracy than others.

Based on above observed results and responses, the five rule base method is more complex and slow than three rule base method but it gives smoother response with high accuracy than the three rule base method. Similarly, nine rule base method system becomes more complex than three and five rule method, which makes system bulky, consequently slowest but its response is much better than others. Since, the three rule base method is much faster than the five rule base method which is then, much faster than nine rule method. In other words, response time of five rule base method is lies between time taken by three rule base method to respond and time taken by nine rule base method to respond. Thus, we need to choose a system which will satisfy all condition or optimum conditions and provide desired output. However, response time five From all above discussion, we conclude that five rule based method which satisfies all the optimum condition is better than the others. Thus, it provides the optimum or desired output.

5. CONCLUSION:

Concluding all the discussions and responses, PID Controller has been successfully designed to control the liquid level on coupled tank system using simulation and implementation. The comparison has been made; simulation techniques perform better result as compared to the implementation.

Usually, industries try to focus more on how to improve the performance of PID controllers as they are more reliable and may not consider intelligent controllers. For the neural network, if the accuracy is increased to reach at least 85%, it can be used in the field instead of the PID controllers, making it reliable.

In that phase, we applied the Intelligent Controller Methodology (FUZZY LOGIC

CONTROLLER) which includes human

knowledge in the form of his/her experience. In the fuzzy logic controller, we design rule base for tank system. In the first tuning of rules, we simply design the three rules and obtain results. Similarly, we also implement the five and nine rule based for tank system and observe results and responses.

We conclude that five rule based method which satisfies all the optimum condition and better than the others. Thus, it provides the optimum or desired output.

Therefore, this implies that a better fuzzy control behaviour and performance can be obtained by the combination of:

 Redefining existing membership function.  Redefining existing rule.

 Adding new membership function and new rules.

We can use more Advanced Controller stratégies to obtain smoother level response in industrial applications.

FUTURE SCOPE: Industrial applications of liquid level control are abound, e.g., in food processing, beverage, dairy, filtration, effluent treatment, and nuclear power generation plants, pharmaceutical industries, water purification systems, industrial chemical processing and spray coating, boilers, and automatic liquid dispensing and replenishment devices.

The level in twin tank control can be controlled by the variation techniques like as:

 Fuzzy based Sliding Mode Controller  Sliding Mode controller

 PID + SMC

 Genetic Algorithm based controller Algorithm and many more.

REFERENCES

[1] “Level Control of a Three Tank Non-interacting System using Intelligent Controller”,

Dr. Munish Vashishath: Associate Professor of Electronics Engg. In YMCAUST Faridabad, Ashok Kumar: M.Tech student in YMCAUST Faridabad & Kapil Dhama: Lecturer of ECE in SCET Palwal; WNTES-2012.

[2] “Coupled Tank Systems”, Elke Laubwald,

www.control-systems principles.co.uk.

[3] “Performance Comparison between PID and Fuzzy Logic Controller in Level Control System of Twin Tank System”, Mohd Fua’ad Rahmat &

Maraim MD Ghazaly, Journal Teknology, 45(D) Dis. 2006: 1-17.

[4] “Robust MIMO Water Level Control in Interconnected Twin Tanks Using Second Order

Sliding Mode Control”, M. Khan and S.K.

Spurgeon, Control Engineering Practice VOL.14, Issue 4, April 2006, pp.375 – 386.

[5] “Design & Simulation of Controller for Coupled Tanks System,” M. Mc Dermott & T.

Brock, Control Engineering Practice VOL. 43, Issue 4, April 2009, pp.35-43.

[6] “Design and application of Rough controller

in three tank system”, Pan Aixian and Gao Yun,

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[7] “Analysis and Synthesis of fuzzy control

system: A model based approach”. Feng G. CRC

Press, p. 272, 2010.

[8] “Introduction to Neural and Fuzzy

Networks”, Dr. Erwin Sitompul, President

University, lecture – 10, 11, 12, 2008.

[9] “Fuzzy Controller- choosing an appropriate and smallest rule set”, Seema Chopra, R. Mitra

and Vijay Kumar, international journal on computational cognition, dec2005.

[10] “Analysis and Synthesis of Fuzzy Control System: A model based approach”, Feng G.,

CRC Press, p. 272, 2010.

[11] “Design of Fuzzy Logic Controllers for Robust Process Control”, Yordanova S., King,