PID-Fuzzy Controller for Grate Cooler in Cement Plant

Awang N.I. Wardana*

* Control Department

Indonesia Cement and Concrete Institute

Jalan Raya Ciangsana, Bogor, 16969, Indonesia.

Phone: +62-21-82403650 Fax: +62-21-82403654

e-mail: awang.wardana@telkom.net

Abstract

This paper studied about application of PID-Fuzzy

controller for grate cooler in cement plant. The

proportional, integral and derivative constant adjusted by

new rule of fuzzy to adapt with the extreme condition of

process. The new algorithm performs in every condition

and already tested in every extreme condition. The result of

this new algorithm is very good; changes of under grate

pressure #1 were reduced and temperature of output clinker

was reduced.

1 Introduction

The efficiency problem is well known in the cement

industry and a standard process control response has

evolved to solving the problem [2]. Cooling air is blown

into the chambers below the clinker grate. This is the means

by which the clinker is cooled and the thermal energy is

recovered from the clinker. The pressure under the grate of

the cooler is monitored and is taken to be directly

proportional to the thickness of the bed of clinker on the

grate.

When extreme condition come for example, the load of

clinker entering the cooler increases the bed thickens and

the pressure under the grate rises. The control response is to

increase the speed of the grate to transport the additional

clinker away from the kiln [4].

The reverse process takes place when the amount of clinker

entering the cooler lessens. The clinker bed thins out and

the pressure under the grate falls, with the control response

being to slow the grate down and retain the clinker on the

grate for longer in order to build up the bed depth. All these

control procedure are described in figure 1.

This apparently straight forward conventional process

control solution is often extremely unpopular with kiln

operators, and sometimes creates more problems than it

solves. The root of the problem is the conventional PID

controller cannot adapt to the dynamics of the process. So

we need some algorithm to adjust PID controller according

to the dynamics of the process. In grate cooler, the dynamic

of the process is nonlinear. So we need algorithm that can

adapt with nonlinear behavior. Fuzzy logic matches to

solve these problems because PID-Fuzzy controller has

some advantages:

Figure 1: Grate Cooler Conventional PID Control

Scheme

1) It has the same linear structure as the conventional PID

controller, but has adjusted coefficient, self-tuned control

gains: the proportional, integral, and derivative gains are

nonlinear functions of the input signals [7].

2) The controller is designed based on the classical discrete

PID controller [6] [7].

3) Membership functions are simple triangular with fuzzy

logic rules [6] [7].

4) Stability of these fuzzy PID controllers is guaranteed [3].

In next section we will explain about design of PID-Fuzzy

control that used in this process. After that we will explain

about the fuzzification, rule and defuzzification of fuzzy

algorithm. And the last section we will explain about

application of this controller in the real plant.

2 Controller Design

In this paper we used two type controllers to detect

performance of these controllers in the real plant. These

controllers are:

2.1 PID Controller

The theoretical PID-controller,

)(1

1)( sEsTsT

KsU d

i

p (1)

Conventional

PID-Control PLANTek uk

grate

speed

rk

setpoint

yk

under grate

pressure #1

where Kp, Ti and Td are the proportional gain, integral time

and derivative time, respectively, E(s) and U(s)are Laplace

transforms of the control signal and the error between the

reference signal and the plant output.

In this paper, we used a PID-controller proposed by Clarke

[1] is used because of its better derivative part. The

controller is of the form

)(1

)(1

1)( sYsaT

sTKsEs

TKsU

d

dp

i

p (2)

where a is the filtering constant at the interval (0,1), and

U(s) is Laplace transform of the plant output. The

implementation of the derivative part is more realistic than

in (1). The low pass filter reduces the effect of the

measurement noise, and only the plant output, which is

continuous, is differentiated. This controller can be

discretized with an approximation hds /1 , where h is

the sampling interval, and d is the delay operator. Thus, the

discretized controller is of the form:

maxmin

maxmin

)(),()()(

))()1(()(

)(

)),()(()1()(

ukuukukuku

kdyKkauTh

Tku

ukuu

keT

HkdeKkuku

dpi

pd

d

d

d

pi

i

ppipi

(3)

where k is a sampling time, e(k)=r(k)-y(k) is the error

signal, de(k)=e(k)-e(k-1) and dy(k)=y(k)-y(k-1) are the

differences. The control signal is restricted to the interval

||umin,umax|. To optimized PID controller we used Ziegler-

Nichols formula [8]:

cdcicp TTTTKK 125.0,5.0,5.0 (4)

where Tc is ultimate period and the process gain Kc

approximately given by:

m

ca

pK

4

(5)

where am is amplitude of limit cycle and p is the relay

amplitude

2.2 PID-Fuzzy Controller

The PID controller that described by equation (3) is

adjusted with fuzzy controller that described in figure 2.

Figure 2: PID-Fuzzy Control Scheme

These fuzzy algorithms that adjust the PID controller are

discussed in the next section.

3 Fuzzification, Rule Base Establishment and

Defuzzification

The fuzzy PID controller was designed by following the

standard procedure of fuzzy controller design, which

consists of fuzzification, control rule base establishment,

and defuzzification as shown by figure 3.

Figure 3: Structure of Fuzzy Logic

3.1 Fuzzification

Fuzzification is mapping from the crisp domain into the

fuzzy domain. Fuzzification also means the assigning of

linguistic value, defined by relative small number of

membership functions to variable. In this research, we have

two input with three output. For all this input and output,

we choice symmetrical triangular membership function that

shown in figure 4. The triangular curve is a function of a

vector, x, and depends on three scalar parameters a, b, and

c, as given by:

0,,minmax),,:(bc

xc

ab

axcbax

(6)

where the parameters a and c locate the "feet" of the

triangle and the parameter c locates the peak. Inputs for

fuzzy algorithms are set point and output of process and the

outputs for these fuzzy algorithms are proportional, integral

and derivative constant.

PID

ControllerPLANT

ek

ukrk yk

Fuzzy

ek-1dek

ek

Linguistic

Rule Set

IF….

THEN….

Fu

zzif

ica

tion

Def

uzz

ific

ati

on

Inp

ut

Ou

tpu

t

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

NB NM NS ZO PS PM PB

Figure 4: Symmetrical Membership Function

3.2 Rule

In this research, classic interpretation of Mamdani [5]

logic operations are applied, for ‘and’ minimum is used,

for ‘or’ also with ‘maximum’. So with IF-THEN rule, we

can describe the rule of fuzzy algorithm with the following

two dimensional table rules.

ek

dek NB NM NS ZO PS PM PB

PB ZO PS PM PB PB PB PB

PM NS ZO PS PM PB PB PB

PS NM NS ZO PS PM PB PB

ZO NB NM NS ZO PS PM PB

NS NB NB NM NS ZO PS PM

NM NB NB NB NM NS ZO PS

NB NB NB NB NB NM NS ZO

Figure 5: Used Rule Base for Kp, Ti and Td

3.3 Defuzzification

In this paper we used centre of area method for

defuzzification. This method determines the centre of the

area of the combined membership functions. This method is

referred to the centre of gravity method because its

computes the center of the composite area representing the

output fuzzy term. Assuming that a control action with a

point wise membership function (zj) has been produced,

with centre of area method crisp output z calculates:

q

j

j

q

j

jj

z

zz

z

1

1

)(

)( (7)

where, zj is the amount of control output at the quantization

level j, (zj) is membership value in zj and q is number of

quantization levels of the output

4 Application of PID-Fuzzy Controller in Grate

Cooler

These fuzzy rules that shown by figure 5 applied to control

grate cooler in cement plants with specification:

Rotary kiln

Clinker cooler with grate hydraulic drive

Preheater two strings 4 stage with precalciner

Total capacity 4,600 M Ton per day

4.1 PID Controller

In first time, we used conventional PID controller to control

under grate pressure #1. Using Ziegler-Nichols formula in

equation (3) at normal condition we get Kp= 150% Ti = 80

s and Td= 20 s. This calculation used to control grate

cooler and the result as shown in figure 6.

Figure 6: PID Controller Result

From figure 6 we can calculate that approximation normal

probability density function under grate pressure # 1.

Figure 7 show this calculation. From experiment we can

get some data:

Standard deviation of under grate pressure is 50

mmH2O

Clinker temperature output 1500

600 650 700 750 800 850 900 9500

20

40

60

80

100

120

140

160

180

200

mmH2O

Figure 7: Probability Density Function Under-Grate

Pressure (#1) with Conventional PID Controller with

Ziegler- Nichols Formula

4.2 PID-Fuzzy Controller

To build PID-Fuzzy controller, first we examine three

extreme conditions and calculated with equation (3) the

optimal PID controller. This three extreme condition yield

result as shown in figure 8:

condition start up snowman kiln upset

proportional

constant

80 % 120 % 200 %

integral

constant

40 s 12.5 s 20 s

derivative

constant

0 s 40 s 90 s

Figure 8: Calculation Result of Kp, Ti and Td in extreme

condition

From this calculation we build rule for PID-Fuzzy

controller as shown in figure 9.

Figure 9: PID-Fuzzy Controller Result

740 745 750 755 760 765 770 775 7800

50

100

150

200

250

300

350

400

mmH2O

Figure 10: Probability Density Function Under-Grate

Pressure #1 with PID-Fuzzy Controller

After PID-Fuzzy controller was applied in operation with

full 2 strings suspension preheater, we can observe the

result that:

With PID-Fuzzy, under grate pressure # 1 as

output variable of process was not deviate more

than 5 mmH2O. This is means that reduced more

that 90 % than controlled with conventional PID

controller. This condition described by

approximated normal probability density function

of under grate pressure # 1 that shown in figure 7

and 10.

Because under grate pressure #1 stable so the bed

depth of clinker on grate cooler relative constant.

Due to that temperature of secondary air that

increases more than 1500C after using PID-Fuzzy

controller. Its means increase efficiency of

calcinations in precalciner.

Also temperature of clinker output is reduce from

around 150oC to around 90oC, its means that with

PID-Fuzzy burn out material can be reduced.

5 Conclusions

With PID-Fuzzy controller, efficiency problem that become

well known problem in cement plant can be solved.

Because used PID-Fuzzy controller we have some

advantages:

Under-grate pressure deviations were reduced

Clinker output temperature were reduced so the

frequency of grate burnout was reduced

Changes in secondary air temperature were

reduced and increase secondary air temperature.

Increase calcinations efficiency in preheater.

References

[1] Clarke D., Automatic tuning of PID regulators, Expert Systems and Optimization in Process Control,

Technical Press, Aldershot, England, 1986.

[2] Clark M.C, Whitehopleman, Efficiency and

Reliability, Resolving the Efficiency: Reliability

Cooler Conflict, Cooler Justification, http://

www.istimaging.com, 1998.

[3] Chen, G and Ying, H, BIBO Stability of Nonlinear

Fuzzy PI Control Systems, Int. J. Intell. Control Syst., vol. 5, pp. 3–21, 1997.

[4] Duda, W. H, Cement Data Book 2: Automation,

Storage, Transportation, Dispatch, Bouverlag

GmbH,1990

[5] Mamdani, M, Application of Fuzzy Algorithm for

Control of Simple Dynamic Plant, Proc. IEE, v. 121,

no.12, pp. 1585-1588, 1974.

[6] Tang K. S., Man K.F., Chen G. and Kwong S, An

Optimal Fuzzy PID Controller, IEEE Transactions on Industrial Electronics, Vol. 48, No. 4, pp.757-765,

2001.

[7] Viljamaa P. and Koivo H.N., Fuzzy Logic in PID Gain

Scheduling, Third European Congress on Fuzzy and Intelligent Technologies EUFIT’95, Aachen,

Germany, August 28 31, 1995.

[8] Ziegler, J.B. and N.B Nichols, Optimum Setting for

Automatic Controllers, Trans. ASME, vol.64, pp.759-

768, 1942.