Summary
The Temperature measurement of liquid in a tank can be controlled by classical and advance control algorithms applying PID, FUZZY LOGIC , SFB, LQR. Here, we consider a three tank noninteracting system. We observed that tank1 affects the dynamic behavior of tank2. Similarly, tank2 affects the dynamic behavior of tank3 and vice versa, because the flow rate F1 depends on the difference between liquid levels h1and h2. Thus, a change in the inlet flowrate affects the liquid level in the tank, which in turn affects the temperature of the liquid. Basically, it is a thermal process. Various types of temperature sensors include RTD, T/C, and Thermistor. In this particular project the author used a mercury thermometer as sensor. Mathematical models of the three tank method give a third order equation. Each tank gives a transfer function of the first order system. They make it easy to check whether a particular algorithm is giving the requisite results. A lot of work has been carried out on the temperature control in terms of its stabilization. Many attempts have been made to control the response of temperature measuring systems.
Excerpt
Table Of Contents
iv
CHAPTER 4- LINEAR QUADRATIC REGULATOR [LQR]
SECTION 4.1- INTRODUCTION ... 22
SECTION 4.2- DESIGN OF RICCATI EQUATION FOR LQR CONTROLLER ... 22
SECTION 4.3- DIFFERENT VALUES OF LINEAR QUADRATIC REGULATOR ... 23
SECTION 4.4- STEP RESPONSE OF THE SYSTEM BY LQR CONTROLLER ... 24
SECTION 4.5- CONCLUSION ... 25
SECTION 4A- NEURAL NETWORK & SOFT COMPUTING TECHNIQUE ... 26
CHAPTER 5- FUZZY LOGIC BASED CONTROLLER [FLC]
SECTION 5.1- INTRODUCTION ... .28
SECTION 5.2- APPLICATION OF FUZZY LOGIC ... 29
SECTION 5.3- PROPERTIES OF FUZZY SET ... 30
SECTION 5.4- PROPERTIES OF CRISP SET ... 30
SECTION 5.5- FUZZY LOGIC OPERATOR ... 31
SECTION 5.6- FUZZY INFERENCE ENGINE ... 31
SECTION 5.7- DESIGN OF FUZZY LOGIC CONTROLLER FOR CONTROLLING
TEMPERATURE ... 32
SECTION 5.8- THE RULE VIEWER ... 34
SECTION 5.9- SIMULINK BLOCK DIAGRAM OF FLC ... 35
SECTION 5.9.1- RESPONSE OF FUZZY LOGIC CONTROLLER ... 36
SECTION 5.9.2- CONCLUSION ... 36
CHAPTER 6- APPENDIX
SECTION 6.1- FUTURE STUDY ... 38
SECTION6.2- MATLAB PROGRAMS ... 39
REFERENCES & BOOKS ... 41
1
CHAPTER 1
Temperature Measurement System
2
1.0 INTRODUCTION:
The Temperature measurement of liquid in a tank can be controlled by classical and advance control
algorithm PID,FUZZY LOGIC ,SFB, LQR.Here we considering a three tank noninteracting system.We
observed that tank1 affects the dynamic behavior of tank2,similarly for tank2 affects the dynamic
behavior of tank3 and vice versa, because the flow rate F
1
depends on the difference between liquid
levels h
1
and h
2
.Thus a change in the inlet flowrate affects the liquid level in the tank,which inturn affects
the temperature of the liquid. Basically it is a thermal process.Various types of temperature sensor
RTD,T/C, Thermistor. In that particular project we used a mercury thermometer as sensor. Mathematical
models of three tank method give a third order equation. Each tank give a transfer function of first order
system. They make it easy to check whether a particular algorithm is giving the requisite results. A lot of
work has been carried out on the temperature control in terms of its stabilization. Many attempts have
been made to control the response of temperature measuring system..
1.1 TANK
SYSTEM:
The system comprises of a mercury-in-glass thermometer placed in a liquid tank to measure the
temperature of the liquid which is heated by steam through a coil system. The temperature of the
liquid(T
F
)varies with time. T is the temperature of the mercury in the well of the thermometer. The
following assumptions are made to determine the transfer function relating the variation of the
thermometer(T) for change in the temperature of the liquid(T
F
) .
(1)The expansion or contraction of the glass walled well containing mercury is negligible(that means the
resistance offered by glass wall for heat transfer is negligible)
(2)The liquid film surrounding the bulb is the only resistance to the heat transfer.
(3)The mercury assumes isothermal condition throughout.
Fig.1.1 a- Diagram of a Temperature Control Tank system
3
1.2 TRANSFER FUNCTION MODELING:
Applying unsteady state heat balance for the bulb,we get
Input heat rate- Output heat rate=Rate of heat accumulation
Fig 1.2 a-Diagram of Three Tank Liquid Filled System
(
F
- ) - 0 =
P
(
F
- ) =
P
---------------------------(1)
Where , A=surface area of the bulb for heat transfer in m
2
M=Mass of mercury in the bulb,kg
C
P
=Heat capacity of the mercury in kj/kg k
U=Film heat transfer coefficient kw/m
2
k
At steady state,the equation(1) can be rewritten as-
(
FS
T
F
) = 0-------------------------------(2)
4
Substracting equation (2) from equation (1)
[(
F
-T
FS
)-(T-T
S
)] = M C
P
(
)
Defining the deviation variables,
F
-T
FS
= T
F1
and T-T
S
= T
1
and substituting in the above equation ,we get,
(
F1
-T
1
) = M C
P
F1
-T
1
= M
-----------------------------(3)
Defining time constant t
p
for the Thermometer,
p
= M
Equation (3) can be rewritten as-
F1
-T
1
=
p
--------------------------------(4)
Taking laplace transform,we get-
F1
(S)-T
1
(S) =
p
s T
1
(S)
( )
( )
=
--------------------------------transfer function of tank. Similarly, for tank2 & tank3 we can able
to get a first order system. So we can able to say that the entire system is a third order system. Here we
can able to construct overall transfer function of the three tank system is-
( ) =
1
(S) *
2
(S) *
3
(S)
=(
) *(
) * (
)
As per our problem ,let us assume-
=time constant for tank1=0.5 miniute
=
time constant for tank2=1.2 miniute
=time constant for tank3=1.5 miniute
5
=0.25 min
=0.30 min
=0.35 min
( ) =
.
.
.
.
-------------------Transfer Function
This transfer function is called plant transfer function.
1.3 OBJECTIVE:
The goal is to determine which control strategy delivers better performance with respect to
temperature as reference input. The non-linearized model can be simulated directly using the
Mat lab application to see result. Therefore, in this project, Three types of controllers will be
simulated. These three controllers can divided into three categories:
1. Conventional Controller: Proportional Integral Derivative (PID) Controller
2. Intelligent Controller: Fuzzy Logic Controller (FLC)
3. Advance Controller: Linear Quadratic Regulator (LQR)
1.4 SCOPE OF THIS THESIS:
The thesis contains six chapters.
Chapter 1 represents introduction, modeling of three tank system,transfer function modeling,scope,
literature review
Chapter 2 presents the initial system response.
Chapter 3 represents a brief description of the PID controller and also different kinds of response curve,
Ziegler Nichols method,tuning.
Chapter 4 indicate an advance controller LQR for stabling the system response at different values
Chapter 5 it consists of FLC, membership function, properties & crisp set, knowledge & rule base,
defuzzification, simulink, response.
Chapter 6 represents the matlab programs, journals, references, book etc.
6
1.5 LITERATURE SURVEY:
From review of literature,it appears that work in that field was carried out by Yunseo Ki [1](2001) .He
performed a lot of experiment on control of temperature by using Fuzzy logic controller. Performance of
the FLC was evaluated and compared with a conventional PID controller. He construct an input
sensor to measure temperature using a thermocouple design an amplifier to magnify input signal
from the thermocouple, construct an output actuator to provide a heating source, design amplifier
to magnify output signal from the computer.
V.Kumar,K.P.S. Rana,V.Gupta[2](2008) , experimented in this paper that how to implement in real time a
fuzzy PD & PI controller and comprise between them.
Quang and Negenevitskyet.al.[3] have proposed a scheme to tune the PI controller in Cascade loop
with Fuzzy Logic.They have given the simulation result only.
Anabik Shome,Dr.S.Denis Ashok[4] (2012),presented a research paper to control thehigh temperature
for boiler. They examined that there are several reasons for using automatic temperature controls
for steam applications.For some processes, it is necessary to control the product temperature to within
fairly close limits to avoid the product or material being processed being spoilt.Steam flashing from
boiling tanks is a nuisance that not only produces unpleasant environmental conditions, but also
damage the fabric of the building. Automatic temperature controls can keep hot tanks just below
temperature.Also for economy, quality and consistency of production, sav-ing in manpower, comfort
control, safety and to optimize rates of production in industrial processes boiler temperature control is
necessary. Conventional control system in power station adopts PID controller.Unfortunately, large
inertiaand lag appear, when we use PID controller which could not adjust the temperature to good
scope.
Klir,G.J. & Yuan,B.[5] ,gave us basic idea about fuzzy logic & its application. We used this book as
reference to get the basic idea about fuzzy logic.In this context, FL is a problemsolving control system
methodology that lends itself to implementation in systems ranging from simple, small, embedded
microcontrollers to large, networked, multichannel PC or work station based data acquisition and
control systems.
Darko Grundler[6], presented a new method is described for complex process control with the
coordinating control unit based upon a genetic algorithm. The algorithm for t he control of
complex processes controlled by PID and fuzzy regulators at the first level and a coordinating unit
at the second level has been theoretically laid out. A genetic algorithm and its application to the
proposed control method have been described in detail.The idea has been verified experimentally and
by simulation in a two stage.
R. Murillo Garciaet.al.[7] have described in this paper the use of Simulink Target for Real-Time Linux (ST-
RTL) to control over a network a horizontal driven inverted pendulum. ST-RTL is an application
developed to provide a cost-effective alternative to the expensive real-time applications that require
specialized software and hardware. A performance comparison with the commercial Windows based
7
version Real-Time Windows Target has also been carried out. The conclusions will show that ST-RTL is a
preferable tool since not only does it perform as well as RTWT, but it also includes remote networking
capabilities to the system.
MehrsanJavan-Roshtkhari et.al. [8] designed an emotional-learning controller which was mentored by
an existing model based controller. In the learning phase they prepared the controller to behave as a
mentor while preventing any instability. Then the controller was softly switched from model based to
emotional one, using a Fuzzy inference system. They presented a new approach in employing model
free controller with learning ability based on soft switching between two phases of learning.
Aritra De(2012)et.al.[9] represents her paper as how to control the error of water temperature in a tank
and correction of this error using microcontroller.This method is very useful for any ambiguous system.
Professor Lotfi Zadeh(1973) [10]proposed the concept of linguistic or "fuzzy" variables. Think of them as
linguistic objects or words, rather than numbers. The sensor input is a noun, e.g. "temperature",
"displacement", "velocity", "flow", "pressure", etc. Since error is just the difference, it can be thought of
the same way.
Ang, K.H., G.C.Y. Chong and Y. Li(2005)[11] presented their paper to discuss how PID controller effect
the system response of any order plant transfer function and they showed how different values of
controller parameters effect the response of the system.
Brian R Copeland et.al.(2008)[12] described in his paper how we have to take the controller parameters
value for step response by Ziegler & Nichols method.He used a closed loop transfer function
8
CHAPTER 2
INITIAL SYSTEM RESPONSE
9
2.0
STEP RESPONSE OF THE SYSTEM:
The step response of a system in a given initial state condition is given below.So,it is clear that system
response is unstable.Now we have to design several controller with their proper optimization & tuning.
Fig 2.1 a.:-
Response of Plant due to step input
2.1 CONCLUSION:
It is concluded from above response that system response is oscillated and hence the system is unstable.
For this we have to design several controller to control the unstable step response into a stable
response.
10
CHAPTER 3
PROPORTIONAL-INTEGRAL-DERIVATIVE CONTROLLER [PID]
Details
- Pages
- Type of Edition
- Erstausgabe
- Year
- 2013
- ISBN (PDF)
- 9783960675303
- File size
- 1.2 MB
- Language
- English
- Institution / College
- Asansol Engineering College – WBUT
- Publication date
- 2016 (April)
- Grade
- M.TECH.
- Keywords
- Fuzzy Logic Temperature Measurement Liquid temperature Tank system Proportional Derivative Integral Controller Temperature control MATLAB
