Abstract— The parameter of PID controller is

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

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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 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

Ki

Kd

PID

0.6*200=120

2/0.2=10

0.2/8=0.025

IV.     DESIGN OF FUZZY CONTROLLER

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

                             Calciner temperature in the cement
manufacturing process was developed using mamdani fuzzy model. It consists of
two inputs and three outputs. First input was error. Second input was rate of
change of error. The three outputs were Kp, Ki and Kd (i.e. controller gains).

Table 4.1:Rule table of fuzzy controller

B.     MAMDANI FIS IMPLEMENTATION
FOR CALCINER TEMPERATURE CONTROL

Figure 4.2: Fuzzy logic toolbox

Figure 4.3: Membership function of inputs

Figure 4.4: Membership function of outputs

Figure 4.5: Rule viewer of mamdani FIS

Figure
4.6: 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. The coefficients of the conventional PID controller are not often
properly tuned for the non-linear plant with unpredictable parameter variations
.Hence, it was necessary to automatically tune the PID parameters.

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 6.3 and 6.4 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 8.1.

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

Fig
6.5: Servo with regulatory response of the PID controller

Fig
6.6: 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

VII.    
 REAL TIME IMPLEMENTATION –CEMULATOR

Contrary to most cement process
simulators, ECS/CEMULATOR was developed on a full 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 effected by the level of skills of plant operators and engineers.                 

A.     REAL TIME RESPONSE OF THE PID CONTROLLER

Figure 7.1: Response of PID controller in real time

B.     REAL TIME RESPONSE OF FUZZY PID CONTROLLER

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:

CALCINER
TEMPERATURE CONTROL USING

ISE

PID
CONTROLLER
 

18.4

FUZZY
CONTROLLER

16.4

 

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 Turkey 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. 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.

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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