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 +62-21-82403654 e-mail:
[email protected] 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 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 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 dynamic of the process is is nonlinear. So we need algorithm algorithm that can adapt with with nonlinear behavior. Fuzzy logic matches to to
solve these problems because PID-Fuzzy controller has some advantages:
k r k setpoint
ek
Conventional PID-Control
uk grate speed
PLANT
yk under grate pressure #1
Figure 1: Grate Cooler Conventional Conventional PID Control 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 De Design
In this paper we used two type controllers to detect performance of these controllers controllers in the the real plant. These controllers are: 2.1 PID PID Contro Controlle llerr The theoretical PID-controller,
U ( s ) K p 1
T d s E ( s ) T i s 1
(1)
where K p, T i and T d d are the proportional gain, integral time and derivative time, respectively, E(s) and U(s)are 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 K p T d s 1 U ( s ) K p 1 s E ( s ) Y ( s ) 1 aT d s T i
H T i
T d h T d
PID Controller
k r k
uk
yk
PLANT
These fuzzy algorithms that adjust the PID controller are discussed in the next section. 3
Fuzzi Fuzzific ficati ation, on, Rule Rule Base Base Esta Establi blishm shment ent 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.
t u p n I
u ( k ) u pi ( k ) u d ( k ), u min u ( k ) u max
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 ||u ||umin ,umax|. To optimized optimized PID controller we we used ZieglerZiegler Nichols formula [8]: (4)
where T c is ultimate period and the process gain K c approximately given by: 4 p a m
dek
Figure 2: PID-Fuzzy Control Scheme
( au d ( k 1) K p dy ( k ))
K c
ek-1
(3)
K p 0 .5 K c , T i 0 .5T c , T d 0 .125 T c
Fuzzy
e( k )),
u min u pi ( k ) u max u d ( k )
ek
(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 s 1 d / h , where h is d is the delay operator. Thus, the the sampling interval, and d is discretized controller is of the form:
u pi ( k ) u pi ( k 1) K p ( de ( k )
ek
(5)
where am is amplitude of limit cycle and p is the relay amplitude 2.2 PID-Fuzz PID-Fuzzy y Controll Controller er The PID controller that described by equation (3) is adjusted with fuzzy controller that described in figure 2.
n o i t a c i f i z z u F
Linguistic Rule Set IF…. THEN….
n o i t a c i f i z z u f e D
t u p t u O
Figure 3: Structure of Fuzzy Logic 3.1 Fuzzi Fuzzific ficati ation on 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 b , and vector, x vector, x,, and depends on three scalar parameters a, b, c, as given by: ( x
x a c x : a , b , c ) max min , , 0 b a c b
(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.
4 NB
NM
NS
ZO
PS
PM
Appl Applica icatio tion n of PID-Fu PID-Fuzzy zzy Contro Controlle llerr in Grate Grate Cooler
PB
1
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 strings 4 stage with precalciner Preheater two strings Ton per day Total capacity 4,600 M Ton
0.8
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0.4
0.2
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
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’. ‘maximum’. So with IF-THEN rule, we can describe the rule of fuzzy algorithm with the following two dimensional table rules.
4.1 PID Contro Controlle llerr In first time, we used conventional PID controller to control under grate pressure #1. Using Ziegler-Nichols Ziegler-Nichols formula formula in equation (3) at normal condition we get K p= 150% T i = 80 s and T d calculation ation used to to control control grate grate d= 20 s. This calcul cooler and the result as shown in figure 6.
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 Rule Base for K p, T i i and T d d 3.3 Defuz Defuzzif zifica icatio tion n 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 (z (z j ) has been produced, z calculates: with centre of area method crisp output z calculates:
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. calculation. From experiment experiment we can get some data: Standard deviation of under grate pressure is 50 mmH2O Clinker temperature output 150 0 200
180
160
140
120
100
q
z ( z z
j
j
( z j
)
j 1
80
)
(7)
q
60
40
j 1
20
0 600
where, z where, z j is the amount of control output at the quantization quantization (z j ) is membership value in z j and q is number of level j, (z quantization levels of the output
650
700
750
800
850
900
950
mmH O 2
Figure 7: Probability Density Function Under-Grate Pressure (#1) with Conventional PID Controller with Ziegler- Nichols Formula
4.2 PID-Fuzz PID-Fuzzy y Controll Controller er To build PID-Fuzzy controller, first we examine three extreme conditions and calculated with equation (3) the optimal PID controller. This three extreme extreme condition yield result as shown in figure 8:
condition proportional constant integral constant derivative constant
start up 80 %
snowman 120 %
kiln upset 200 %
40 s
12.5 s
20 s
0s
40 s
90 s
K p, T i i and T d Figure 8: Calculation Result of K d in extreme condition
From this calculation we build rule for PID-Fuzzy controller as shown in figure 9.
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 90 oC, 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 Figure 9: PID-Fuzzy PID-Fuzzy Controller Result Result
[1]
Clarke Clarke D., D., Autom Automatic atic tuning tuning of PID regulators regulators,, Expert Systems and Optimization in Process Control, Technical Press, Press, Aldershot, England, 1986.
[2]
Clark Clark M.C, M.C, Whiteho Whitehople pleman man,, Effici Efficienc ency y and Reliability, Resolving the Efficiency: Reliability Cooler Conflict, Cooler Justification, Justification , http:// www.istimaging.com, www.istimaging.com, 1998.
[3]
Chen, G and and Ying, Ying, H, H, BIBO BIBO Stability Stability of Nonlin Nonlinear ear Fuzzy PI Control Systems, Int. Systems, Int. J. Intell. Control Syst ., Syst ., vol. 5, pp. 3–21, 1997.
[4]
Duda, W. H, Cement Data Book 2: Automation, Storage, Transportation, Dispatch , Bouverlag GmbH,1990
[5]
Mamdani, Mamdani, M, Applicati Application on of of Fuzzy Fuzzy Algorithm Algorithm for Control of Simple Dynamic Plant , , Proc. IEE , v. 121, no.12, pp. 1585-1588, 1974.
400
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0 740
745
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mmH O 2
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:
[6] Tang Tang K. S., S., Man Man K.F., K.F., Chen Chen G. and and Kwon Kwong g S, An An Optimal Fuzzy PID Controller, IEEE Transactions on Industrial Electronics, Electronics, Vol. 48, No. 4, pp.757-765, 2001.
[7]
Viljamaa Viljamaa P. and Koivo H.N., H.N., Fuzzy Fuzzy Logic Logic in in PID Gain Scheduling, Third European Congress on Fuzzy and Intelligent Technologies EUFIT’95 , Aachen, Germany, August 28 31, 1995.
[8]
Ziegler, Ziegler, J.B. and N.B N.B Nichols, Nichols, Optimum Optimum Setti Setting ng for Automatic Controllers, Trans. ASME , vol.64, pp.759768, 1942.
