1. Project Proposal
Liquid Heating Control
Presented to:
Dr. Lamia Iftekhar
Presented By:
Game of Controls
Mohammad Abu Sayed [31]
Arif Md Nasir [32]
Israt Zahan Tamanna [35]
Fall, 2016

2. 1
Acknowledgement:
We, ‘The Game of Controls’ team would like to express my special thanks of
gratitude to my teacher Dr. Lamia Iftekhar who gave us the golden opportunity to
do this wonderful project on the topic ‘Liquid Heat Control’, which also helped us
in gathering a lot of knowledge about so many new things of Control System. This
project helps us to know the use and importance of control system in our real life.

3. 2
Table of Contents
1.0 Overview of the system……………………………………………………………….
1.1 ABSTRACT
1.2 Objectives
3
2.0 INTRODUCTION…………………………………………………………………………… 4
3.0 APPLICATIONS…………………….…………………………………………………….... 5
4.0 Diagram……………………………………………………………………………………….
4.1 Free Body Diagram
4.2 Block Diagram
5
5.0 Modelling…………………………………………………………………………………….
5.1 Mathematical Model
5.2 Transfer Function of The System
7
6.0 Analysis……………………………………………………………………………............
6.1 Pole Zero plot
6.2 Steady state response Graph
10
7.0 Purpose of using controller…………………………………………………………. 12
8.0 Appendix…………………………………………………………………………………...
8.1 Pole Zero Plotting Code
8.2 Steady state response Graphing code
13
9.0 References…………………………………………………………………………………. 16

4. 3
1.0 Overview of the system:
A little discussion about the system is given in abstract and objective.
1.1 ABSTRACT:
Liquid heat system is a thermodynamic process which uses to any kind of energy
resources for heating the liquid from its current temperature to a desire
temperature. It is an automatic storage tank liquid heating system. So, it generates
heat when heat falls of the system. And this system is automatically turned off
when it reaches the desire temperature. There is the assembly of the modeling of
the system, mathematical model with transfer function analysis and other MATLAB
objectives of this liquid heating system.
Keywords: Modelling, Analysis, MATLAB
1.2 Objectives:
Main purpose of liquid heat control system is to control the temperature of a liquid
automatically to save more energy resources, making our system faster by fixing
steady-state error with low cost.

5. 4
2.0 INTRODUCTION:
Heated liquid like water, material, or chemical components are used in domestic or
industrial or medical purpose. Previously, an old unprofessional system was used
to heat any component. So, there was too many wastage and the processes was
also costly. So, the liquid heat control system is the new innovation of science to
reduce the cost and wastage of resources.
There are many types of liquid reactor or heater to melt components. But, storage
tank liquid heater is more professional. It is less costly as well as easy to use.
This liquid heater is a feedback control system. This system measures the
temperature of liquid with a sensor. If temperature is dropped, the heat will be
increased automatically. Voltage is supplied as power and the sensor gives the
temperature value.
The system is used simulation as well as design in a emblematical control system
development. MATLAB is used to simulating system. The graph showing us the
effect of the system response and information. Then, it is analyzed and controlled
the system using proper controller to fix all the errors.

6. 5
3.0 APPLICATIONS:
Liquid heating system is most common in use to do any work easy and faster now-
a-days. Here are some applications of liquid heater.
 Liquid heater mostly use in different types of Industries to melt anything,
like, steel, iron any many other casting process.
 It is using to heat water in house hold instrument like bathtub or shower.
 It is using in many engineering or mechanical instruments.
 Different types of constructions like road constructions.
4.0 Diagram:
Here is the free body diagram and block diagram of the system.
4.1 Free Body Diagram:
The free body diagram of liquid heat control system:
fig 1: Liquid heating system diagram

7. 6
4.2 Block Diagram:
Block diagram of the system:
fig 2: Liquid Heat control system block diagram

8. 7
5.0 Modelling:
Mathematical model and transfer function of the system is given bellow with
proper parameter and values.
5.1 Mathematical Model:
Mathematical Model of this system is:
h V =m C
𝑑𝑇
𝑑𝑡
+
𝑇−𝑇0
𝑅
fig 3: Liquid heat control system

9. 8
Here,
V= applied voltage to the heater;
T= Temperature of the liquid;
𝑇0= Temperature of surrounding;
h= constant provided by the constructor of the heater;
m= The mass of liquid;
C= The heat capacity of liquid;
R= The thermal resistance of tank wall (In this system, tank is made by steel);
5.2 Transfer Function of The System:
Input of the system, u(t)=V(t);
Output of the system, y(t)= T( 𝑡);
So,
h u(t) = m C
𝑑𝑦(𝑡)
𝑑𝑡
+
𝑦(𝑡)−𝑇0(𝑡)
𝑅
;
h u(t) = m C 𝑦̇ (𝑡)+
𝑦(𝑡)−𝑇0(𝑡)
𝑅
;
the temperature of the surrounding in Standard Temperature Pressure (STP)
𝑇0=0 𝑜
𝐶;
so,
h u(t)=m C 𝑦̇ ( 𝑡) +
𝑦(𝑡)−0
𝑅
;

10. 9
h u(t)=m C 𝑦̇ ( 𝑡) +
𝑦(𝑡)
𝑅
;
Let,
L {u(t)}= U(s);
L {y(t)}= Y(s);
Taking Laplace transformation both side,
L {h u(t)} = L {C 𝑦̇ (𝑡) } + L {
𝑦(𝑡)
𝑅
};
h U(s) = C s Y(s) +
1
𝑅
Y(s); [assuming initial conditions are zero]
h U(s) = Y(s) (C s +
1
𝑅
);
𝑌(𝑠)
𝑈(𝑠)
=
ℎ
𝐶 𝑠 +
1
𝑅
h, C and R are constant parameter.

11. 10
6.0 Analysis:
Pole Zero plot and Steady state response Graph is described in analysis part.
6.1 Pole Zero plot:
Use m= 1liter & heat capacity of water as liquid, C=4181.3 J/kg.k, thermal resistance
of steel R= 0.00102c/W to plot the pole zero graph of the system.
graph 1: pole-zero of the system.
In this graph, the pole value is at the left side, where p= - 0.0469.
So, the system is Stable.
Pole-Zero Map
Real Axis (seconds-1
)
ImaginaryAxis(seconds-1)
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
System: k
Pole : -0.0469
Damping: 1
Overshoot (%): 0
Frequency (rad/s): 0.0469

12. 11
6.2 Steady state response Graph:
Use m= 1liter & heat capacity of water as liquid, C=4181.3 J/kg.k, thermal resistance
of steel R= 0.00102c/W to plot the steady state response graph of the system.
graph 2: step response of the system
The system takes 127 seconds to be stable.
Step Response
Time (seconds)
Amplitude
0 20 40 60 80 100 120 140 160 180 200
0
0.2
0.4
0.6
0.8
1
1.2
x 10
-3
System: k
Time (seconds): 127
Amplitude: 0.00102

13. 12
7.0 Purpose of using controller:
From the pole zero plots, this have one pole (p = -0.0469) and it stays on the left
side of the imaginary part. So, the system is Stable. There is no oscillation in our
system.
From Steady state response Graph, it remains 127 seconds to go to the desire
temperature or to be stable. So, this system is little bit slow. Again, from the step
response curve, the steady-state error is (1-.001=0.99) 99% which is very much
large indeed.
So, it is important to use a controller to decrease the rising time of the system and
fixing the steady state error.

14. 13
8.0 Appendix:
The MATLAB codes of the system.
8.1 Pole Zero Plotting Code:
clc; %Pole Zero of the system -- -- Team name: The Game of Controls
close all;
clear all;
h=1; % assuming the constant provided by the constructor of the heater
m=5; % assuming the mass of water
C=4181.3; % assuming the heat capacity of water
R=.00102; % assuming the thermal resistance of the wall
num=[h]; % numerator
den=[m*C 1/R]; % denominator
k=tf(num,den)
[z,p]=tf2zp(num,den)
pzmap(k)
axis([-1 1 -1 1])
k =
1
------------------

15. 14
2.091e04 s + 980.4
Continuous-time transfer function.
z =
Empty matrix: 0-by-1
p =
-0.0469
Published with MATLAB® R2014a

16. 15
8.2 Steady state response Graphing code:
clc; % Steady state response of the system -- -- Team name: The Game of Controls
close all;
clear all;
h=1; % assuming the constant provided by the constructor of the heater
m=5; % assuming the mass of water
C=4181.3; % assuming the heat capacity of water
R=.00102; % assuming the thermal resistance of the wall
k=tf(h,[m*C 1/R]);
step(k)
grid on;
Published with MATLAB® R2014a

17. 16
9.0 References:
 J.L. Guzm´an ,K.J.Astr¨om,S. Dormido,T. H¨agglund ,Y. Piguet, M. Berenguel , Interactive Learning
Learning Module: Basic Modelling and Identification Concepts. Proceedings of the 17th World
Congress The International Federation of Automatic Control Seoul, Korea, July 6-11, 2008.
 K.J. °Astr¨om and T. H¨agglund. Advanced PID Control. ISA - The Instrumentation, Systems, and
Automation Society, Research Triangle Park, NC 27709, 2005.
 http://homepage.mac.com/sami_ashhab/courses/control/lectures/lecture_3/Lecture_3.html.
 MATLAB Software tool 2014a.