FUZZY the raw mix sent into the kiln.

 

FUZZY
BASED PID FOR CALCINER TEMPERATURE CONTROL

Mrs.Z.Brijet*1, M.B.Sri Padmadarshan*2, S.Vigneshwaran*3,
P.B.Mohankrishna*4 
*1 Assistant
Professor – III, Department of Electronics and Instrumentation Engineering,
Velammal Engineering College, ‘Velammal New-Gen Park, Ambattur-Red Hills
Road, Chennai – 600066, India
*[email protected]
*2,3,4 4th
year Bachelor’s degree, Department of Electronics and Instrumentation
Engineering, Velammal Engineering College, ‘Velammal New-Gen Park,
Ambattur-Red Hills Road, Chennai – 600066, India
*[email protected],*[email protected],*[email protected]

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Abstract— The Calciner Unit plays an important role in the modern
cement industries as it is used for preheating the raw materials like limestone
which are fed into the kiln. The mathematical model of the calciner unit is
designed using System Identification technique for the real time data obtained
from the plant. A conventional PID controller has been designed to control the
temperature of the calciner unit. The parameter of PID controller is tuned
using Ziegler – Nichols tuning method. In order to achieve optimum controller
parameter a Self Tuning Fuzzy
PID controller is developed. The performance of the calciner unit has improved
significantly compared to conventional PID controller.

 

I.     INTRODUCTION

Calciner temperature control process
is one of the most important processes in cement manufacturing. It is used to
maintain the raw mix texture, size of the mixture and perfect blending of the
raw material to produce more valuable clinker. Calciner unit is used to preheat
the raw mix sent into the kiln. The product obtained is “clinker” (cement).
Normal temperature of kiln is to be maintained at 800-960 °C and a normal coal
feeding is 10-20 t/hr. There are four basic processes in cement manufacturing. It
starts with quarry where the raw material is extracted and crushed. Then it
will be sent to raw mill wherein the blending process takes place (raw mix).
The resultant from the above process was sent to the calciner where the raw mix
was preheated and fed into the kiln. The raw mix and fuel was sent into the
kiln. Clinker and exit gases come out. The clinker was sent to finish mill,
after which the size was reduced to obtain the final product ‘cement’. The
basic schematic diagram of cement manufacturing plant is shown in Fig.1.1.

 

 

 Figure 1.1: Schematic diagram of cement
manufacturing plant

II.     IDENTIFICATION OF SYSTEM

A.    
 ANALYZING AND PROCESSING DATA

When preparing
data for identifying models, it was mandatory to specify information
such as input-output channel names, sampling time (10s). The toolbox helps to
attach this information to the data, which facilitates visualization of data,
domain conversion, and various preprocessing tasks.  Measured data often has offsets, slow drifts,
outliers, missing values, and other anomalies. The toolbox removes such
anomalies by performing operations such as de-trending,
filtering, resampling, and reconstruction of missing data. The
toolbox can analyze the suitability of data for identification and provide
diagnostics on the persistence of excitation, existence of feedback loops, and
presence of nonlinearities. The toolbox estimates the impulse and
frequency
responses of the system directly from measured data. Using these
responses, system characteristics, such as dominant time constants, input
delays, and resonant frequencies can be analyzed. These characteristics can
also be used to configure the parametric models during estimation.

B.    
ESTIMATING
MODEL PARAMETERS

Parametric
models, such as transfer functions or state-space models use a small number of
parameters to capture system dynamics. System Identification Toolbox estimates
model parameters and their uncertainties from time-response and frequency-response
data. These models can be analyzed using time-response and frequency-response
plots, such as step, impulse, bode plots, and pole-zero maps.

C.    
VALIDATING
RESULTS

System Identification Toolbox helps
to validate the accuracy of identified models using independent sets of measured data from
a real system. For a given set of input data, the toolbox computes the output
of the identified model and lets to compare that output with the measured
output from a real system. One can also view the prediction error and produce
time-response and frequency-response plots with confidence bounds to visualize
the effect of parameter uncertainties on model responses.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.1: Shows
the process of selecting the range for validation and estimation of data.

D.     LINEAR MODEL IDENTIFICATION

                          System Identification
Toolbox lets to estimate multi-input, multi-output continuous or discrete-time transfer functions with a specified number of poles and zeros.
One can specify the transport delay or let the toolbox determine it
automatically. In this work, transfer function model was used for system
identification.

E.    
ESTIMATING
TRANSFER FUNCTION MODEL

Estimate
continuous-time and discrete-time transfer functions and low-order process
models. Use the estimate models for analysis and control design. Polynomial and
state-space
models can be identified using estimation routines provided in the
toolbox. These routines include autoregressive models (ARX, ARMAX), Box-Jenkins
models, Output-Error models, and state-space parameterizations. Estimation techniques
include maximum likelihood, prediction-error minimization schemes, and subspace
methods based on N4SID, CVA, and MOESP algorithms.  A model of the noise affecting the observed
system can also be estimated. Figure 2.2 depicts the process of obtaining the
transfer function model.

 

 

 

 

 

 

 

 

 

 

 

Figure 2.2: Obtaining
transfer function model

 

F.    
ESTIMATING
STATE-SPACE MODEL

A state space model is commonly
used for representing a linear time invariant system. It describes a system
with a set of first order difference equation using inputs, outputs and state
variables. In the absence of the equation, a model of desired order can be
estimated for measured input, output data. The model was widely used in modern
control application for designing controllers and analyzing system performance
in the time domain and frequency domain. The models can be applied to nonlinear
system or system with a non-zero initial condition.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.3: Obtaining
state space model

III.     DESIGN OF PID CONTROLLER FOR CALCINER

A.    
PID
CONTROLLER:

P-I-D
controller has the optimum control dynamics including steady state error, fast
response, less oscillations and higher stability. The necessity of using a
derivative gain component in addition to the P-I-D controller is to eliminate the
overshoot and the oscillations occurring in the output response of the system. One
of the main advantages of the P-I-D controller was that it can be used with
higher order processes including more than single energy storage.

From a mathematical viewpoint,
the PID control works to reduce the error e(t) to zero, where e(t) was the
difference between output response and the set point.

 The control response
u(t) is given by:

                        u(t)=Kpe(t)+Ki?e(t)dt+Kd
de(t)/dt

where kp, ki, kd are scale
factors for the proportional, integral and differential terms respectively.

 

B.    
ZIEGLER –
NICHOLS TUNING METHOD:

The parameters of PID controller
were tuned using Ziegler – Nichols tuning method.

 The basic steps in Z-M method are

1. The value of Kd and
Ki were set to zero.

2. The value of Kp was
slowly increased such the sustained oscillation occurs (constant amplitude and
periodic).

3. The value of Kp ­at
which sustained oscillation occurs was ultimate gain Ku and the
period of oscillation was ultimate period Pu.

From the
calculated value of Ku and Pu, the parameters of PID
controller were calculated using the formula.

The table
3.1 shows the PID controller parameter tuned using Ziegler – Nichols method.

Table 3.1: PID controller tuning parameters

Control type

Kp= 0.6Ku

Ki=2/Pu

Kd= Pu/8

PID

0.6*200=120

2/0.2=10

0.2/8=0.025

IV.     DESIGN OF FUZZY CONTROLLER

The fuzzy logic controller
consists of the following blocks. The block diagram of fuzzy controller has
been shown in Figure 4.1.

Figure
4.1: General block diagram of fuzzy logic controller

A.    
FUZZY
INFERENCE SYSTEM

                 A Fuzzy inference system (FIS)
was a system that uses fuzzy set theory to map inputs to outputs. There are two
types of FIS .They are mamdani and Takagi sugeno FIS. In this project there are
two inputs and three outputs. Therefore, mamdani type FIS was used in this
project.

        
i.           
MAMDANI FIS

                             Mamdani FIS is
widely accepted since it can be applied for both MIMO, MISO systems whereas
sugeno can be implemented only for MISO systems. In mamdani, the membership
functions can be chosen even for outputs whereas it was not possible in sugeno
type. Hence mamdani FIS was used for our project.

       
ii.           
DEVELOPMENT OF MAMDANI TYPE FIS

The MAMDANI type fuzzy
inference system consists of two inputs and three outputs. First input was
error and the second input was rate of change of error. The three outputs were
Kp, Ki and Kd (i.e. controller gains). The rule table for fuzzy controller was shown in Table
4.1.

Table
4.1:Rule table of fuzzy controller

Here
e was error and de/dt was rate of change of error. Meaning of linguistic
variables in FIS(Fuzzy Inference System) are

                                VH-Very High

                                 H-High

                                 M-Medium

                                 L-Low

                                 VL-Very Low

 

B.    
MAMDANI FIS
IMPLEMENTATION FOR CALCINER TEMPERATURE CONTROL

The two inputs of the process
have three triangular membership functions and outputs have five membership
functions respectively. The membership functions of both the inputs and the
outputs are taken in the range of -1 to +1.The membership functions of the
input and output is as shown in the figure 4.2 and 4.3.

Figure
4.2: Membership function of inputs

Figure 4.3: Membership function of outputs

The rules viewer of the
mamdani FIS is as shown in the fig.6.5. 

Figure
4.4: Rule viewer of mamdani FIS

Surface viewer of the mamdani
FIS is as shown in the fig 6.6.

Figure 4.5: Surface
viewer of mamdani FIS

V.     IMPLEMENTATION OF FUZZY PID CONTROLLER

A.    
STRUCTURE OF
FUZZY-PID CONTROLLER

Self tuning fuzzy-PID controller means that the three
parameters Kp, Ki, and Kd of PID controller are tuned by using fuzzy tuner.

 

Figure 5.1: Structure of the
self tuning fuzzy-PID controller

 

The
error and the derivative of its error are sent to the fuzzy controller. The PID
parameter Kp, Ki and Kd is calculated according to the rules in the fuzzy
controller, at the same time, Kp was also refined by P controller which was the
immune PID controller, so the Kp, Ki and Kd can be continuous updated according
to error e(t) and its derivative de/dt.

                                                        

 

VI.     SIMULATION RESULTS AND DISCUSSION

A.    
SERVO
RESPONSE OF PID AND FUZZY PID CONTROLLER

          Simulation studies are carried out to
demonstrate the tracking capability of tuned PID controller and fuzzy PID
controller. The performance of process for tuned PID and fuzzy PID were shown
in figures 6.1 and 6.2 respectively. From the response, it was observed that
the calciner temperature follow the given set points and the servo response of
the PID and fuzzy PID were compared in the table 6.1.

Fig 6.1: Servo
response of the PID controller

Fig 6.2: Servo
response of the fuzzy PID controller

Table 6.1: Comparison of performance
indices of PID and FUZZY PID tuned controller for servo response

 

CALCINER TEMPERATURE CONTROL USING

ISE

IAE

ITAE

PID CONTROLLER

1.559 e^(+05)

416.9

3975

FUZZY CONTROLLER

1.045 e^(+05)

279.3

2138

 

From the responses, it was
observed that the performance criterion such as ISE, IAE and ITAE of Fuzzy PID
controller was better compared to conventional PID controller. It was also
observed that fuzzy PID controller settles quickly than PID controller
response.

B.    
SERVO
WITH REGULATORY RESPONSE OF PID AND FUZZY PID CONTROLLER

Simulation
studies have been carried out to show the disturbance rejection capability of
tuned PID and fuzzy PID controller. A step disturbance was introduced. The
servo with regulatory responses of both PID and fuzzy PID controller was shown
in figures 6.3 and 6.4 respectively and the regulatory response of the PID and
fuzzy PID controller were compared in the table 6.2.

Fig 6.3: Servo with regulatory
response of the PID controller

Fig 6.4: Servo with regulatory
response of the fuzzy PID controller

 

 

 

 

Table 6.2: Comparison of
performance indices of PID and FUZZY PID controller for servo with regulatory
response

 

CALCINER
TEMPERATURE CONTROL USING

ISE

IAE

ITAE

PID CONTROLLER

1.605e^(+05)

622.8

9293

FUZZY
CONTROLLER

1.294 e^(+05)

410.9

4294

 

From the responses, it was
observed that the performance criterion such as ISE, IAE and ITAE of Fuzzy PID
controller was better compared to conventional PID controller.

VII.    
 REAL TIME
IMPLEMENTATION –CEMULATOR

Contrary to most cement process simulators,
ECS/CEMULATOR was developed on a fully functional control systems platform
enabling the complete set of functions and features of a modern control system
environment for the users. Having a skilled team of operators plays a crucial
role in beneficial and safe operation of industrial plants. Especially in the
cement industry, with the significant high cost of investment, practical
knowledge and experience of plant operation have a direct effect on production
economy. Insufficient insight in process dynamics and interactions, high stress
factors in real time operation conditions, and lack of adequate experience in
utilizing the existing control system are typical reasons for incorrect
operator actions. The consequences of this may result in low production quality,
production interrupts, and equipment damage, in worst case risk on human safety.
The increasing demand on production sustainability in the recent years has resulted
in requirements of which the degree of fulfillment is affected by the level of
skills of plant operators and engineers.                 

A.     REAL
TIME RESPONSE OF THE PID CONTROLLER

The response of the PID
controller in the real time plant is as shown in the figure 7.1.

 

Figure 7.1: Response of PID controller in real time

B.     REAL
TIME RESPONSE OF FUZZY PID CONTROLLER

The response of Fuzzy PID
controller in real time plant is as shown in figure 7.2.

 

Figure 7.2: Response of Fuzzy PID controller in
real time

 

Comparison of performance
indices of PID and FUZZY PID controller for the real time response is shown in
Fig. 7.1 and 7.2.

 

Table 7.1:
Comparison of performance indices of PID and FUZZY PID controller

 

CALCINER
TEMPERATURE CONTROL USING

ISE

PID CONTROLLER
 

18.4

FUZZY CONTROLLER

16.41

 

From the table 7.1 it has been observed that
Integral Square Error (ISE) value of fuzzy PID controller is reduced as
compared to PID controller.

 

 

 

VIII.     CONCLUSION

 

               The main aim of the project was
to control the calciner temperature and to obtain a good quality clinker. The
transfer function model of calciner for the process has been derived using
system identification tool. The simulink model of calciner has been developed
in MATLAB using real time steady state values of cement power plant. The open
loop response of the process where observed and the interaction effect has been
studied. The parameters for PID were obtained using Ziegler – Nichols tuning. The
fuzzy rules were written using FAM table and the rules are inserted in the FIS
using mamdani method which is used to tune the PID parameters. Thus Fuzzy PID
controller was implemented and then optimized values were obtained. It is
observed that the performance criteria namely the ISE, IAE, ITAE, and settling
time in Fuzzy PID controller is better than the PID controller. Also from the
responses, it has been observed that the proposed method has better tracking
and faster settling time. Using the tuned values of PID, the fuzzy PID
controller was implemented for cement calciner unit.

IX.     Appendix

DATA FROM REAL TIME CALCINER UNIT

 
 
S.NO

CALCINER TEMPERATURE

CALCINER COAL FEED

KILN TOTAL FEED

1

894.7916

9.6501

588.4775

2

894.7916

9.6401

589.4781

3

896.5278

9.6359

585.4742

4

898.9583

9.6276

588.4867

5

901.3889

9.6184

594.3333

6

904.1666

9.6096

590.6599

7

902.7778

9.6029

588.5881

8

900.6944

9.6033

590.9871

9

899.3055

9.6079

591.7212

10

901.3889

9.6074

589.3926

11

903.1249

9.6

585.8295

12

901.7361

9.5952

584.7019

13

900.6944

9.5972

586.1656

14

901.0416

9.5997

590.9084

15

903.1249

9.5979

590.3184

16

906.2499

9.5892

591.2415

17

904.8611

9.5817

590.2633

18

903.1249

9.5822

591.3748

19

902.7778

9.5847

591.8418

20

906.9444

9.5828

585.3685

 

 

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