Universidade Federal de Juiz de Fora

Faculdade de Engenharia

Departamento de Engenharia de Producao e Mecanica

Curso de Graduacao em Engenharia Mecanica

Leonardo Araujo Serapiao

Type-2 Fuzzy Logic System Applied to a Temperature Control of an Electric

Oven

Juiz de Fora

2016

Leonardo Araujo Serapiao

Type-2 Fuzzy Logic System Applied to a Temperature Control of an Electric

Oven

Trabalho de Conclusao de Curso apresen-tado ao Curso de Graduacao em EngenhariaMecanica da Universidade Federal de Juizde Fora, na area de concentracao de Enge-nharia Mecanica, como requisito parcial paraa obtencao do tıtulo de Bacharel em Enge-nharia Mecanica.

Orientador: Eduardo Pestana de Aguiar

Coorientador: Daniel Discini Silveira

Juiz de Fora

2016

Serapiao, Leonardo.Type-2 Fuzzy Logic System Applied to a Temperature Control of an

Electric Oven / Leonardo Araujo Serapiao . – 2016.34 f. : il.

Orientador: Eduardo Pestana de AguiarCoorientador: Daniel Discini SilveiraTrabalho de Conclusao de Curso – Universidade Federal de Juiz de Fora

, Faculdade de EngenhariaDepartamento de Engenharia de Producao e Mecanica . Curso de Gradu-acao em Engenharia Mecanica , 2016.

1. Type-2 fuzzy logic system. 2. Type-1 fuzzy logic system. 3. Temper-ature control. I. Aguiar, Eduardo Pestana de, orient. II. Silveira, DanielDiscini, coorient. III. Tıtulo.

Leonardo Araujo Serapiao

Type-2 Fuzzy Logic System Applied to a Temperature Control of an ElectricOven

Trabalho de Conclusao de Curso apresen-tado ao Curso de Graduacao em EngenhariaMecanica da Universidade Federal de Juizde Fora, na area de concentracao de Enge-nharia Mecanica, como requisito parcial paraa obtencao do tıtulo de Bacharel em Enge-nharia Mecanica.

Aprovado em 23 de Novembro de 2016.

BANCA EXAMINADORA

Prof. Eduardo Pestana de Aguiar - OrientadorUniversidade Federal de Juiz de Fora

Prof. Daniel Discini Silveira - CoorientadorUniversidade Federal de Juiz de Fora

Prof. Washington Orlando Irrazabal BohorquezUniversidade Federal de Juiz de Fora

Prof. Luiz Gustavo Monteiro GuimaraesUniversidade Federal de Juiz de Fora

ACKNOWLEDGMENT

I thank God for giving me health and strength to overcome difficulties.

To my parents, Cecılia and Paulo, my heroes, who did everything possible and

impossible for me to achieve this goal, and to my sister, Nancy, for their support during

this journey.

To my great friends and brothers in the friendship, who were part of my formation

and who will continue to be present in my life, as well as my laboratory companions.

To my advisor, Eduardo, for guidance during these years, support and trust and to

all teachers for providing me with not only rational knowledge, but the manifestation of

the character and affectivity of education in the process of professional training.

To the Mechanical Engineering course, the Faculty of Engineering and the Federal

University of Juiz de Fora for the structure, support and encouragement.

And finally, to all who have been directly or indirectly part of my training, thank

you very much.

“If I have seen further than others, it is by standing

upon the shoulders of giants.” (Isaac Newton)

ABSTRACT

The control of non-linear systems is a difficult task, requiring efficient control algorithms

and good accuracy. Systems that operate with heating or cooling are examples of this

challenging situation. The control of these processes requires a good ability to deal with

uncertainties, essentially caused by changes on the environment of the system. This work

presents three different control algorithms, which are used to perform the control of the

temperature of an electric oven. To address this problem, a prototype oven was built,

connected to a PC through embedded electronics, allowing the test and validation of

three different control algorithms. A comparison was done among the proposed models:

rule-based control algorithm, type-1 fuzzy logic system and type-2 fuzzy logic system.

Also, it is analyzed their effectiveness based on their performance and ability to deal

with uncertainties. Experimental results show that type-2 fuzzy logic system has a better

response in comparison with type-1 fuzzy logic system and rule-based control algorithm,

having an improved rise time, minimum overshoot and the best performance compared to

the experimented control algorithms. It also showed a continuous response, with a better

approximation of the desired result, and an excellent ability to handle uncertainties.

Key-words: Type-2 fuzzy logic system, Type-1 fuzzy logic system, Temperature Control,

Electric Oven.

LIST OF FIGURES

Figure 1 – Model flowchart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Figure 2 – Oven with sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 3 – Schematic of the connections of the optocoupler and the TRIAC. . . . 15

Figure 4 – Synthesis of the embedded electronic board. . . . . . . . . . . . . . . . 16

Figure 5 – Data colletion and power transmission board. . . . . . . . . . . . . . . 16

Figure 6 – PWM signal with 15% duty cycle. . . . . . . . . . . . . . . . . . . . . . 17

Figure 7 – PWM signal with 50% duty cycle. . . . . . . . . . . . . . . . . . . . . . 17

Figure 8 – PWM signal with 90% duty cycle. . . . . . . . . . . . . . . . . . . . . . 18

Figure 9 – Relation between temperature and the duty-cycle of the PWM. . . . . 18

Figure 10 – Closed-loop control system. . . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 11 – Control system diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 12 – Rule-based control algorithm. . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 13 – Type-1 MF for Tout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 14 – Type-1 MF for ∆E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 15 – Type-1 MF for %P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 16 – Type-2 MF for Tout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 17 – Type-2 MF for ∆E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 18 – Response of the controllers. . . . . . . . . . . . . . . . . . . . . . . . . 26

LIST OF TABLES

Table 1 – Environment Temperature Corrections . . . . . . . . . . . . . . . . . . . 19

Table 2 – Decision Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Table 3 – T2FLC MF parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Table 4 – Controllers Experimental Results . . . . . . . . . . . . . . . . . . . . . . 27

LIST OF ABBREVIATIONS

FLS Fuzzy Logic System

FLC Fuzzy Logic Controller

PC Portable Computer

AC Alternating Current

PWM Pulse-Width Modulation

T1FLC Type-1 Fuzzy Logic Controller

T2FLC Type-2 Fuzzy Logic Controller

RBCA Rule-based Control Algorithm

GUI Graphical User Interface

PID Proportional Integral Derivative

LIST OF SYMBOLS

T Temperature

∆E Error

%P Percentage of the PWM duty-cycle

W Watt

C Celsius degrees

Hz Hertz

Ω Ohm

V Voltage

R Resistance

F Farad

µ Membership function

Subscribed

out Output

set Set-point

cc Constant current

ac Alternating current

in Input

SUMMARY

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 MEASUREMENT SETUP . . . . . . . . . . . . . . . . . . . . . 14

2.1 EXPERIMENTAL OVEN . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2 EMBEDDED ELECTRONIC BOARD . . . . . . . . . . . . . . . . . . 14

2.2.1 Analysis of PWM pulse . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.2 Equipment set-up and boundary conditions . . . . . . . . . . . . . . . . 19

3 CONTROL DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1 RULE–BASED CONTROL ALGORITHM . . . . . . . . . . . . . . . . 21

3.2 FLS CONTROL ALGORITHMS . . . . . . . . . . . . . . . . . . . . . . 23

4 EXPERIMENTAL RESULTS . . . . . . . . . . . . . . . . . . . 26

5 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

APPENDIX A – Publications . . . . . . . . . . . . . . . . . . . 33

APPENDIX B – Term of Acceptance . . . . . . . . . . . . . . 34

11

1 INTRODUCTION

Systems working with heating or cooling cycles are required in many practical

applications, e.g. ovens, furnaces and air conditioning. The objective of temperature

control is to heat up a system to a limit, and maintain the temperature as long as necessary.

In this period, only small variations are accepted [1], characterizing a stable process of heat

transfer between oven and system being heated. This is normally achieved by maintaining

the temperature constant all along the process and useful lifetime of the oven or furnace,

independent of ambient variations, like room temperature, mains voltage fluctuations,

position of the oven and other heat sources which can interfere at this control. Focusing

on electric ovens, it is a difficult task to have good accuracy in the set point temperature,

especially caused by the inefficiency of oven insulation and environment disturbances.

Achieving maximum accuracy in the system is still a challenge. Different studies were

designed to achieve high accuracy in temperature control for electric ovens, using different

approaches, such as [2] and [3].

Studies modeled this kind of control as nonlinear systems [4], where the input is

the heating element and the output is the temperature inside the oven. The temperature

control of an electric oven with electric resistances generally can be done by means of

variation of two parameters: phase angle of AC mains or sending a finite number of

AC cycles, switching on and off the resistances in a short period of time. This can be

accomplished by a pulse-width modulation signal, as seen in [5]. This methodology has

shown to be effective, and can be used with several methods, as PID control [6, 7], fuzzy

rule-based system [8] and smith predictor methods [9], or with multiple procedures like

those combined.

Those systems are, however, sensible to random disturbances. Those disturbances

lead the control network to send inappropriate signals to the heating control process, con-

sidering a state that is no longer real. In [10], this problem is addressed by using nonlinear

equations to predict and eliminate possible instabilities that affect the temperature of the

oven. A simple way to characterize external disturbances is to place a sensor outside the

oven. This data is then also send to the controller, which includes the external temperature

in the calculations.

Another challenge for controlling this type of system is the considerable time

between the control signal sent by the controller (a computer) and the response of system.

Called long dead-time process, these plants do not present an immediate response to

the commands of the controller, so that different methods are developed to accomplish

this control, using innovative tuning parameters [11] or compensators [12]. An intelligent

solution to predict the behavior of the system is to implement control by derivatives, such

as [13], applied to a open loop, where the output response cannot be measured right after

12

input be sent.

Based on the above challenges to design a proper controller, the main objective

of this work is to present a control system which can be used in any oven, addressing all

problems stated above, and also considering the modification of a few factors, such as the

method of heat transfer, operating voltage, temperature range and ambient conditions,

that could change for different ovens. This controller shall perform well because it does not

consider constructive information of the oven, presenting good efficiency on temperature

control [14] and joining the best qualities of several studies in this field, as its architecture

just considers variations of temperature inside and outside the oven.

To allow the comparison of different controllers, it was developed a specific routine,

presented in Fig. 1, designed to improve the response time and the efficiency of the system.

The communication with the computer was accomplished using a serial port interface. The

control loop initiates defining a set-point temperature. Then, the controller defines the

duty-cycle of the PWM, based on the temperature measured by LM35 sensors. Finally,

the loop repeats until the set-point is reached.

The strategy chosen to design the final controller was to combine fuzzy logic [15,16]

and an embedded micro processed hardware. Also like in [8], effort was done in order

to implement this idea using low cost hardware, so it could be used in different kinds of

heating plants, such as industrial ones and home appliance.

Fuzzy logic systems (FLS) [17] have been applied massively in control issues, showing

different qualities that establishes a whole new level of applications. Plants that demands

lots of processing can be easily transformed into very accurate process [18–20]. Those

systems have been used on cases which is necessary constant observation of process [21]

and predictive actuation simultaneously [22]. The control plant has to be able to normalize

random disturbances, to predict the behavior of the system being controlled, and also

to analyze possible variations and to make decisions based on a pre programmed code.

This controller optimizes the process to the best output as possible [23]. Type-1 FLSs

have been massively applied aiming to solve the problem of oven temperature control [24].

Although type-1 FLSs offer a reasonable performance, some uncertainties associated with

the control problem is something that type-1 FLS may not properly handle. According

to [17], the type-2 FLS have the potential to handle larger uncertainties than a type-1,

therefore it has the ability to adjust to the variations that the system may suffer.

This work proposes then a comparison between type-1 and type-2 FLSs control

algorithms [25], and also an ordinary rule-based control algorithm, in order to define the

most appropriate controller to handle large uncertainties in the experimented system, and

achieve the maximum accuracy and efficiency.

13

initializeGUI

Serial port LM35

defineset-point

temp.

set PWMduty-

cycle bycontroller

send PWMpulse

to oven

updatemodel

reachedset-pointtemp.?

stop

no

yes

1 [s]

Figure 1 – Model flowchart.

Major expected conclusions are as follows:

• Type-2 FLS has more precisely convergence rate, eliminating disturbances effects on

main proposal and less variation on temperature;

• Low cost hardware interface, using simple electronic components, such that the oven

with this additional hardware does not have a price higher than its benefits.

The monograph is organized as follows: Section II aims to discuss details of the

setup adopted. Section III discusses the controllers adopted. Section IV discusses the

results of the tests. Section V states the main conclusions regarding the proposals.

14

2 MEASUREMENT SETUP

The measurement setup is composed by a prototype oven and a embedded electronic

board connected to a PC running Matlab, allowing the control of the oven temperature

by means of the duty cycle of a PWM signal. Those components will be detailed in this

section.

2.1 EXPERIMENTAL OVEN

The ordinary electric oven chosen for the experiment and measurements has two

independent resistances, one at the top and one at the bottom. Each one consumes a

maximum power of 750 [W], resulting in a final total power of 1500 [W].

A prototype oven was then built based on this oven to allow the control of the

amount of power delivered to each resistance. This experimental oven was built with high

temperature resistant silicon wiring for power supply and data collection of these sensors.

The temperature is measured by six LM35 temperature sensors, one in the middle (for very

accurate temperature measurements of an object under test), one at the front door, one in

the back, and two located on both sides of the oven. Another sensor is located outside

the oven for ambient temperature measurement. They are also rated for full −55[C]to 150[C] range, without need of external calibration, having an accuracy of 0.5[C] at

25[C]. A picture of the oven with sensors is shown in Fig. 2.

2.2 EMBEDDED ELECTRONIC BOARD

The control of the temperature of the oven was made possible by the variation of the

duty cycle of a pulse width modulation (PWM) signal, practically an on-off configuration.

Among many types of converters, the PWM has the better response to deal with on-off

power supply switching [26]. Although the control of the pulse width is very precise, this

method adds uncertainty about the actual value of temperature, if used in an open loop

configuration. So it was necessary not only generate the PWM signal with variable duty

cycle to control the oven, but also to collect the actual temperature precisely, this way

enabling the closed loop control of the oven.

An embedded control board was then built, having an MSP430G2553 microcon-

troller that receives commands from the PC and generate PWM pulses to drive the

zero-cross phototriac driver optocouplers (MOC3063). This square wave PWM control

signal has a frequency of 3 [Hz], with a variable duty cycle defined by the user. These

pulses will determine the amount of power delivered by the high current Triacs (TIC246)

to the resistances of the oven. The schematic of this sector of the embedded board is

presented in Fig. 3.

15

Figure 2 – Oven with sensors.

Figure 3 – Schematic of the connections of the optocoupler and the TRIAC.

The microcontroller is also programmed to collect the data generated by the LM35

sensors, using its internal 10 bits ADC. It transmits this vector of data to the PC as required.

The control software running at the PC was configured to collect sensor temperature

information every second. A synthesis of all elements of the control system is presented in

Fig. 4.

16

Oven

uController

Board

(TI MSP430)

PWM Signal

5 sensors

Ambient Air

Temp.

sensor

Serial

Figure 4 – Synthesis of the embedded electronic board.

Then, from a fixed frequency and variable duty cycle signal of the microcontroller,

embedded circuits optimally switch the 60 [Hz] sine wave from the energy provider for

resistances located at the top and at the bottom of the oven, converging to a dedicated

interface board for signal conditioning composed of regulators, LM358 opamps, and

protection circuits, as shown in Fig. 5.

Figure 5 – Data colletion and power transmission board.

The processing software was built in MATLAB graphical user interface (GUI).

17

2.2.1 Analysis of PWM pulse

The selected method of control of the oven temperature was by varying the duty-

cycle of a PWM pulse. This variation is shown by figures obtained by oscilloscope

time-domain measurements at the point 4 of the Fig. 3 are shown in Figs. 6, 7, 8, showing

the duty cycle at 15%, 50%, and 90% respectively. The input of the MOC3063 requires a

low state to turn the TRIAC on, so a 15% duty cycle means that the TRIAC is on at 85%

of the time, as shown in the figures.

Figure 6 – PWM signal with 15% duty cycle.

Figure 7 – PWM signal with 50% duty cycle.

18

Figure 8 – PWM signal with 90% duty cycle.

It is desirable to know with a good precision the relation of the duty-cycle signal of

the PWM needed to heat up the system and also to stabilize the internal temperature

of the oven in a given temperature. In order to achieve this objective, different pulses

were generated and the temperature achieved was analyzed. After numerous tests, it was

possible to generate a graph that shows the percentage of the duty-cycle needed to stabilize

at different temperatures. This relation is presented in Fig. 9.

0 20 40 60 80 100

0

0.2

0.4

0.6

0.8

Stabilization time

Duty

-cycl

eof

the

PW

M

Pulse Needed to Stabilization

40o

50o

60o

70o

80o

Figure 9 – Relation between temperature and the duty-cycle of the PWM.

19

2.2.2 Equipment set-up and boundary conditions

To ensure the highest accuracy possible in the experiment, few conditions were

established:

• The ambient temperature was set in 28[C] controlled by an air conditioner, in all

trials, to secure no external temperature disturbances;

• The oven was preheated at 30[C] to guarantee an uniform temperature distribution

in entire oven;

• The heating process was defined with two stages of warming and stabilization, with

temperatures of 50[C] and 60[C];

• Restricted use of computer to data collection system, to ensure that all processing is

available to the software, where the data collection is performed at frequency of 1

[Hz].

Table 1 presents the correction factors that were heuristically defined in order to

adjust the duty-cycle of the PWM regarding the ambient temperature. In this work, as we

set the ambient temperature in 28 [C], the correction factor adopted was equal to 0.92.

Thus, the output of the controller is multiplied by those factor.

Table 1 – Environment Temperature Corrections

Temperature Range [ C] Correction Factor

15–20 1.00

20–25 0.96

25–30 0.92

30–35 0.88

20

3 CONTROL DESIGN

Control theory is an interdisciplinary branch of engineering and mathematics that

deals with the behavior of dynamical systems with inputs, and how their behavior is

modified by feedback. The usual objective of control theory is to control a system, often

called the plant, so its output follows a desired control signal, called the reference, which

may be a fixed or changing value. To do this a controller is designed, which monitors the

output and compares it with the reference. The difference between actual and desired

output, called the error signal, is applied as feedback to the input of the system, to

bring the actual output closer to the reference. Some topics studied in control theory are

stability (whether the output will converge to the reference value or oscillate about it),

controllability and observability [27].

Extensive use is usually made of a diagrammatic style known as the block diagram.

The transfer function, also known as the system function or network function, is a

mathematical representation of the relation between the input and output based on the

differential equations describing the system [27,28]

In closed loop control, the control action from the controller is dependent on the

process output. A closed loop controller therefore has a feedback loop which ensures

the controller exerts a control action to give a process output the same as the ”reference

input” or ”set point”. For this reason, closed loop controllers are also called feedback

controllers [27,28].

The output of the system y is fed back through a sensor measurement F to a

comparison with the reference value r. The controller C then takes the error e (difference)

between the reference and the output to change the inputs u to the system under control

P. This is shown in Fig. 10. This kind of controller is a closed loop controller or feedback

controller [27,28].

Figure 10 – Closed-loop control system.

In this work, we consider P as the electrical oven that were described in Chapter 2

- Measurement Setup. The structure C can be assume the Rule Base Control Algorithm

(RBCA), Type-1 Fuzzy Logic Controller (T1FLC) or Type-2 Fuzzy Logic Controller

(T2FLC) and all these models will be described in Chapter 3 - Control Design.

21

The objective of the controller in this work is to perform the control of the output

temperature of an electric oven, Tout[C], as a function of duty-cycle of the PWM . The

Fig. 11 presents the closed-loop control system proposed. To establish efficient results,

three control systems have been proposed.

GUI

Tout [°C]

ControllerSet-point

SystemPWMTset [°C]

Figure 11 – Control system diagram.

3.1 RULE–BASED CONTROL ALGORITHM

The first one presents a rule-based control algorithm (RBCA), as seen in Fig. 12.

This algorithm runs according two main steps:

• Sets temperature ranges equally divided respecting the oven maximum and minimum

temperatures, collecting the instantaneous temperature at the center of the oven,

Tout, and calculates the error, ∆E[C] = Tset − Tout.

• Using this information, it sets limits, summarized between l1 and l4, to determine

the percentage of the duty cycle of the PWM.

This cycle repeats at a frequency of 1 [Hz].

22

Figure 12 – Rule-based control algorithm.

23

3.2 FLS CONTROL ALGORITHMS

The two other controllers are FLSs control algorithms, respectively type-1 fuzzy

logic controller (T1FLC) and type-2 fuzzy logic controller (T2FLC). The T1FLC is chosen

considering the best performance to handle uncertainties, associate with non-linear response

of the oven, i.e. the heating process is described by differential equations.

The inference method was determined as Takagi-Sugeno [29] fuzzy model. Numerous

results on stability analysis, nonlinear control and controller synthesis have been developed

for those models [30–38]. Two inputs were selected. Tout[C] is temperature in sensor five,

which represents the center of the oven, and discriminates stabilization (ST), small (SM),

medium (ME), big (BG) and very big (VB). ∆E[C] is the difference between the setpoint

and actual temperature, and discriminates medium negative (MN), small negative (SN),

zero (ZO), small positive (SP) and medium positive (MP).

The output selected is the duty-cycle of the PWM , %P , and discriminates stabi-

lization (ST), small (SM), medium (ME), big (BG) and very-big (VB). Table 2 presents

the decision matrix to compute the values of %P .

Table 2 – Decision Matrix

∆E

Tout MN SN ZO SP MP

20 ST ST ST SM ME

30 ST ST SM ME ME

40 ST SM ME ME ME

50 SM ME ME ME BG

60 ME ME ME BG VB

70 ME ME BG VB VB

80 ME BG VB VB VB

We consider singleton fuzzification, max-product composition, product implication,

centroid defuzzifier [39] and triangular membership functions.

The input variables Tout, ∆E and the output variable %P are shown in Figs. 13,

14, and 15, respectively. The corresponding ranges are [20,80], [-37.5,37.5], [0,24] Celsius

degrees for Tout and ∆E, and percentage for %P, respectively.

24

Temperature (Celsius)

µT

ou

t

ST SM ME BG VB

20 30 40 50 60 70 80

0.5

1

Figure 13 – Type-1 MF for Tout.

Temperature (Celsius)

µ∆

E

NM NS ZO PS PB

-37.5 -25 -12.5 0 12.5 25 37.5

0.5

1

Figure 14 – Type-1 MF for ∆E.

T2FLC has the potential to handle dynamic uncertainties [40]. In order to deal with

the limitation that exists in defining the membership functions for T1FLC, the concept of

type-2 fuzzy sets is introduced [41]. Researchers have been worked in recent years towards

demonstrating better properties of the T2FLC over the T1FLC [42–46]. In this work, we

present a T2FLC as an extension of T1FLC, and both have the same variables and MFs

ranges.

For T2FLC, we defined gaussian membership functions for Tout and ∆E, as pre-

sented in Figs. 15 and 16. %P presents MF with constant values. T2FLC presents

equivalent sets according as defined for T1FLC. The mean and standard deviation for

each MF of T2FLC are described in Table 3.

Table 3 – T2FLC MF parameters

Variable Left Mean (|m) Right Mean (m|) Deviation (σ)

Tout [28,38,48,58,68] [32,42,52,62,72] 4

∆E [-22.5,-10,-2.5,10,22.5] [-27.5,-15,2.5,15,27.5] 4

25

Percentage

µ%

P

ST SM ME BG VB

0 4 8 12 16 20 24

0.5

1

Figure 15 – Type-1 MF for %P .

Figure 16 – Type-2 MF for Tout.

Figure 17 – Type-2 MF for ∆E.

We chose center of gravity as the method of defuzzification and type-reducing [47].

All T2FLC operators are equivalent to T1FLC.

26

4 EXPERIMENTAL RESULTS

In order to compare the control systems, each test was performed three times, the

average response was saved in a data file. Every attempt was made following the boundary

conditions proposed by establishing two temperature levels, 50[C] and 60[C]. The mean

responses of each controller are arranged in Fig. 18. Although they are not presented here,

the proposed models are consistent and offer similar response for the other temperature

levels.

Based on the experimental results, it is possible to ensure the optimized configura-

tion for the system, in terms of ascertaining the best rising ramp in order to minimize

the percent overshoot. T2FLC presents the better approximation of the desired response,

since it had the minimum rise time with the smallest overshoot. Furthermore it is noticed

that for higher temperatures, a higher heat input is required, to maintain the stabilization

temperature. Moreover, it was observed that even with a minimum pulse, the oven heats

continuously, as long is provided an stabilization value, which is established as 5% of the

duty-cycle of the PWM.

Figure 18 – Response of the controllers.

The three control algorithms accomplished the proposed task, since all reached the

temperature set point and showed some stability. However, considering the purpose of the

work, which is to maximize performance and improve the ability to deal with uncertainties,

RBCA and T1FLC did not show excellent performance.

27

On the other side, the system operating with T2FLC presents an undeniable

accuracy with respect to the uncertainties, having an improved rise time, maximized when

compared to other controllers. Although T2FLC presents a larger rise time than RBCA, it

also shows minimum overshoot, especially caused by the system that controls the value of

the derivative of the rising ramp. Table 4 presents the rise time and the maximum error,

occurred in the overshoot, for the two temperature levels experimented.

Table 4 – Controllers Experimental Results

Parameter RBCA T1FLC T2FLC

Rise Time [s] at 50[C] 585 612 616

Rise Time [s] at 60[C] 1736 2214 1747

Max Error [C] at 50[C] 1.9 0.2 0.1

Max Error [C] at 60[C] 2.7 0.1 0.1

28

5 CONCLUSION

This work presented three different control algorithms, used to perform the control

of the temperature of an electric oven. A comparison was done among RBCA, T1FLC

and T2FLC, and analyzed their effectiveness based on their performance and ability to

deal with uncertainties.

The numerical results, obtained through experiments, showed that the T2FLC

has a better response than any other controller, having an improved rise time, minimum

overshoot and the best performance compared to the experimented control algorithms. It

also showed a continuous response, with a better approximation of the desired result, and

an excellent ability to handle uncertainties.

Future work is to improve the controller by addiction of an neural fuzzy control

algorithm and also prototype an equipment to be integrated into any kind of ovens, in

order to perform the on-line temperature control.

29

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33

APPENDIX A – Publications

This Appendix presents the list of publications.

• L. A. Serapiao, E. P. de Aguiar, A. B. dos Santos, T. V N. Coelho, M. M. B. R.

Vellasco, D. D. Silveira. Type-2 Fuzzy Logic System Applied to a Temperature

Control of an Electric Oven, Neural Computing and Applications, submitted in Sep.

2016, under review.

34

APPENDIX B – Term of Acceptance

TERMO DE ACEITE PARA REALIZACAO DO

TRABALHO DE CONCLUSAO DE CURSO EM LINGUA INGLESA

O presente termo, tem como objetivo acertar entre as partes envolvidas, sendo banca

examinadora, orientador, coorientador e discente, a respeito da confirmacao da realizacao

em lıngua inglesa, do Trabalho de Conclusao de Curso, apresentado ao curso de graduacao

em Engenharia Mecanica, do discente Leonardo Araujo Serapiao, como requisito

parcial para obtencao do tıtulo de Bacharel em Engenharia Mecanica.

E, por estarem, assim, de comum acordo, as partes assinam o presente termo em quatro

vias de igual teor, para ser anexado as copias finais do Trabalho de Conclusao de Curso.

Juiz de Fora, 23 de Novembro de 2016.

Leonardo Araujo Serapiao – DiscenteUniversidade Federal de Juiz de Fora

Prof. Eduardo Pestana de Aguiar – OrientadorUniversidade Federal de Juiz de Fora

Prof. Daniel Discini Silveira – CoorientadorUniversidade Federal de Juiz de Fora

Prof. Washington Orlando Irrazabal BohorquezUniversidade Federal de Juiz de Fora

Prof. Luiz Gustavo Monteiro GuimaraesUniversidade Federal de Juiz de Fora