Water Tank Level Control System using Self-Adaptive Fuzzy-PID Control

International Journal of Engineering Research & Technology (IJERT)

ISSN : 2278-0181

Presentation by : Noviyanti Sagala

Introduction

Metodology

Fuzzy Logic Controller

ResultConclusion

1

Basic problem in the industries is water level controlling systemControl system consists of many constraints like non linearity, inertial lag,

time delay, time varying parameters which are very difficult to develop the mathematical model of such systems.

Fuzzy Logic Controller is applicable to non-linear system and doesn’t depend on the precise mathematical model.

Fuzzy Logic can be understood as computation using linguistic variables instead of numbers, whereas fuzzy control uses IF-THEN statements instead of equations.

PID controller requires the exact model of the system while Fuzzy control is an intelligent control method and this feature makes it self-adaptive.

Automatic water tank level control system

2

Water level measurement and precise water level control is an important process in improving the manufacturing quality of products.

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e u S

Mathematical Model

Assume R=2 Valve Lag (Measurement Lag (

• Transfer function of measuring lag • Transfer function for control valve lag The complete transfer function of the given system by using Ziegler-Nicholas method tuning of PID controller

By substituting Calculation for balancing criterion: -) +

Real part : Imaginary part:

The ultimate period = 28.54Calculation of PID controller using Z-N method

= 0.6 = 7.62 = = 14.27 = = 3.55

X-axis: Time (sec)Y-axis: Level (mm)

PID Controller Response

Adaptive Fuzzy Logic Controller

Fuzzifier

Database

Fuzzy Rule Base

Inference engine defuzzifierinput output

3

Block Diagram of Fuzzy PID

The main system is PID controller while the function of fuzzy logic is to repair the response and recovery time of disturbance.

1. Input and Outputa. Deviation the difference between the desired height of water and the actual height of water

Positive error the actual height of water below the reference height of waterNegative error the actual height of water above the reference height of water

b. Deviation change the difference between delayed-error value and new error value

Positive Delta error error tends to going downNegative delta error error tends to going up

c. Valve Position

2. Fuzzification• The process of transforming crisp values into grades of membership corresponding to fuzzy

sets using linguistic terms• Membership functions which used are Gaussian and triangular membership as the limit

value range.

Membership Function of input variables1.Deviation

2. Rate of deviation change

Fuzzy Variable Crisp input rangeHigh (0.3, 1)Zero (0.3, 0)Low (-0.3, -1)

Fuzzy Variable Crisp input rangePositive (0.03, 0.1)Zero (0.03, 0)Negative (-0.03, -0.1)

Membership function of Output variable

3. Valve Position

Fuzzy Variable Crisp Output Range

Close fast (CF) (-1.0, -0.9, -0.8)Close Slow (CS) (-0.6, -0.5, -0.4)No change (NC) (-0.1, 0, 0.1)Open Slow (OS) (0.2, 0.3, 0.4)Open Fast (OF) (0.8, 0.9, 1.0)

3. Fuzzy Rule Base

DatabaseThe database is a component for defining the fuzzy set of input and output • Fuzzy Rule BaseFuzzy rule base is a collection of statements of rules ' IF- THEN ' which is based on expert knowledge . The method used in determining the fuzzy rule base is using MIN.This method has the form of rules such as the following equation : IF x is A and y is B then z = C • Rules Component The goal is to get the output.Fuzzy set is obtained by taking the maximum value of rule, then use it to modify fuzzy area and implement it to the output.

Rule Editor

4. Fuzzy Inference Engine

a. FIS also called fuzzy inference engine is a system that can perform reasoning with similar principles as humans do reasoning with the expert instincts .

b. FIS used is mamdani which works based on linguistic rules and has a fuzzy algorithm which provides a aproximator to input mathematical analysis .

Defuzification

• can be defined as the process of changing the amount of fuzzy presented in the form of associations with the output fuzzy membership function to regain the form he asserted ( crisp )

• The result of defuzification which is used to adjust the value of Kp, Ki, and Kd

For example:We assume that Error = 0.3, 𝛥error=0.061. Determining the membership degree of error From the membership function, we get that 0.3 is belonging to low and zero, so:i. Fuzzy Lowii. Fuzzy Zero2. Determining the membership degree of error From the membership function, we get that 0.06 is belonging to low and zero, so:i. Fuzzy Zeroii. Fuzzy Positive3. Determining the membership of output

Min (, ) 4. Determining the fuzzy variable of the output

0.2 is belonging to Open Slow (OS)

So, the result will be : IF error is Low and 𝛥error is Zero then Valve position is Open Slow

Min (, )

Min (, )

Simulation Diagram & Result

• Fuzzy inference is the process of formulating map from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can be made, or patterns discerned.

• Mamdani-type inference, expects the output membership functions to be fuzzy sets. After the aggregation process, there is a fuzzy set for each output variable that needs defuzzificationIn the controller, the proportional factor Kp=7.71, the integral factor Ki=0.074, the differential factor Kd=3.55, the proportion factor of fuzzy output Ku= 0.833, simulation time is 500sec.

4

Conclusion• The control method adapted in this paper infers that the self-adaptive

fuzzy-PID controller has small settling time, minimum peak overshoot and has high disturbance rejection capability compared to conventional PID controller.

• The future scope is that the adapted strategy can be applied for higher order systems with more number of physical constraints and increased rules.

5X-axis: Time (sec)Y-axis: Level (mm)