Book, intelligent hvac contror for high energy efficiency in buildings

Intelligent HVAC Systems Control for High Energy Efficiency and
Comfortable Buildings
By
RAAD Z. HOMOD
And
KHAIRUL SALLEH MOHAMED SAHARI
2014

I dedicated this book to my beloved mother, father, wife and children

i
ACKNOWLEDGMENT
First and foremost, we are very grateful to Allah for giving us the
strength, good health and allowing us to complete this book.
We would like also to express our appreciation to many people
who helped significantly in preparing this book. First, we would like
to sincerely thank our friends Dr. Haider A.F. Almurib and Dr.
Farrukh Hafiz Nagi for their help and advice on the subject area of
artificial intelligent controls and their application. And then we
would like to thank our friends inside and outside of petroleum
engineering faculty in Basrah University and Universiti Tenaga
Nasional.
We would also like to thank the Ministry of Higher Education
Malaysia for their support under the FRGS research grant.
Finally, we would like to express our great appreciation for our
parents and family for their patience and encouragement. Last but not
least, we wish to give our sincere gratitude and deepest love to our
wives and children for their continuous love and support, which
enabled the completion of this book.
Authors

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TABLE OF CONTENTS
Page
ACKNOWLEDGMENT....................................................................................... I
TABLE OF CONTENTS......................................................................................II
LIST OF FIGURES ............................................................................................ VII
LIST OF TABLES.................................................................................................X
LIST OF NOMENCLATURE, SYMBOLS AND ACRONYMS......................XI
1- LIST OF ABBREVIATIONS .......................................................................................XI
2- LIST OF SYMBOLS.................................................................................................XII
3- SUBSCRIPTS..........................................................................................................XV
CHAPTER 1 INTRODUCTION........................................................................... 1
1.1 INTRODUCTION .................................................................................................... 1
1.1 THE HVAC SYSTEMS MODEL ............................................................................. 1
1.1.1 Mathematical model of HVAC system.................................................. 2
1.1.2 Black box model of HVAC system........................................................ 3
1.1.3 Gray-box models of HVAC system....................................................... 4
1.2 THE HVAC SYSTEM CONTROL ............................................................................ 5
1.3 THE HVAC SYSTEM SIMULATION ....................................................................... 6
1.4 PROBLEM STATEMENT......................................................................................... 7
1.5 BOOK OBJECTIVES............................................................................................... 8
1.6 SCOPE OF STUDY.................................................................................................. 9
1.7 BOOK OUTLINE ................................................................................................... 10
1.8 SUMMARY........................................................................................................... 11
CHAPTER 2 HVAC SYSTEM LITERATURE REVIEW............................. 12
2.1 INTRODUCTION ................................................................................................... 12
2.2 BUILDING AND AHU MODEL .............................................................................. 12
2.2.1 The evolution of modelling HVAC system .......................................... 14
2.2.2 Mathematical model.............................................................................. 15
2.2.3 Black box model ................................................................................... 17
2.2.4 Gray box model..................................................................................... 19
2.3 INDOOR THERMAL COMFORT MODEL .................................................................. 20

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2.3.1 The evolution of thermal comfort ......................................................... 21
2.3.2 The predicted mean vote (PMV) index................................................. 22
2.3.3 PMV models ......................................................................................... 23
2.4 HVAC SYSTEM CONTROL .................................................................................. 26
2.4.1 The evolution of HVAC system control ............................................... 26
2.4.2 PID control for HVAC system.............................................................. 27
2.4.3 Fuzzy logic control for HVAC system ................................................. 30
2.5 THE SHORTCOMING IN PREVIOUS WORKS AND ALTERNATIVES.......................... 33
2.5.1 Modelling of building and AHU........................................................... 33
2.5.2 Modelling of indoor thermal comfort ................................................... 34
2.5.3 The control algorithms.......................................................................... 36
2.6 SUMMARY........................................................................................................... 37
CHAPTER 3 MODELLING OF HVAC SYSTEM ........................................... 39
3.1 INTRODUCTION ................................................................................................... 39
3.2 MODIFICATION OF HVAC SYSTEM ..................................................................... 40
3.3 BUILDING AND AHU MODEL .............................................................................. 40
3.3.1 System description ................................................................................ 43
3.3.2 Modeling approach ............................................................................... 44
i. Thermal transmittance ................................................................................ 44
ii. Moisture transmittance .............................................................................. 45
iii. Model linearization................................................................................... 45
3.3.3 Model development............................................................................... 46
i. Pre-cooling coil........................................................................................... 47
ii. Mixing air chamber.................................................................................... 50
iii. Main cooling coil...................................................................................... 53
iv. Building structure...................................................................................... 55
a) Opaque surfaces...................................................................................... 55
b) Transparent fenestration surfaces........................................................... 59
c) Slab floors................................................................................................ 64
v. Conditioned space...................................................................................... 66
3.4 INDOOR THERMAL COMFORT MODEL................................................................... 71
3.4.1 General idea .......................................................................................... 73
3.4.2 Data pre-processing............................................................................... 75
3.4.3 Identification of TS model .................................................................... 75
3.4.4 Tuning of TS model .............................................................................. 78

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3.5 SUMMARY........................................................................................................... 80
CHAPTER 4 CONTROL OF HVAC SYSTEM................................................. 82
4.1 INTRODUCTION ................................................................................................... 82
4.2 DESIGN AND STRUCTURE OF TSFF CONTROLLER................................................ 83
4.3 TS CONTROL MODEL........................................................................................... 85
4.3.1 The related factors for input/output data sets........................................ 85
4.3.2 General idea for clustering outputs ....................................................... 86
4.3.3 Identification of TS model .................................................................... 87
4.3.4 Offline learning of TS model................................................................ 89
4.4 ONLINE TUNING PARAMETERS ............................................................................ 91
4.5 SUMMARY........................................................................................................... 95
CHAPTER 5 SIMULATION OF HVAC MODEL AND CONTROL.......... 96
5.1 INTRODUCTION ................................................................................................... 96
5.2 SIMULATION ENVIRONMENT ............................................................................... 96
5.3 SIMULATION OF THE BUILDING AND AHU MODEL .............................................. 99
5.3.1 Subsystem block diagram .................................................................... 101
5.3.2 Overall block diagram model............................................................... 102
5.3.3 HVAC system Model validation.......................................................... 106
5.4 SIMULATION OF THE INDOOR THERMAL COMFORT MODEL ................................. 107
5.4.1 Parameters and weight layers identification procedures...................... 108
5.4.2 TS Model validation............................................................................. 109
5.4.3 Application to combined PMV with building Model .......................... 109
5.5 SIMULATION OF THE TSFF CONTROL................................................................. 113
5.5.1 TS control model layers identification procedures .............................. 113
5.5.2 TS control model validation................................................................. 114
5.5.3 Online tuning parameters and weight .................................................. 114
5.6 SIMULATION OF THE ENERGY SAVING AND MODEL DECOUPLING ....................... 116
5.6.1 Energy saving calculation .................................................................... 117
5.6.2 The model decoupling.......................................................................... 125
5.7 SUMMARY.......................................................................................................... 127
CHAPTER 6 ANALYSIS OF RESULTS ......................................................... 129
6.1 INTRODUCTION .................................................................................................. 129
6.2 BUILDING AND AHU MODEL ............................................................................. 129
6.2.1 Open loop response.............................................................................. 130

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6.2.2 Psychrometric process line analyses.................................................... 131
6.2.3 Validation of the hybrid modeling method.......................................... 132
6.2.4 Case study: evaluation of hybrid ventilation........................................ 133
i. Ventilation at daytime................................................................................ 135
ii. Ventilation at night................................................................................... 137
iii.Psychrometric process line analyses ........................................................ 138
iv. The PMV comparison .............................................................................. 140
6.3 INDOOR THERMAL COMFORT MODEL.................................................................. 143
6.3.1 Defining the range of comfort temperature.......................................... 144
6.3.2 Comparing thermal sensation comfort with temperature..................... 146
6.4 TSFF CONTROL ................................................................................................. 148
6.4.1 Nominal operation conditions.............................................................. 149
6.4.2 Validating robustness and disturbance rejection.................................. 153
6.4.3 The sensitivity of noise and sensor deterioration................................. 154
6.5 SUMMARIZED PERFORMANCE RESULTS.............................................................. 158
6.6 ENERGY SAVING AND MODEL DECOUPLING........................................................ 162
6.6.1 Model decoupling ................................................................................ 163
6.6.2 Energy saving....................................................................................... 165
6.7 SUMMARY.......................................................................................................... 168
CHAPTER 7 CONCLUSIONS AND FUTURE WORKS ............................. 170
7.1 INTRODUCTION .................................................................................................. 170
7.2 CONCLUSION ..................................................................................................... 170
7.2.1 Modelling of building and AHU.......................................................... 171
7.2.2 The indoor thermal comfort model ...................................................... 172
7.2.3 TSFF control algorithm........................................................................ 173
7.3 RECOMMENDATION FOR FUTURE WORKS ........................................................... 174
7.3.1 Modelling of building and AHU.......................................................... 174
7.3.2 The indoor thermal comfort model ...................................................... 175
7.3.3 TSFF control algorithm........................................................................ 175
LIST OF REFERENCES..................................................................................... 177
APPENDICIES..................................................................................................... 196
APPENDIX A: DERIVING PRE-COOLING COIL TRANSFER FUNCTION .......................... 196
APPENDIX B: DERIVING MIXING AIR CHAMBER TRANSFER FUNCTION..................... 201
APPENDIX C: DERIVING MAIN COOLING COIL TRANSFER FUNCTION ........................ 204

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APPENDIX D: DERIVING CONDITION SPACE TRANSFER FUNCTION............................ 210
APPENDIX E: THE INPUT FACTORS FOR THE BUILDING AND AHU MODEL................ 217
APPENDIX F: DERIVING THE MODEL TRANSFER FUNCTION ...................................... 229
APPENDIX G: CONVERT THE MODEL TRANSFER FUNCTION TO EXPLICIT .................. 235
APPENDIX H: THE LAYERS PARAMETERS AND WEIGHT ARE CALCULATED BY
MATLAB M-FILE...................................................................................................... 255

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LIST OF FIGURES
Page
Figure 1.1 Illustrate model staircase boxes with complexity and SNR.................... 2
Figure 1.2 The main fields of the HVAC system.................................................... 10
Figure 2.1 The main framework of the book........................................................... 13
Figure 3.1 Flowchart for the design of HVAC systems .......................................... 41
Figure 3.2 Representation of subsystem using control volume concept for
prototypical buildings with HVAC system ............................................................. 44
Figure 3.3 Thermal and moisture variation through pre-heat exchanger ................ 47
Figure 3.4 Thermal and moisture variation through air mixing chamber ............... 50
Figure 3.5 Heat transfer by face temperature difference......................................... 57
Figure 3.6 Heat transfer through fenestration and windows ................................... 61
Figure 3.7 Heat and humidity flow in/out of conditioned space ............................. 69
Figure 3.8 Basis and premise membership functions with relation to cluster
centers...................................................................................................................... 74
Figure 3.9 Tuning schedule of GNMNR for the TS model..................................... 75
Figure 3.10 Parameter values of a with respect to and , ............................... 77
Figure 3.11 The TS model structure........................................................................ 78
Figure 4.1 Control structure of TSFF...................................................................... 84
Figure 4.2 Basis and premise membership functions in relation to main
cooling coil clustering data...................................................................................... 87
Figure 4.3 The TS model structure.......................................................................... 89
Figure 4.4 Offline learning schedule of GNMNR for the TS model....................... 90
Figure 5.1 The geometry of the building chosen to get model parameters ............ 101
Figure 5.2 Subsystems model block diagram......................................................... 102
Figure 5.3 Simulation model for subsystem buildings and AHU........................... 103
Figure 5.4 HVAC system model block diagram .................................................... 104
Figure 5.5 Indoor temperature response to outdoor temperature variation............ 107
Figure 5.6 Indoor relative humidity response to outdoor humidity ratio
variation.................................................................................................................. 107

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Figure 5.7 Compared PPD performance with TS and Fanger’s model.................. 109
Figure 5.8 Comparison of absolute error for TS and Fanger’s model.................... 110
Figure 5.9 The TS model response......................................................................... 111
Figure 5.10 Schematic diagram of condition space reference control ................... 113
Figure 5.11 Comparison of chilled water flow rate between TS model and
calculated result with absolute error....................................................................... 115
Figure 5.12 Simulation diagram for TSFF online tuning....................................... 116
Figure 5.13 Matlab block diagram for three systems simulations.......................... 127
Figure 6.1 HVAC plant open loop response for indoor temperature and
humidity ratio ......................................................................................................... 130
Figure 6.2 HVAC plant open loop response for indoor temperature and
relative humidity..................................................................................................... 131
Figure 6.3 Indoor thermodynamic properties transient response for whole
building and HVAC plant....................................................................................... 131
Figure 6.4 Complete HVAC cycle and transient model response.......................... 133
Figure 6.5 Indoor temperature and humidity ratio response to real outdoor
variation.................................................................................................................. 134
Figure 6.6 Indoor temperature and humidity ratio response to natural and
mechanical ventilation of daytime.......................................................................... 136
Figure 6.7 Indoor temperature and relative humidity response to natural and
mechanical ventilation of daytime.......................................................................... 137
Figure 6.8 Indoor temperature and humidity ratio response to natural
ventilation at night.................................................................................................. 138
Figure 6.9 Indoor temperature and relative humidity response to natural
ventilation at night.................................................................................................. 139
Figure 6.10 The ideal and real process line for night and day natural
ventilation............................................................................................................... 140
Figure 6.11 Indoor temperature and PMV comparison results between the
two types of ventilation .......................................................................................... 141
Figure 6.12 The optimization result for the indoor temperature and PMV............ 143
Figure 6.13 The PPD as a function of the operative temperature for a
typical summer and winter situation....................................................................... 145
Figure 6.14 The difference between the temperature and PPD by the
response of the open loop system of the TS model................................................ 146

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Figure 6.15 Cycle path indoor temperature within 24 hours compared with
PMV ....................................................................................................................... 147
Figure 6.16 The effect of relative humidity on the PPD ........................................ 148
Figure 6.17 Comparison of the control performances of the HVAC system
process with TSFF, normal Sugeno and hybrid PID-Cascade controllers ............. 151
Figure 6.18 Comparison of the indoor temperature behavior for TSFF,
normal Sugeno and hybrid PID-Cascade controllers ............................................. 152
Figure 6.19 Comparison of the indoor relative humidity behavior for TSFF,
normal Sugeno and hybrid PID-Cascade controllers ............................................. 152
Figure 6.20 Comparison of the control signal variation for the main cooling
coil chilled water valve for TSFF, normal Sugeno and hybrid PID-Cascade
controllers............................................................................................................... 153
process for the robustness and disturbance rejection.............................................. 154
Figure 6.22 Comparison of the indoor temperature behavior of the HVAC
system process for the robustness and disturbance rejection ................................. 155
Figure 6.23 Comparison of the output control signal of the HVAC system
process for the robustness and disturbance rejection.............................................. 155
process due to applied noise and sensor deterioration............................................ 157
Figure 6.25 Comparison between three temperature curves of the HVAC
system process due to applied noise and sensor deterioration ............................... 157
Figure 6.26 Comparison of the output control signal of the HVAC system
process due to applied noise and sensor deterioration............................................ 158
Figure 6.27 PMV Comparison results between the three different system
designs .................................................................................................................... 164
Figure 6.28 Indoor temperature comparison results between the three
different system designs ......................................................................................... 165
Figure 6.29 Indoor relative humidity comparison results between the three
Figure 6.30 Controllers’ signal comparison results between the three
Figure 6.31 Comparison results of the consumed energy by the cooling coil
load between the three different system designs .................................................... 166
Figure 6.32 Comparison results of the power consumption between the
three different system designs ................................................................................ 168

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LIST OF TABLES
Page
Table 3.1 Input parameters range and increments................................................... 76
Table 5.1 Material properties of model building construction............................... 100
Table 6.1 Performance indices comparison results for three types
ventilation strategies............................................................................................... 142
Table 6.2 ASHRAE Standard recommendations [132].......................................... 145
Table 6.3 Performance indices results for hyprid and TS model ........................... 159
Table 6.4 Performance indices comparison results of TSFF, hybrid PID and
fuzzy fixed for controlling indoor PMV in nominal state of operation.................. 160
fuzzy fixed for controlling indoor PMV under disturbance ................................... 160
fuzzy fixed for controlling indoor PMV under noise and sensor
deterioration conditions.......................................................................................... 161

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LIST OF NOMENCLATURE, SYMBOLS AND ACRONYMS
1- List of Abbreviations
AHU Air Handling Unit
AI Artificial Intelligent
ANN Artificial Neural Network
ARMA AutoRegressive Moving Average
ARMAX AutoRegressive Moving Average with eXogenous
input
ARX Auto-Regressive model structure with eXogenous
inputs
ASHRAE American Society of Heating, Refrigerating, and Air-
conditioning Engineers
BJ Box–Jenkins
CAV Constant Air Volume
COG Centre Of Gravity
DDC Direct Digital Control
ET Effective Temperature
FIS Fuzzy Inference System
FLC Fuzzy Logic Control
FTC Fault Tolerant Control
GA Genetic Algorithm
GNMNR Gauss-Newton Method for Nonlinear Regression
HVAC Heating, Ventilation, and Air Conditioning
IMC Internal Model Control
LPC Linear Predictive Control
LQR Linear Quadratic Regulator
MIMO Multi-Input Multi-Output
MPC Model Predictive Control
NNARX Neural Network based nonlinear AutoRegressive
model with eXternal inputs
OpT Operative Temperature
PID proportional, integral and derivative
PMV Predicted Mean Vote

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PPD Predicted Percentage of Dissatisfaction
RELS Recursive Extended Least Squares
RLF Residential Load Factor
SISO Single-Input Single-Output
SNR Signal-to-Noise Ratio
TAR Thermal Acceptance Ratio
TSFF Takagi-Sugeno Fuzzy Forward
TSFIS Takagi-Sugeno Fuzzy Inference System
VAV Variable Air Volume
VWV Variable Water Volume
2- List of Symbols
surface area,
fenestration area (including frame),
building exposed surface area, and unit
leakage area,
the set of linguistic terms
Building and flue effective leakage area,
area of slab floor,( )
net surface area,
and fuzzy parameters function
C heat capacitance,
DR cooling daily range, K
The rate of change in the total storage energy of
the system,
Total energy entering the system,
Total energy leaving the system,
L length
mass of air in mixing box, in heat exchanger, heat
exchanger, and wall,
specific heat of moist air, heat exchanger, water
and wall,
mass flow rate of ventilation, return, mixing air at
time t,
heat capacitance of air for mixing air chamber,

xiii
Mixing, outside, outside supply, return and
supply air stream temperature at time t,
Wall, Heat exchanger and chilled water out in
temperature at time t,
Wall and glass windows inside and outside
temperature at time t,
Humidity ratio of supply, mixing, outside, outside
supply and return air stream,
Water latent heat of vaporization,
Internal/external heat transfer coefficient,
opaque surface and slab cooling load, W
CF surface cooling factor,
U construction U-factor,
cooling design temperature difference, K
opaque-surface cooling factors
fenestration cooling load and sensible infiltration
heat transfer rates, W
slab cooling factor, ( )
Heat capacitance of slab floors, (J/k).
surface cooling factor,
Fenestration (National Fenestration Rating
Council) U-factor,
the matrix of partial derivatives of the function
Gradient of error
Change in error
cooling design temperature difference, K
the vector parameters matrix
the step length along the steepest ascent axis
peak exterior irradiance, including shading
modifications,
fenestration rated or estimated NFRC solar heat
gain coefficient
interior shading attenuation coefficient
fenestration solar load factor
peak total, diffuse, and direct irradiance,

xiv
Transmission of exterior attachment (insect
screen or shade screen)
fraction of fenestration shaded by permanent
overhangs or fins
site latitude, °
exposure (surface azimuth), ° from south (–180 to
+180)
shade line factor from
depth of overhang (from plane of fenestration), m
vertical distance from top of fenestration to
overhang, m
height of fenestration, m
shade fraction closed (0 to 1)
interior attenuation coefficient of fully closed
configuration
infiltration air volumetric flow rate,
,
infiltration driving force for cooling and heating,
Sensible and latent cooling load from internal
gains, W
conditioned floor area of building,
number of occupants (unknown, estimate as
+ 1)
number of bedrooms (not less than 1)
mass of furniture and conditioned space-air, kg
specific heat of furniture and air,
thermal resistance,
temperature of the furniture, k
roof solar absorptance
Time constant, Sec.
infiltration coefficient
Icl thermal resistance of clothing, (m2
k/w)
fcl
ratio of the surface area of the clothed body to the
surface area of the nude body
m the number of input variables
the rule linguistic values
the antecedent variable

xv
W external work, (w/m2
)
trr the room mean radiant temperature, (°C)
va the relative air velocity (m/s),
tcl the surface temperature of clothing, (°C)
Ps
saturated vapor pressure at specific temperature,
(pa)
RH the relative humidity in percentage
consequents of the fuzzy rule piece-wise outputs
N the set of linguistic terms,
Pa the water vapour presure, (pa)
the consequent upon all the rules
fuzzy basis functions
indoor-outdoor humidity ratio difference,
3- Subscripts
a air
c characteristic
air in mixing box/ main cooling coil
i inside or rule number
j the cluster number
heat exchanger
the number of tuning iterations
air in heat exchanger
leakage
Glass
heat of vaporization
infiltration
fenestration
f Indoor and outdoor
t at time t
flue effective
exposed
unit leakage

xvi
mHe main heat exchanger
internal gains
latent
sensible/ supply
furniture
closed
slb slab floor
o outside
opaque
outside supply
out Outside room
r room/ return
room Inside room
w water
Win water input
Wout water output
wall

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CHAPTER 1
Introduction
1.1 Introduction
The study of the Heating, Ventilation, and Air Conditioning (HVAC)
system is a broad topic because of its relationship with environmental,
economical and technological issues. This study is concerned with indoor
thermal sensation, which is related to the model of building, HVAC
equipments, indoor thermal and control. Therefore, this chapter will briefly
review the general aspects of relevant subjects for indoor thermal sensation.
1.1 The HVAC Systems Model
The HVAC system modelling implies to the modelling of building, indoor,
outdoor, as well as HVAC equipments. It is normally difficult for one
HVAC system's model to be completely comprehensive. Therefore, it is
possible to divide the comprehensive model into a sub-model which may
be appropriate in some instances. The key to any successful indoor thermal
analysis lies upon the accuracy of the model of the indoor conditioned
space within building and HVAC equipments.
The simple hand-calculation methods were available to find out the
cooling/heating load until the advent of computer simulation programs for
HVAC systems in the mid of 1960s. The first simulation methods

2
attempted were to imitate physical conditions by treating variable time as
the independent [1]. Most of the earliest simulation methods were based on
a white or mathematical (physical) models, which are preferred over other
models such as a black box and gray box model because they are easy to
analyse even though they are complex than others as shown in Figure 1.1.
Model boxes in Figure 1.1 are based on the complexity versus the fidelity
of the model or signal-to-noise ratio (SNR) [2].
Figure 1.1 Illustrate model staircase boxes with complexity and SNR
1.1.1 Mathematical model of HVAC system
There are two types of the white box or mathematical model; the lumped
and distributed parameter. The main advantage of a lumped parameter
model is it is much easier to solve than a distributed model.

3
The mathematical models are very popular for HVAC systems to represent
the processing signal. The processes' signals are constructed based on
physical and chemical laws of conservation, such as component, mass,
momentum and energy balance. These laws describe the linking between
the input and output which is transparently represented by a large number
of mathematical equations. Furthermore, the mathematical model is a good
tool to understand the behaviour of the indoor condition by describing the
important relationships between the input and output of the HVAC system.
In general, the modelling process of HVAC systems leads to dynamic,
nonlinear, high thermal inertia, pure lag time, uncertain disturbance factors
and very high-order models. The whole model can be described by several
sub-models to alleviate the complexity of the model [3]. These sub-model
processes are related to fluid flow and heat-and-mass transfers between
interfacing sub-models, which can be governed by mass, momentum, and
energy conservation principles. These principles are usually expressed by
differential equations, which may be implemented by time domain or S
(frequency) domain where the S domain can be represented by a transfer
function or state space function. The limitations of the early building
mathematical models are mainly due to the limitation in the computer
hardware since the models needed intensive computational process. But the
situation is changing as computational tools capacity has improved by the
evolution in software and hardware of computers. The recent mathematical
models are being developed to solve the large set of equations that also
incorporate sub-models mathematical equations.
1.1.2 Black box model of HVAC system
The concept of the black-box model is to fit transfer function model to the
input/output real model data to yield coefficient polynomials that can be
factored to provide resonance frequencies and characterizing of damping

4
coefficients without knowledge of the internal working. Hence, it does not
reflect any specific physical or mathematical structure of the existing
behaviour in the real model. The mathematical representations of this
model include time series such as Auto-regressive moving average
(ARMA), Auto-regressive model structure with exogenous inputs (ARX),
recurrent neural network models and recurrent fuzzy models. For real-time
operation and control, the black-box models are simple enough. On the
contrary, physical or mathematical modelling involves detailed analysis of
the relationships between all parameters that affect the system. Due to the
complex nature of HVAC systems and the large number of parameters
involved, it is difficult to mathematically model the system [4]. Romero [5]
mentioned that the mathematical models require detailed facility
information that is sometimes hardly found.
Therefore, the black box is the simplest solution, but at the same time has
to be regularly updated as operation conditions changes. Thus, it cannot be
used for prediction outside the range of the training data, and such models
have poor performance in general.
1.1.3 Gray-box models of HVAC system
Some physical processes of HVAC system are less transparently described
where there is much physical insight available, but certain information is
lacking. In this case, mathematical models could be combined with black
box models where the resulting model is called a gray box or hybrid model.
Furthermore, some white box model of the HVAC system needs
modification to provide better performance; this can be accomplished by
using a gray-box technique to mimic the output of the white-box analysis.
This method is implemented by Leephakpreeda [6] when building a gray
box model based on the white box model to predict indoor temperature.
Some black box models for the HVAC system are modified to become gray

5
box model to improve its performance as done by Zhao et al. [7] when they
identified the non-linear link model parameters by a neural network to
represent heat exchanger. This means that the main function of a gray box
is to improve the performance of the white or black box model.
1.2 The HVAC system Control
The HVAC system capacity is designed for the extreme conditions where
most of the operations are acting as a part load design due to the variables
such as ambient temperature, solar loads, equipment and lighting loads,
occupancy, etc. vary throughout the day. Therefore, the HVAC system will
become unstable without the controller system to avoid overheating or
overcooling in the space.
The first requirement of HVAC system control design is it has to be stable
at a closed-loop state. The nonlinearity and uncertainty in the HVAC
systems are the two major difficulties that can make the design of stable
control systems to be difficult. Nonlinearities act to reduce, or eliminate our
ability to use tractable linear mathematics and uncertainties compel us to
sacrifice performance in order to ensure adequate control over a range of
plants behaviour. Furthermore, there are some factors that make the HVAC
control system designs difficult such as pure lag time, big thermal inertia,
large-scale system and constraints.
In order to overcome these factors, researchers used many types of control
algorithms in HVAC systems. The most popular of these controllers (from
the simplest to more complicated) are the cycling on-off or called two
position or bang- bang controller, traditional controller such as
proportional, integral and derivative (PID) controller, modern controller
such as linear quadratic regulator (LQR) and model predictive control
(MPC) controller, model based control such as internal model control
(IMC) and fault tolerant control (FTC) controller, robust controller such as

6
H2 and H controller and artificial intelligent (AI) controller such as
artificial neural network (ANN), fuzzy logic control (FLC) and genetic
algorithm (GA) etc. These controllers become further complicated by the
new load-management technologies and development of building and
HVAC system over time, where it had taken natures of modernization.
Therefore, the old controllers become feeble against these challenges of
changes, resulting in some researchers applying some intelligent controller
to their HVAC system, for example [8-14], that uses methods such as
neural network (NN), fuzzy logic control, etc.
1.3 The HVAC system Simulation
To reduce the design cost as well as the design process for testing and
developing the HVAC systems, this study adopted simulation methods for
modelling systems, result analyzing and controller design. Obtaining better
performances of the simulated systems become easier [15] because of the
progress of the digital computer has taken a quantum jump which allows
the possibility for HVAC systems to be examined and assessed through
model simulation [16].
There are three main driving forces influencing the simulation
development process and its evolution [17].
a) the developments in computer software and hardware,
b) the upturned understanding of the fundamental physical processes,
and
c) the expertise gained from constructing the previous generation of
models.
The influence of these three driving forces helped to solve probable areas
of uncertainty and limitations by simulation methods.
The observations on a synthetic HVAC system by simulation are referred
to imitate the performance for a real system. In the numerical simulation,

7
the equations of a model are converted into a computer program by a
numerical algorithm. Using the computer to implement the algorithm is one
of the most powerful and economical tools currently available for the
design and analysis of complex systems such as HVAC system. The most
early simulation work in HVAC system was sponsored by the American
Society of Heating, Refrigerating, and Air-conditioning Engineers Inc.
(ASHRAE) in the USA. There is a vast amount of specialized programs in
the field of HVAC system such as TRNSYS [18], HVACSIM+ [19], IDA
[20], SIMBAD [21], SPARK [22, 23], BEST [24], BLAST [25],
EnergyPlus [26] and HAM-tools [27]. But each program has limited
applicability because they are specific for only a particular range, not
covering all the implementation range to complement certain calculations
required for analysis or simulation. Furthermore, most of these programs
are not suitable for modelling innovative building elements such as
building integrated heating and cooling systems, solar walls and ventilated
glass façades, as these have not been defined in the program [28, 29].
MATLAB and SimuLink from MathWorks are adopted in this study
because they are appropriate and efficient environment tools for designing
and testing of modelling and controllers analysis in a simulation setting
[30].
1.4 Problem Statement
Until now, many HVAC system modeling approaches are made available
and the techniques have become quite mature. But there is no combined
model for the comprehensive HVAC system with subsystems in detail
although the literature presented two types of HVAC system's model;
steady-state models and unsteady-state models.
The thermal comfort is a relative term for feeling and is very difficult to
represent mathematically without the assistance of modern computers.

8
Previous studies show that the human thermal feeling depends on human
variables as well as environmental variables. The environmental variables
are dry bulb temperature of conditioned air, humidity of air, air velocity
and mean radiant temperature. The human variables are thermal resistance
of clothes and activity level. To control the environmental variables within
a comfort region, the HVAC hardware models and the whole building
model are required to be integrated into one model, resulting in more
complicated building model. The integration process will act to accumulate
the defective characteristics of all the hardware and building models, which
leads to the increase in the nonlinear characteristics of these systems. Some
of these characteristics on the HVAC system control have been previously
pointed out; nonlinear, pure lag time, big thermal inertia, uncertain
disturbance factors, large scale system and constraints. Furthermore, the
indoor thermal comfort is a function on the temperature and relative
humidity in which they are coupled with each other. The conventional
controller like PID which is widely used in HVAC system is insufficient
when dealing with these characteristics. One of the challenges of this study
is to confront the control algorithm in a simulation environment with the
above-mentioned problems. And the second challenge is to represent all of
these characteristics in the models.
1.5 Book Objectives
The goal of this study is to design TSFF intelligent control algorithm to
provide the indoor thermal comfort within standard range, which depends
on many controllable and uncontrollable parameters. To achieve this task,
the fallowing objectives are stipulated:
• To emulate the modelling of building and air handling units (AHU)
through the development of physical empirical hybrid concept based
on thermal and moisture dynamic phenomena.

9
• To identify the indoor thermal comfort model by converting the
empirical model into novel identification method based on Takagi-
Sugeno (TS) fuzzy rules.
• To design TSFF intelligent control algorithm to manipulate inherent
characteristics of comprehensive model.
The first two objectives, which are development / enhancement of building,
AHU and indoor environment models, will lead to investigation of new
method for controller design, which minimizes the dependency on
traditional models that are very simple in structure. Since simple building
models are reduction of a real model, secondary dynamics is often
neglected and unforeseen system changes reduces the accuracy of the
model. On the other hand, these types of models are easy to implement by a
simple control algorithm since most of the complex inherited
characteristics are excluded. This study is considering all these complex
characteristics during HVAC system modelling such as a nonlinearity of
the large scale system including pure lag time, big thermal inertia,
uncertain disturbance factors and constraints. On the other hand, indoor
thermal comfort is affected by both temperature and humidity which are
inter-related between each other.
1.6 Scope of study
The scope of this study is to cover the main goal of this research (indoor
thermal comfort) that can be achieved by achieving the three objectives of
the book. This is done by mathematically modelling the building, AHU and
indoor thermal comfort and design applicable control algorithm capable of
manipulating the developed models. The building and AHU can be divided
into subsystems where each is modeled separately and then combined to
form the overall system model. There are six attributes to the physical
space that influence comfort; lighting, thermal, air humidity, acoustical,

10
physical, and the psychosocial environment. Of these, only the thermal
conditions and air humidity can be directly controlled by the HVAC
system. Therefore, the construction of building models discussed in this
book is based on these two attributes. And these attributes are closely
related to the building and the air supplied to the building by AHU as
shown in Figure 1.2.
Figure 1.2 The main fields of the HVAC system
1.7 Book outline
The subsequent chapters are as follows; Chapter 2 provides information
about literature researches regarding modelling of building, AHU and
indoor thermal comfort as well as HVAC system control algorithms. These
include discussion and related literature on the three objectives of the book
and also references related to HVAC systems with nonlinearities, pure lag
time, big thermal inertia, uncertain disturbance factors, large-scale system,
constraints and uncertainty.
Chapter 3 shows the modelling method in detail and how the two types of
models are designed. The controller architecture and algorithm are
explained in Chapter 4. The simulation for both the models and the
controller are presented in Chapter 5, which provides the baseline of

11
application and the validation of the results. Chapter 6 shows the results for
the models and control performance and discussion on the results analyses.
Conclusions and future works are given in Chapter 7, which provides a
concise description of what has been achieved and what we can improve by
recommendation for future works. The appendix provides the proof of the
models' derivation that is repeatedly used in Chapters 5 and 6, and shows
the details of the m-file program used in calculation and analysis of the
study.
1.8 Summary
This chapter has described the topics related to this study where it shows in
general the types of a model and what are the advantages and
disadvantages of each one of them, and it is clear from the introductory
description that the gray box type is the best model type. This chapter also
briefed the types of controllers applied on a HVAC system, and basically
most of the controllers developed before the last decade are linear types,
sparking evolution in nonlinear controllers over the past decade or so.
HVAC system simulation softwares are also presented in this chapter for
the past and current decade where most of these programs are specialized
in the specific scope of study. For this extensive study, it requires the usage
of a comprehensive software such as Matlab. The problem statement
section presented the main challenges that will be encountered through the
proceeding to this study. The objectives of the study are clearly specified to
solve the problem statements. Based on these objectives, the scope of study
is specified, which is described in the subsequent chapters.

12
CHAPTER 2
HVAC SYSTEM LITERATURE REVIEW
2.1 Introduction
Since the ancient time, human beings have sought to build a hut in order to
alleviate the harshness of the climate to provide a suitable indoor
environment. The evolution of research has been reflected on the evolution
of indoor environment by development and enhancement of buildings and
HVAC equipments. In general, research on indoor environment can be
divided into two main categories; design-oriented research and research-
oriented design as explained by Fallman [31]. This study followed the
second category where it depends on the previous research outcomes to
develop design that enhances the indoor thermal comfort. This category is
further divided into two fields of study; control and modelling research
orientated and simulation design research orientated. The main body of this
book is based on these fields where the first three chapters are related to the
investigation field while the later chapters are related to the implementation
field as shown in Figure 2.1.
2.2 Building and AHU model
The commercial and residential buildings are facing a new era of a growing
demand for intelligent buildings worldwide. Intelligent buildings are
referred to as energy and water saving and provide healthy environmental.

13
Figure 2.1 The main framework of the book

14
The first intelligent building was introduced in the late 1970s when
buildings were equipped with IT equipments [32]. The developments of
improved building and AHU models are essential to meet the requirements
of an intelligent building [33].
2.2.1 The evolution of modelling HVAC system
Building and AHU modelling has been used for decades to help HVAC
system scientists design, construct and operate HVAC systems. The
pioneering development in the building and the HVAC equipment industry
is the heat conduction equation model by Joseph Fourier published in 1822,
which is the most cited model [e.g.34-37].
The earlier simulation work in building structure by Stephenson and
Mitalas [38, 39] on the response factor method significantly improved the
modeling of transient heat transfer through the slabs, opaque fabric and the
heat transfer between internal surfaces and the room air. The heat balance
approaches were introduced in the 1970s [40] to enable a more rigorous
treatment of building loads. Rather than utilizing weighting factors to
characterize the thermal response of the room air due to solar incident,
internal gains, and heat transfer through the fabric, instead, the heat balance
methodology solves heat balances for the room air and at the surfaces of
fabric components.
Since its first prototype was developed over two decades ago, the building
model simulation system has been in a constant state of evolution and
renewal. Numerical discretization and simultaneous solution techniques
were developed as a higher-resolution alternative to the response factor
methods [41]. Essentially, this approach extends the concept of the heat
balance methodology to all relevant building and plant components. More
complex and rigorous methods for modeling HVAC systems were
introduced in the 1980s. Transient models and more fundamental

15
approaches were developed [42] as alternatives to the traditional approach
which performed mass and energy balances on pre-configured templates of
common HVAC systems. The delivery of training and the production of
learning materials [43] are also receiving increased attention. Additionally,
many validation exercises have been conducted [44] and test procedures
developed [45] to assess, improve, and demonstrate the integrity of
simulation tools.
The literature presented two types of HVAC system's model; steady-state
models, which are extensively presented such as [46-51], and unsteady-
state models presented by [52, 53]. Unsteady-state models can be further
categorized into two extreme modeling approaches. The first approach,
called physical or mathematical models, builds up models entirely based on
universal laws, physical laws and principles [54]. The second approach,
called empirical or black box models, constructs models entirely based on
experiments or data [55-57].
2.2.2 Mathematical model
Mathematical models have been widely used in areas as diverse as
engineering, economics, medicine, ecology and agriculture for many kinds
of different purposes to satisfy scientific curiosity, prediction, control, fault
diagnosis and inadequacies, simulation and operator training.
In the field of HVAC system modelling, the most complicated model part
is the building model. This is because components that need to be modelled
for building are not limited to building construction, such as roof, walls,
floor slab, windows and external shading. Internal loads such as the activity
within the space, the number of people, and the heat gain from lighting
must also be modelled as well. The subdivision of the building model is an
extensive scope of the HVAC models' field, and there are rarely studies that
include the entirely scope of a building model. For example, Lu [58]

16
studied the transmission of heat and moisture throughout the walls, roofs
and ceilings to estimate the indoor air temperature and humidity. He didn’t
consider the transmission of heat and moisture throughout ventilation,
filtration (doors and windows) and internal load. Furthermore, the moisture
conservation equation used assumed the temperature to be the same in all
the phases. He constructed his model by applying the conservation of mass
and energy theory based on the fundamental thermodynamic relations. For
mass conservation law, he implemented this in moisture transmission by
applying Darcy’s law and Fick’s law. For energy, he implemented
Fourier’s law. He used distributed white box model where partial
differential equations is discretized in space by using finite element with
time marching scheme and Crank-Nicolson scheme.
On the other hand, Ghiaus and Hazyuk [59] used mathematical model to
estimate the heating load in dynamic simulation by using steady-state heat
balance for normalized outdoor conditions. They applied the superposition
theorem for electrical circuits to obtain their model's parameters. And they
assumed that the thermal model of the building is linear, thermal capacity
of the wall and the indoor air is lumped and considered that the time series
of disturbances (such as weather, internal loads) and occupational programs
are known because they used model predictive control (MPC) which
proposed an unconstrained optimal control algorithm to solve the load
estimation problem. They obviously have imposed many assumptions to
facilitate the calculations of heating load, which leads to lack of accuracy in
the results. In addition, they used a single input single output (SISO) type
model that doesn’t consider the moisture transmission, an important
element in deciding thermal comfort.
For the air handling unit (AHU) mathematical model, Wang et al. [60- 63]
built models of heat exchanger for air handling unit based on the
conservation of energy and applied thermal balance equation on control

17
volume for heat exchanger. This model is characterized as a SISO model
since it does not take into account the effect of the mixing air chamber and
assumed the temperature of air supplied to conditioned space is equal to the
surface temperature of heat exchanger. Furthermore, they neglected the
humidity of the moisture air supplied to the conditioned space because they
do not want to include the effectiveness of humidity variation on thermal
comfort. Therefore, they supposed that the type of cooling coil is of a dry
type and there is no indoor latent load.
2.2.3 Black box model
The physical model involves detailed study of the relationships between all
parameters that affect the hygrothermal (the variation of humidity and
temperature) system. Due to the complex nature of hygrothermal systems
and the large number of parameters involved, physical modelling has
become more complicated in application. Usage of black box model is
sometimes preferred because it is straightforward to construct and there is
no need to have knowledge of the system’s internal structure.
Mustafaraj et al. [64] identified the humidity and thermal behaviour models
of an office in a modern commercial building by using different methods of
the black box model such as Box–Jenkins (BJ), autoregressive with
external inputs (ARX), autoregressive moving average exogenous
(ARMAX) structure and output error (OE) models. They adopted linear
parametric models to predict room temperature and relative humidity for
different time scales. The linear model is adopted to obtain a simple and
low number of model parameters, but this caused downbeat on the
accuracy, especially in the representation of the heat storage or flywheel
effect on the instantaneous load. In this group of models, they found out
that BJ model is suitable for the winter season where the ARMAX and
ARX models give good results for the summer and autumn seasons and OE

18
is appropriate for summer season. This means that there is no specific
model can represent indoor temperature and humidity for all four seasons.
Furthermore, Mustafaraj et al. [65] created the neural network based
nonlinear autoregressive model with external inputs (NNARX) model,
which is suitable to predict indoor office temperature and relative humidity
for summer season. The learning of NNARX model is done off-line
because this type of model is well known for having a sluggish learning
process. On top of this, they used Optimal Brain Surgeon (OBS) strategy
which made the learning much slower, so it is not suitable to apply online
learning process [66].
Yiu and Wang [67] created a generic SISO and MIMO black box model for
AHU. The ARX and ARMAX structures are used, where their parameters
are identified by using the recursive extended least squares (RELS)
method. In general, the selection of model structure, between SISO and
MIMO as well as between ARX and ARMAX, is a compromise between
model simplicity and accuracy. The accuracy of the anticipated model
outputs is in contrary with simplicity and the time period of updating
weight. Furthermore, the more the accurate the ARMAX structure is, the
more complex it becomes, which will also yield more residual white noise.
Barbosa and Mendes [68] integrated the works of a group of researchers in
order to obtain a comprehensive model, for the chiller model is quoted
from CA [69] by applying empirical equations based on regression
functions. The cooling tower model used is based on Merkel’s theory for
the mass and sensitive heat transfer between the air and water in a counter
flow cooling tower. The pumps and fans model are quoted from
Brandemuehl et al. [70] where power for variable flow is calculated from a
regression of part-load power consumption as a function of part load flow
with the assumption that motor efficiency is constant. For the cooling and
dehumidification coil model, there are three possible conditions for the

19
coil: completely dry, partially wet or completely wet. The model for all
three conditions is quoted from Elmahdy and Biggs [71] based on coil
outside surface temperature and air dew-point temperature. The room
building model for heat and moisture transfer is based on the Philip and
DeVries theory, which solves the partial differential governing equations
for room control volume within the porous building element, which is
quoted from Mendes et al. [72], where it is assumed that the water vapour
behaves like a perfect gas and the vapour exchanged between the wall and
the air is in a linear function of the differences between the temperature and
moisture content.
2.2.4 Gray box model
The Grey box model, sometimes called semi-physical or hybrid model is
created by a combination of physical and empirical models, which is to
compensate for their deficiencies as individual approaches.
In some gray box modelling, the model structures are derived
mathematically from physical or thermodynamic principles, while their
parameters are determined from catalogue, commissioning or operating
data. This is what Braun et al. [73] and Wang et al. [74] did when they
developed an effective model through introducing the idea of air saturation
specific heat. Catalogue data at an operating condition are used to obtain
the number of transfer units, which is then employed to obtain the
performance at other operating conditions.
Based on the same concept of Braun et al., Wang et al. [75] built their gray
box model for predicting the performance of chilled water cooling coils in
a static state. The mathematical part they built was based on heat transfer
mechanism and the energy balance principle. A model with no more than
three characteristic parameters that represent the lumped geometric terms
was developed. Procedures for determining the unknown parameters using

20
commissioning or catalogue information by linear or nonlinear least
squares methods are used. Using this method, the model captures the
inherent nonlinear characters of the AHU. Both Braun’s and Wang’s
models have a high level of uncertainties because they evaluated models
parameters depending on catalogue and operation data where most of these
data are estimated from ideal operation conditions. Some data are measured
from the real operation but these parameters value will eventually change
due to the aging of the HVAC system.
Meanwhile, Ghiaus et al. [76] used a gray box model to identify the AHU
by imposing in the mathematical part that air temperature difference occurs
in cooling coils and the humidity ratio difference occurs in the humidifier
only, meaning that the cooling coil is of dry type, and there is no change in
the air temperature through the humidifier. This is to separate the transfer
functions for each element in order to overcome the coupling between the
temperature and humidity, where the parameters of the discrete form of
these models are then experimentally identified. It is obvious that the
assumptions made by the authors are too unrealistic and cannot be achieved
except in some rare cases. This lead to avoidable inaccuracy in the model’s
output data.
2.3 Indoor Thermal comfort model
Indoor thermal comfort model is a major indicator for an HVAC system
which is designed based on a number of variables that physiologically
affect human comfort. This based on the fact that human body loose heat
continually due to metabolized food. The rate of body heat loss is the factor
that determines whether one feels cold or hot. The objective of literatures
on human thermal comfort is to substantiate the criterion of thermal
comfort for evaluating the indoor thermal sensation. The researchers are

21
proceeded to identify the variables which affected human comfort over the
past three decades.
2.3.1 The evolution of thermal comfort
The climate criteria of the thermal comfort index is continuously/gradually
developed over time; such as wet bulb temperature (Tw) [77], effective
temperature (ET) [78], operative temperature (OpT) [79], thermal
acceptance ratio (TAR) [80], wet bulb dry temperature (WBDT) [81], and
so on. However, the major and widely used thermal comfort index is the
Predicted Mean Vote (PMV) index. The PMV model is developed by
Fanger in 1972 [82]. Based on this model, a person is said to be in thermal
comfort based on three parameters: 1. the body is in heat balance; 2. sweat
rate is within comfort limits; and 3. mean skin temperature is within
comfort limits [83]. Based on these parameters, Fanger established his
empirical model by using the estimation of the expected average vote of a
panel of evaluators.
There are also criteria not related to climate which are also developed over
time. These criteria depend on variables that can affect how comfortable a
person feels in a given situation, such as: age [84-86], acclimatisation,
clothing, sex [87-90], activity and health [91, 92], and subcutaneous fat.
Furthermore, the geographic location criterion could have an influence on
thermal comfort. Parsons [91] argues that this is not being shown to be the
case in some research such as [92, 93]. Thermal comfort also depends on
the activity, metabolism of physiology and thermoregulatory system of the
body [94-99]. However, the variation of the metabolism and activity in
residential buildings is hard to predict compared to commercial buildings.
The same can be said about the type of clothing worn in the residential
buildings. These factors make the criteria for comfort conditions difficult,

22
making it more difficult to predict indoor thermal comfort in residential
buildings compared to those in commercial buildings.
2.3.2 The predicted mean vote (PMV) index
There are numerous mathematical relationships to represent the thermal
comfort, as previously mentioned.
In 1967, Fanger studied the physiological processes of a human when they
are close to steady-state condition to define the real comfort equation. His
studies [100] initiated with the assumption that physiological processes
influencing heat balance can be determined from the mean skin
temperature and sweat rate as a function of activity level. Then he used
data from an investigation by McNall et al. [101] to obtain a linear
relationship between sweat rate and activity levels and proceed with an
investigation to obtain a linear relationship between the mean skin
temperature and activity levels. These two linear relationships are used in
heat balance equations to formulate a thermal comfort equation to describe
all integrations of the six PMV input factors that result in a neutral thermal
sensation. The thermal comfort equation is corrected by combining data
from Nevins et al. [102], taking into account situations where human do not
feel neutral [82]. At that time, the Fanger model was accepted to be the
closest one to the real behavior of the indoor actual model, and that is the
reason why it is adopted in ASHRAE Standard 55-92 [103] and ISO-7730
[104]. Therefore, it is widely used for PMV calculations.
The PMV is dependent on two variables. The first variable is the composite
of skin temperature and the body's core temperature to give a sensation of
thermal neutrality. The second variable is the body's energy balance: heat
lost from the body should be equal to the heat produced by the metabolism.
The range value of PMV is from -3 to +3, where a cold sensation is shown
as a negative value, the comfort situation is close to zero and hot sensation

23
is shown as a positive value. The PMV is also used to predict the number
of people likely to feel uncomfortable as a cooling or warming feeling. This
feeling is cited under the Predicted Percentage of Dissatisfied (PPD) index.
The output of the PPD is classified into two categories, comfortable and
uncomfortable, according to human sensation. The variation behavior of
PPD versus PMV is imperative for the HVAC system to control indoor
desired conditions as implemented by many researchers [54, 105-109].
2.3.3 PMV models
The process of calculations and obtaining PMV value from Fanger’s model
requires a long time since the number of input variables takes a long
routine due to some of them require iterations. For iteration loops, if the
initial guess of the input variables is far from the root, it might take a long
time for it to converge to the root. The Fanger’s model has been used
directly by using a spreadsheet or numerical methods to obtain a thermal
comfort index [110-112], while others converted it into a black-box model
[113-116].
Since Fanger’s model involves implicit equation, calculation of the PMV
manually by a spreadsheet will take a long time due to the presence of an
iteration process. Furthermore, the main two disadvantages of a spreadsheet
as follow: - First it does not have any built-in transaction-control
capabilities, meaning that any error occurred on the spreadsheet cannot be
repaired; in this case, the spreadsheet must be restored from a backup.
Second, is doesn’t capture some of the model characteristics such as a
thermal dependence [117].
Therefore, since the Fanger’s or PMV equation is not an explicit function
of the six factors that affect thermal sensation and to avoid the iterative
process, the implicit calculation by black box model is identified to predict
PMV value by many researchers such as Hamdi et al. [118]. Furthermore,

24
the Fanger’s equation is cumbersome to calculate the PMV index and is not
suitable for feedback control of HVAC systems [105, 119].
The black box model of the thermal sensation index which is designed by
Hamdi et. al. [118] is based on the basis of neuro-fuzzy logic theory by
learning Fanger’s equation. The neuro-fuzzy model of thermal sensation
provides a quick and direct calculation of the thermal sensation index
which makes it an attractive index for feedback control of HVAC systems.
But Hamdi used Mamdani’s fuzzy inference system's model, where this
model requires a large number of rules to meet the asymptotic
representation of the real Fanger’s model. Furthermore, he used back-
propagation algorithm to tune the fuzzy model where this type of algorithm
has notorious long training time requirement [120].
On the other hand, many researchers used black box models by employing
neural network to identify the PMV model [121, 122]. Mistry and Nair
[121] used feed-forward neural network model, which allows real time
determination of the thermal sensation index quantitatively. They also
contributed to the field of function approximation for thermal comfort
index by modeling of PMV index using back propagation neural networks.
Out of the six input factors, two input are considered as constants and
corresponding to these constant input factors, correction networks have
been added in the neural network structural design. Atthajariyakul and
Leepahakpreeda [122] developed feed-forward neural network architecture
model to capture the relations of the conventional thermal sensation model
by Fanger, also quantitatively. They also use back propagation algorithm in
the training process to tune the two hidden layers' weights of the PMV
model structure. However, this model showed significant margin of error
when its outputs are compared with Fanger’s model outputs within 9 hours
at day.

25
Other researchers such as Lute and Paassen [123] described the indoor
PMV by an ARMAX model, which estimates the indoor thermal comfort
by a recursive estimation algorithm. The disadvantage of this ARMAX
model is it becomes very complex by increasing the model order when
converted into a MIMO model [124]. To reduce the complexity of model,
Lute and Paassen [123] fixed all the inputs’ parameters at certain values
and only used the temperature as the input. They also assumed the indoor
air temperature and the mean radiant temperature to be the same to convert
the model to SISO type. This approach leads to a simple model where its
output is easy to control using a linear predictive control (LPC). But this
affects the model accuracy and does not represent the real indoor PMV.
In the last few years, adaptive thermal comfort for PMV model is proposed
by some researchers [125-131] to represent a dynamic indoor thermal
sensation, which is determined by the combination of three criteria:
behavior adaptation, physiological adaptation and psychological adaptation
[132]. This type of model is fairly capable of representing the dynamic
situation of the indoor thermal sensation, but it does not include human
clothing or activity or the four classical thermal parameters that have a
well-known impact on the human heat balance and therefore on the thermal
sensation [133]. Another great disadvantage of the adaptive thermal model
is its application range, which is limited to workspaces and offices only,
while the Fanger’s PMV model can be applied throughout to almost all
types of buildings [134]. In addition, adaptive models are not suitable for
energy saving due to their static value for a daily period [54]. Therefore, it
can be said that Fanger’s thermal comfort model represents a deep analysis
that relates variables that contribute in thermal sensation [135].

26
2.4 HVAC System Control
The main objective of the HVAC system control is to maintain the design
condition of thermal comfort in conditioned space. Other objectives
include; reducing human labor, minimizing energy consumption and costs,
keeping equipment operation at safe levels and so on. To achieve the main
objective of the HVAC system control, there must be at least one
controllable variable to be controlled by a controller device, which is
developed through time.
2.4.1 The evolution of HVAC system control
Basically, there are two types of controls theory; open loop or closed loop
control. Open loop or feed forward control is a system without monitoring
whether the control system is working effectively or not. In the closed loop
or feedback control system, the controller responds to the error between the
controlled variable and the set-point. The closed loop control can be
broadly classified into two categories; two position control (On-Off) and
continuous control.
The first closed loop control in the HVAC system was a regulator space-
heating system using bimetallic strip. The bimetallic strip was the first
device used; it controlled the boiler output using a combustion air damper
to control the rate of combustion. This device was known as a regulator,
which is used again to control steam radiators and steam heating coils
[136]. Dr. Andrew Ure (1778 – 1857) was the first person to call his
regulator a thermostat, which is soon used to control temperatures in
railway cars, incubators, restaurants, and theatres [137].
Two other devices were developed to compete with the bimetallic strip.
They are mercury thermometer column, mercury switch, capillary
thermostat and proportional thermostat, which are still used to control
countless processes in HVAC systems [138, 139]. Early controls for

27
comfort air conditioning systems were used to maintain the desired supply
air temperature in USA Capitol building since 1928 using pneumatic type
control [140]. Shavit [141] indicated the possibility of using a
thermocouple for remote monitoring of conditioned space temperature,
which is implemented in the first centralize monitoring system with a
remote set point change and central panel installed in the White House in
1950 by using pneumatic local control systems. Shavit also said that in
Dallas, Texas, the first on-line computer was introduced 1967, where the
first set of energy conservation software was installed that includes chiller
optimization, enthalpy control, optimum start/stop, demand limit, reset
according to the zone of highest demand and night purge. Another
significant milestone occurred in 1970, when solid-state components
improved the scanning process and serial transmission as well as reduced
many wires in the trunk wiring to a single pair. In 1981, the first
microprocessor-based direct digital control (DDC) which used software
programmed into circuits to affect control logic was introduced [140]. The
most common algorithm for control logic appropriate for HVAC system is
called proportional plus integral plus derivative (PID). The control action
logic of the PID adds a predictive element to the control response, which
takes care of sudden changes in deviation due to disturbances. This
controller combines proportional control with two additional adjustments,
which helps the HVAC system to compensate automatically for changes in
the conditioned space.
2.4.2 PID control for HVAC system
PID controllers are widely used in HVAC systems field because of their
simple structure and their relative effectiveness, which can be easily
understood and executed by practical implementations [142]. However,
PID controllers are reliable only if the parameters of the system under

28
consideration do not vary too much. On the other hand, variations in the
operating condition of the HVAC system will cause changes in the
parameters of the system. These variations can be due to many factors such
as water’s chilled temperature, weather and occupancy level, which
changes from day to night. In short, the system is time variable and highly
nonlinear. For these reasons, even for a single HVAC system, the use of a
constant set of PID parameters will not give best results [143, 144]. To
obtain good PID control performance, the PID parameters should be tuned
continuously, which is time-consuming and dependent on the experience of
the one who adjusts them. Furthermore, despite the non-stop continuous
research on improving PID algorithms, requirements for high product
quality, subsystem unification and energy integration have resulted in
nonlinearity and pure lag time for most of modern HVAC systems.
Some researchers have incorporated PID with other algorithms to provide
a new hybrid controller to cover the wide range of HVAC system operation
conditions [145, 146]. Several of these hybrid controllers are capable of
managing two controlled variable such as the controller developed by Paris
et al. [145] when they combined two parallel control structures based on
PID and fuzzy controllers. The hybridization structure of the PID-fuzzy for
the indoor temperature controller allowed efficient management of energy
resources in buildings. By this combination, they took advantage of the
properties of the two structures to control the indoor temperature and
energy consumption without referring to the variation of indoor humidity
and other factors affecting the thermal comfort which causes the
controller's efficiency degradation or may also cause disability to control
the plant system.
Meanwhile, Xu et al. [146] developed a hierarchical structure control
scheme that incorporates generalized predictive control (GPC) into the PID
controller. This is to address the issues of advanced tuning methods

29
normally lack explicit specifications and the AHU operators unfamiliarity
with the parameters tuning. This structure control strategy consists of two
levels, a basic level and an optimization level, for the basic level is
represented by the conventional PID controller, and the optimization level
is used to vary the gain values of the PID controller. This type of controller
is implemented in modeling of cooling coil for AHU by using controlled
autoregressive and integrated moving average model (CARIMA) to control
supply air temperature and flow rate without looking into air humidity,
which is difficult to control since it is coupled with temperature.
The process of PID hybridization with a cascade control structure is
adopted by many researchers in HVAC systems since it is efficient and
transparent when compared with the single-loop PID controller since these
controllers have cascade control algorithm to evaluate the data from the
sensor network and manipulate AHU parameters such as supply air
temperature, air and chilled water flow rate [61, 147-151]. However, the
tuning procedure of hybrid PID-cascade controller is tedious and it is
difficult to obtain the inner and outer loop PID parameters simultaneously.
To avoid tuning difficulty, some researchers adopted hybrid PID auto-tune
cascade control systems, for example Song et at. [147] when they
established a model based on PI tuning rules for Ziegler-Nichols method
which is applied to tune the inner loop, and the outer loop tuning is applied
by model matching algorithm to obtain the PID control parameters for the
overall system performance. Both inner loop and outer loop process model
parameters are identified using relay feedback by utilizing the physical
properties of the proposed structure. This method is straightforward for
cascade control structure with the possibility to be integrated into an
existing auto-tuning system to control the overall system performance. The
disadvantage of this structure is it can be implemented only with SISO
model.

30
Other researchers [61, 148-151] implemented hybrid PID-cascade control
to improve control system performance over single-loop PID control
whenever disturbances affect a measurable intermediate for inner loop
controlled variable or secondary process output that directly affects the
primary process (outer loop) output which is the main controlled variable.
Furthermore, the hybrid PID-cascade control system has advantages over
PID single loop in anti-jamming capability, rapidity, flexibility and quality
control [151].
From previous literature, it is obvious that both single-loop PID and hybrid
controller types are suitable for SISO system plants. However,
requirements for high product quality, subsystem unification and energy
integration have resulted in nonlinearity and pure lag time for most of the
modern HVAC systems. These main characteristics have rendered many
PID tuning techniques as insufficient for dealing with these modern HVAC
systems, which are categorized as a Multi-Input Multi-Output (MIMO)
process [152, 153]. Furthermore, the tuning of PID parameters in MIMO
plants is difficult to obtain because tuning the parameters of one loop
affects the performance of other loops, occasionally destabilizing the entire
system. Therefore, most studies in the field of the HVAC system control
tends to belong to artificial intelligence; neural network (NN) [154, 156],
fuzzy control [10, 154], adaptive fuzzy neural network [8-12], etc.
2.4.3 Fuzzy logic control for HVAC system
Fuzzy logic imitates human intuitive thinking by using a series of Zadeh’s
fuzzy set, almost intuitive, if-then rules to define control actions. Zadeh’s
fuzzy set theory [157] is a foundation of fuzzy logic control [158], and the
first application of Zadeh’s theory was developed by Mamdani in 1974,
when he designed an experimental fuzzy control system for a boiler and

31
steam engine combination by synthesizing a set of linguistic control rules
obtained from experienced human operators [159].
Fuzzy logic controller operates similarly with PID conventional controller,
but able to manage complex control problems through heuristics and
mathematical models provided by fuzzy logic, rather than via mathematical
equations provided by PID algorithm. This is useful for controlling
nonlinear systems by presenting the essential knowledge of the dynamics
nonlinear systems behaviour in the form of a linguistic rule base.
The fuzzy logic control is used in HVAC systems for its capability in
dealing with non-linearity as well as its capability to handle MIMO plants.
Moreover, in most cases, fuzzy logic controllers are used because they are
characterized by their flexibility and intuitive use [160]. Two types of
fuzzy inference system (FIS) models, Mamdani FIS and Sugeno FIS, are
widely used in various applications [161]. The differences between these
two FIS models befall in the consequents of their fuzzy rules, differing in
their aggregation and defuzzification procedures. Researchers found that
Sugeno FIS runs faster, is more dynamic to input changes and is more
economical in the number of input fuzzy sets compared to Mamdani FIS. It
is also observed that Sugeno FIS is more accurate since the results that
were generated were closer to what was expected [162-164]. Jassbi [165]
concluded that Sugeno FIS performs better than Mamdani FIS with respect
to noisy input data. Furthermore, Sugeno FIS is more responsive and that is
due to the fact that when the noise becomes too high (i.e. when the input
data has drastically changed), Sugeno FIS reacts more strongly and its
response is more realistic. In recent years, the learning methods based on
using fuzzy control emerged as a vital tool in applications used to control
nonlinear systems, including HVAC systems. For large scale HVAC
systems, iterative tuning controller makes a system better by obtaining
minimum cost on a system level [166].

32
The first fuzzy control application in the HVAC system was in late 1989 by
Imaiida et. al. [167] when he developed a fuzzy logic control system using
Mamdani FIS, which is designed to control temperature in commercial
buildings, achieving a high comfort level with energy savings up to 25%.
The dominant majorities of the fuzzy controls implemented on HVAC
system were of Mamdani FIS type because it is straightforward and can be
smoothly applied. On the contrary, Sugeno FIS type, which was adopted by
some of the researchers [168-170] requires a proper mathematical equation
which makes it difficult to tune its parameters instead of consequent fuzzy
rule in Mamdani FIS.
Sousa et al. [168] was the earliest to implement Takagi–Sugeno (TS) fuzzy
control in the HVAC system's field when he presented a sophisticated
approach of predictive TS control tested on temperature control in an air-
conditioning system. He demonstrated that the TS control requires fewer
computations and achieves better performance than a nonlinear predictive
control scheme based on iterative numerical optimization. He was using
offline tuning by employing a least-squares method to estimate consequent
parameters.
Ghiaus [169] designed TS fuzzy control based on an identification fuzzy
model then demonstrated that the nonlinearity of the heat exchange process
can be well identified by a rather simple fuzzy scheme and showed that the
fuzzy control resulted in improved performance and eliminated the offline
retuning process required by the classical PID controller. However, the
variable airflow rate which account for much of the nonlinearity and time
varying characteristics in variable air volume (VAV) scheme was not
considered in the work. He also concluded that the advantage of fuzzy
controller resides in the easiness of understanding and including linguistic
scheduling and expert type knowledge; or based on Lotfi Zadeh’s words,

33
“in almost every case you can build the same product without fuzzy logic,
but fuzzy is faster and cheaper.”
He et al. [170] used TS fuzzy models for AHU in HVAC systems based on
a multiple model predictive control (MMPC) strategy. The controller
system was constructed by a hierarchical two-level structure. The higher
level was a fuzzy partition based on AHU operating range to schedule the
fuzzy weights of local models in lower level, while the lower level was
composed of a set of TS models based on the relation between manipulated
inputs and system outputs corresponding to the higher level. He assumed
that the temperature of the chilled water is constant, and the airflow rate
varies in correspondence to the cooling load demand of the conditioned
space. He used offline tuning to identify the consequent parameters for
each cluster by using the stable-state Kalman filter method [171].
2.5 The Shortcoming in Previous Works and Alternatives
From the reading through the literature in the topics of this research’s
objectives which are summarized in the previous sections, faces some
shortcomings that prevent the possibility to be implemented in the
simulation environment. Thus, it can be concluded that the most important
discouraging gaps to implement the analysis simulation properly and
accurately for each objective are listed as follows:
2.5.1 Modelling of building and AHU
There are a lot of deficiencies for each of the model studied that needs to be
addressed. These deficiencies resulted from various simplifying
assumptions to reduce the complexity of thermal interactions, unmeasured
disturbances, uncertainty in thermal properties of structural elements and
other parameters which makes it quite a challenge to obtain reliable
analytical models.

34
The most prominent shortcoming in this area of studies is the fact that there
is no model that includes both building and AHU with all the details. The
other shortcoming is the existing building models do not represent the lag
time cooling load and solar gains incident on the surfaces of wall, roof and
window. In addition, the AHU model represented only the cooling coil
without pre-cooling coil and neglected the effectiveness of air mixing
chamber. Furthermore, there are some studies where the models are
simplified, eliminating many of the important features such as humidity
transmission, the change of air temperature through humidifier. Besides,
most of the literature of previous works presented SISO type model which
is easy to manipulate using linear controller. And the most important of all,
a lot of studies assume that the cooling coil is dry, which is contrary to the
reality.
To address these shortcomings in the existing model, the following
building and AHU model procedures are suggested for this study:
1) Use a physical-empirical hybrid modelling to describe the HVAC with
its various thermal inertia parts.
2) Systematize the HVAC system into five subsystems to reduce the
complexity of the modelling process.
3) Use the variable air volume (VAV) which is friendly with an
empirical residential load factor (RLF) method for thermal load's
calculations to enhance energy savings.
4) Use pre-cooling coil to control indoor humidity and such method
results in reducing energy waste.
2.5.2 Modelling of indoor thermal comfort
From literature review, it is noted that there are a lot of thermal comfort
standards, but apparently Fanger’s PMV index is the closest to reality.

35
Despite the importance of the subject concerning PMV model and its
impact on the indoor thermal comfort, only a few publications in the
literature can be found. These publications have many shortcomings that
affect the outcome precision and the most important shortcomings are as
follows: First the models were built in the form of black box type and
hence it is difficult to analyze the processes mathematically such as
prediction and extrapolation. The other shortcoming is most of the models
used back propagation algorithm, which is slow in the learning process,
making it difficult to be used in the online tuning. The literature of previous
works also clarified that in recent years, adopted adaptive PMV model is
used in many studies, which can be characterized by having small dynamic
properties but at the same time neglects a lot of features that affect human
comfort. For example, it does not include human clothing or activity or the
four classical thermal parameters that have a well-known impact on the
human heat balance and therefore on the thermal sensation. Its application
range is limited to only workspaces and offices and is not suitable for
energy saving due to its static value for a daily period. Based on these
shortcomings, the study proposes the development of a comprehensive
model with the following specifications:
1) Usage of the PMV index model which is suitable to be target set
values for the indoor conditioned space rather than temperature
because the PMV changes dynamically.
2) Building of a hybrid RLF-PMV model to properly control indoor
thermal comfort in HVAC systems.
3) Usage of a white-box fuzzy PMV predictive indicators model to
evaluate indoor thermal comfort.

36
4) Usage of the clustering concept of learning data set to reduce the
number of rules and number of iterations and provide small margin
error when compared with other methods.
5) Usage of Takagi-Sugeno model tuned by Gauss-Newton nonlinear
regression algorithm for obtaining model’s parameters layer.
2.5.3 The control algorithms
From literature review, it is found that the classical controllers such as PID
are used widely in HVAC systems, although they are limited to the usage
of the first order or second order plus time delay models to represent
process dynamics [170]. However, as explained earlier, the HVAC model
is a sophisticated MIMO model of a 13th
order and therefore classical
control strategies like a PID controller will fail to control it effectively.
Furthermore, the PID controllers are reliable only if the parameters of the
system under consideration do not vary too much. On the other hand,
variations in the operating condition of the HVAC system will cause
change in the parameters of the system.
The first shortcoming in the most intelligent controllers available is they
use temperature as a reference signal while the temperature itself does not
represent the thermal sensation.
Recent studies showed that the controlled variable PMV can be fitted
(optimized) by the controller according to the amount of impact on the
reference output. Therefore, using the PMV index as the target set value for
the indoor conditioned space is a better and more suitable choice than using
temperature because the PMV changes dynamically so as to suit the
constantly changing indoor environment, and this will be useful to HVAC
control systems aimed at both controlling thermal comfort and energy
consumption [172]. In addition to the use of temperature as a signal
reference, it was noted that the identifications of TS models in the literature

37
are tuned by only offline methods such as least-squares, PID or stable-state
Kalman filter. That resulted in limitations on the valid input ranges for the
models that are reflected on the performance of controllers and accuracy of
the plant's outputs. Furthermore, the conventional fuzzy controllers such as
Mamdani and TS fixed parameters use the feedback principle, which is
characterized as slow for the indoor responses.
The solutions to these shortcomings are that the new proposed controller
will have following specifications:
1) Designing of an auto-tuned Takagi-Sugeno Fuzzy Forward controller
to control thermal comfort in HVAC system.
2) Using the GNMNR algorithm for offline model training and the
gradient algorithm for online controller tuning.
3) Using memory layers structure for the parameters of PMV sensors and
controller models for faster calculations.
4) Adopting predicted mean vote to avoid thermal sensitivity and
temperature-humidity coupling, and to save energy.
2.6 Summary
This chapter has reviewed numerous previous works related to each of the
3 objectives of this research to guide the study to develop the best and
rational solutions for the problem statements of the current HVAC system.
Through literature review which is summarized by this chapter for different
types of model for HVAC system, a lot of advantages, disadvantages and
shortcomings of the current models have been discovered. The review of
the models' literatures are aimed at figuring out which type of model is the
most suitable to represent the behaviour of the real HVAC system. By
displaying the advantages and disadvantages of each of the three model
types, it became evident that the gray box model has many features which

38
discriminates it from the other models by closely representing the real
behaviour of an HVAC system.
Meanwhile, from the literature, the representation of the indoor thermal
comfort is best represented by Fanger’s formula which is the closest to
reality. And because of this formula being implicit, mathematically
complicated and includes iterations process, there is a need to convert it
into an explicit model. The methods of converting the implicit formula into
an explicit model are different from one researcher to another; this chapter
reviewed the features of each method, showed the general shortcomings for
each method, and suggests an alternative method.
Review on the existing controller algorithms of the common and widely
used controllers in the field of HVAC system was also conducted. It is
found that the classical controllers are dominant in this field, in spite of
their inability to manage the modern buildings and indoor conditioned
space to meet the desired requirements for thermal comfort and energy
saving. The modern and intelligent controller algorithms are advent in the
last few decades. They improved the performance of HVAC system to
control indoor thermal comfort, resulting in decline in the usage of the
classical controllers. This improvement in the controller’s performance is
continuing despite the increase of the complexity of buildings and HVAC
system equipments, which produce the non-linearity and other undesirable
characteristics. The literature review explained that intelligent controllers
are proven to be important to improve the efficiency of HVAC system
compared with other controllers, but there is a difference in the types and
the structure of each type of these controllers. The fuzzy logic control
algorithm type presented in the literature review is the most suitable for
HVAC system because of its flexible characteristic and intuitive use.

39
CHAPTER 3
MODELLING OF HVAC SYSTEM
3.1 Introduction
This chapter and the next chapter describe the proposed modifications in
the design of HVAC system, and its control algorithm based on the
shortcomings discussed in the previous chapter. The modifications of the
HVAC system modelling presented in this chapter are based on
reorganizing of the subsystem models. The first model for the HVAC
system is divided into two parts; building and AHU model and indoor
thermal comfort model. The building and AHU model adapted is based on
hybridization between two methods; physical and empirical methods,
depends on the thermal inertia quantity. Physical laws are used to build a
sub-model for subsystems that have low thermal inertia while the empirical
method is used to build a sub-model for subsystems with high thermal
inertia. The empirical method used is the residential load factor (RLF). The
second model is to evaluate indoor thermal comfort situations using
predicted mean vote (PMV) and predicted percentage of dissatisfaction
(PPD) indicators. These indicators are identified by a Takagi-Sugeno (TS)
fuzzy model and tuned by Gauss-Newton method for nonlinear regression
(GNMNR) algorithm.

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