Self Tuning Fuzzy Logic Controller with Smith Structure for Controlling Glycerin Bleaching

TemperatureZakariah Yusuf#1, Zuriati Janin#2 and Mohd Nasir Taib#3

#Faculty of Electrical Engineering,

Universiti Teknologi MARA, Malaysia.zakariahyusuf@yahoo.com

Abstract─Controlling process with lag is not an easy task. The lag can easily cause oscillation that lead to instability of the controller response. The conventional method of controlling thiskind of system is not capable of giving satisfactory result. Many delay compensator and predictor methods are introduced to handle system with lag and one of the popular methods is a Smith Predictor. The problem with model base control structure is the mismatch or inaccurate model used as a predictor. This work introduced a Self Tuning Fuzzy Logic controller as analternative method to solve a process with mismatch delays problem. With advantages of Smith Predictor and Self TuningFuzzy Logic Controller the purpose control structure is found giving better performance compare with conventional Fuzzy Logic controller with Smith Predictor Structure.

Keywords─ Smith Predictor, Self Tuning Fuzzy Logic Controller, Glycerin Bleaching process.

I. INTRODUCTION

Bleaching process is a process of removing the pigment color of a crude raw material[1, 2]. Controlling the glycerinbleaching temperature is very important in the bleaching process because this is the slower part in the glycerin bleaching process and it is found in [3] that the quality of the bleaching product can be increase with proper temperature control.

To obtain a good quality glycerin, a good controller for thetemperature is much needed. Many of bleaching process plant is developed in a batch process system, the increment of the batch cycle means increasing the production yield. It is found in the Glycerin Bleaching Pilot Plant installed at DCS Lab UiTM Shah Alam test the slowest part in the bleaching process is to maintain the temperature at the desired set point.

Most of the controllers in the industry still use the conventional PID controller in their application. For application with large time delay the conventional controller cannot give satisfactory result [4]. The Smith predictor structure [5] is very popular in controlling process with time delay, the implementation of this structure can be found in many literature and industry. Some of the successfulapplication of the Smith Predictor in the control structure is inliterature such as in [6-8] .

However it is found in that application of conventional controller with Smith Predictor can give oscillatory response when the delay of the model inaccurate or mismatch with the actual process [9, 10]. These happen when the delay of the model is underestimated with the actual process. In a Glycerin bleaching process, this problem can occurs because of many factors, such as different thermal condition of the raw material between the modeling with actual process, the capacity of the raw material and the different typecomposition of the raw material.

This paper presents the implementation of Self Tuning Fuzzy PD (proportional plus derivative) with Smith Predictor structure to overcome the oscillatory step response of the a Glycerin Bleaching Temperature control with mismatch delay.

II. SMITH PREDICTOR CONTROL STRUCTURE

The Smith Predictor is one of the popular methods to controlling process with time delay. Figure 1 show the typical structure of Smith predictor.

Fig. 1 Smith Predictor Control Structure

The transfer function of this structure can be represented by Equation 1.

])()([)()()(1

)()(

)(

)(LmsLps

Lps

esGmesGpsGcsGmsGc

esGpsGc

sR

sY

(1)

Assume )()( sGmsGp and sLmsLp ,

The equation 1 can be simplified to:

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)()(1

)()(

)(

)(

sGmsGc

esGpsGc

sR

sY sLp

(2)

)(sGp is an actual process and Lpse is the delay of the actual

process. )( sGm is the process model and Lmse is the delay

of the process model. )( sGc is the controller transfer

function. The delay of the process that represented by sLpe will normally contributes to the instability of the system

[5].

III. FUZZY LOGIC CONTROLLER

Fuzzy Logic Controller has been implemented in many process control applications. Fuzzy Logic Controller consists of Fuzzification, Interface rule and Defuzzification. The ability of the controller to perform well compared with conventional controller make this controller chooses in many applications. Figure 2 show the Fuzzy Logic Control structure[11].

Fig. 2 General Structure of Fuzzy Logic Controller

A. Fuzzy PD Controller

Fuzzy PD controller is inspired by PD controller. This controller using two inputs which is error and the change of error. Figure 3 show the conventional Fuzzy PD controller that has been applied in many applications.

Fig. 3 Conventional Fuzzy PD Controller

This structure can be described using following equations:

dt

tdeKdteKpkU

)()()(

(3)

In discrete, Equation (3) can be written as:

))1()(()()( kekeKdkeKpkU (4)

Where,)()( kyyspke (5)

)1()()( kekeke (6)

Kp is the proportional gain of the controller while Kd is

derivative gain.

IV. SELF TUNING FUZZY LOGIC CONTROLLER WITH SMITH

PREDICTOR

In this work the self tuning Fuzzy Logic controller is designed to cope with the changes of dynamic properties of the process. This structure is equipped with self tuning capabilities by changing the controller gain which is output scaling factor (OSF) of the Fuzzy Logic Controller. Tuning of OSF also implemented in [12] to increase robustness of the controller. The OSF is update as the response change using fuzzy mechanism. Figure 4 show the purpose structure of Self Tuning Fuzzy Logic Controller with Smith Predictor.

Fig. 4 Structure of Self Tuning Fuzzy Logic Controller with Smith Predictor

For this work, 3 membership functions with 9 fuzzy rules are used. Table I shows the fuzzy rules for Fuzzy Logic Controller where NE is Negative, ZE is Zero and PO is Positive. Figures 5, 6 and 7 show the inputs and output membership functions of the Fuzzy Logic controller.

TABLE IRULES FOR FUZZY LOGIC CONTROLLER

ECE

NE ZE PO

NE NE ZE PO

ZE NE ZE PO

PO NE ZE PO

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Fig. 5 Input Error Controller Membership Function

Fig. 6 Input Change of Error Membership Function

Fig. 7 Output Membership Function

A. Designing OSF Tuning Rules

The development of tuning rules for the output scaling factor adjustment is simple, the controller must have lower OSF when the error is small and bigger OSF when the error is big. The tuning rules in this work are uses 3 membership functions with 9 rules. Table II shows the tuning rules that for output scaling factor of Fuzzy Logic controller, where SO is Small Output, MO is Medium Output and BO is Big Output.Figure 8 shows the OSF tuning with 3 membership function.

TABLE IITUNING RULES FOR OUTPUT SCALING FACTOR

ECE

NE ZE PO

NE SO MO BO

ZE SO MO BO

PO SO MO BO

.

Fig. 8 Output Scaling Factor Tuning Membership Function

B. Defuzzification

Center of gravity (COG) is one of popular and best defuzzification methods [13, 14]. In this development COG type of defuzzification is used at the output membership function. Equation (8) represents the COG method of

defuzzification, where Ui the center of output membership is function and )( y is the degree of fulfillment area.

l

i

l

i

y

yUiU

1

1

)(

)(

(8)

V. MODELLING

First order plus dead time (FOPDT) model is normally used in the industry to describe the process model. Equation (9)

represents the general form of FOPDT model, where is the dead time, T is the time constant and K is a process gain. The Glycerin temperature model is obtained from step test at the glycerin bleaching pilot plant at DCS Lab UiTM Shah Alam. The full procedures of obtaining FOPDT model are described in [15]. The FOPDT model that used in this experiment is shows in Equation (10). All the simulations works are done using Labview software and plotted using Matlab.

)1(

)(

Ts

KesG

s

(9)

)13818(

8.4 314

s

e s

(10)

VI. RESULTS

For a match and +25% of the delays, from actual process it found that both of the controllers can track the set point without any major problem. The step response both of the controllers at match and +25% cases are show in Figure 9 and 10 respectively.

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Fig. 9 Actual process delay match with process model

Fig. 10 +25% delay from process model

The problem rise at the +50% of the delays when the conventional Fuzzy Logic controller start to give oscillate response, but with the self tuning Fuzzy Logic controller itcan give smooth and accurate step response with same performance of rise time and overshoot. Figure 11 shows the step response performance of the Fuzzy Logic controller and self tuning Fuzzy Logic controller at +50% delays.

Fig. 11 +50% delay from process model

The oscillation of the Fuzzy Logic controller is become much obvious when the delay is increase at +75% from process model however self tuning Fuzzy Logic controller can better performance without loosing in a rise time. At +100% delays self tuning Fuzzy Logic controller still can track the set point while the conventional fuzzy logic controller has bigger oscillation till the end. Figure 12 and 13 show the step response performance at +75 and +100% delays from process model used by Smith Predictor.

Fig. 12 +75% delay from process model

Fig 13 +100% delay from process model

VII. CONCLUSION

This work demonstrates the implementation of Self Tuning Fuzzy Logic Controller to solve the “mismatch” time delay problem in Smith Predictor control structure. From the results it can be concluded that the purpose self tuning control structure can solve the oscillations or instability of the conventional Fuzzy Logic controller in controlling process with inaccurate time delay estimation for Smith Predictor. The purposed structure also still can give satisfactory response up to +100% delays different from the process model.

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ACKNOWLEDGEMENT

The authors would like to thanks Faculty of Electrical Engineering UiTM for support this work.

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[10] T. Zhang and Y.-C. Li, "A Fuzzy Control of Time-Varying Delay Systems Based on Time Delay Identification," in Proceeding of Second International Conference on Machine Learning and Cybernetics, Xi'an, 2003, pp. 614-619.

[11] K. M. Passino and S. Yurkovich, Fuzzy Control: Addison Wesley Longman, Inc., 1997.

[12] Z. Yanan and E. G. Collins, Jr., "Fuzzy PI control design for an industrial weigh belt feeder," Fuzzy Systems, IEEE Transactions on, vol. 11, pp. 311-319, 2003.

[13] D. Driankov, H. Hellendroorn, and M. Reinfrank, An Introuction to Fuzzy Control: Springer-Verlag, 1993.

[14] S. N. Sivanandam, S. Sumathi, and S. N. Deepa, Introduction to Fuzzy Logic using MATLAB: Springer-Verlag Berlin Heidelberg, 2007.

[15] C. A. Smith and A. B. Corripio, Principle and Practice of Automation Process Control, 2nd ed.: John Wiley & Sons, Inc., 1997.

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