F
UZZY MODEL P
REDICTIVE CONTROL FO
R
ENERGY CONSUMPTION
OPTIMIZATION BY HEAT
ING AND COOLING SYST
EMS IN BUILDINGS
Mariusz Nowak
Andrzej Urbaniak
Institute of Computing Science
Poznan University of Technology
Piotrowo 2,
60

965 Poznan, Poland
E

mail:
{
Mari
usz.Nowak

Andrzej.Urbaniak
}
@put.poznan.pl
KEYWORDS
energy management,
fuzzy model predictive control, fuzzy
modelling
, HVAC systems,
intelligent control
systems
,
thermal comfort.
ABSTRACT
In the paper the problems of optimal control for indoor
thermal
comfort in buildings equipped with HVAC
(Heating, Ventilation and Air Conditioning) systems
are
presented
.
It is important that the design of such control
systems allows to minimize the energy consumption.
The
article presents the results of research to de
velop an
intelligent control air

conditioning system. Predictive
algorithms are used to control. Fuzzy modelling was used
for the synthesis of predictive algorithms. In the paper the
quality control for the classic c
ontrollers and the fuzzy
model predictiv
e
controllers
(FMPC)
was compared. The
mathematical model of closed room was developed to
verify the proposed control system of air

conditioning. The
effectiveness of developed intelligent control system of air

conditioning and solutions based on classica
l control
algorithms were compared. The simulation tests were
conducted in
Matlab & Simulink environment.
INTRODUCTION
Traditional buildings consume about 40% of the total fossil
fuel energy in EU
. The building sector contributes up to
30% of global annual
greenhouse gas emissions.
Increasing
energy efficiency
of buildings
is one of the fundamental
issues they are working on the authorities and scientific
institutions of the European Union
(Energy priorities for
Europe 2013)
.
In March 2007 the EU’s leaders
endorsed an integrated
approach to climate and energy policy that aims to combat
climate change and increase the EU’s energy security while
strengthening its competitiveness. They set 20/20/20 targets
to be me
e
t by
year
2020: 20% reduction of GHG emission
s
by 2020
in comparison with
to 1990, 20% share of
renewable energy in final energy consumption, 20%
reduction in EU primary energy consumption,
in
compar
ison with
projected levels, to be achieved by
improving energy efficiency
(Energy priorities for Europ
e
2013)
.
Buildings are seen as the largest cost effective saving
potential and individual goals are set by Member States.
The rooms are emitted pollution, heat and moisture gains.
To maintain an appropriate level of
microclimate
comfort
in a closed room m
ust ensure adequate air exchange, to lead
the process of heating or cooling the air inside the room.
Realization of
processes of heat and mass transfe
r
associated with costs that are the most
important
component of the overall costs of the buildings. Conti
nuing
increases in energy prices and new European Union
guidelines on minimizin
g the consumption energy, forces
us
to seek ways to reduce the energy consumption of air
conditioning systems. These systems must also provide
adequate
microclimate
comfort. It
is therefore necessary to
develop advanced control systems to minimize the energy
consumption of air conditioning systems for buildings.
T
he
desired thermal comfort in buildings
depends on the
p
ower
efficient systems
.
Thus
,
th
is
paper presents a proposal
to reduce energy
consumption through the use of advanced computer control
of
air conditioning system in the building.
The requirement
to optimize energy consumption forced transition from the
well

known simple methods of tuning of controllers to the
system
s based on accumulated knowledge about the current
operation of the system.
This
paper presents results of a comparison of the classical
room climate control system and intelligent room climate
control system.
Synthesis of intelligent control algorithms
h
a
ve
been made
in the universal computing environment,
scientific and technical

Matlab & Simulink. Simulation
studies were
implemented
in Matlab & Simulink
environment.
As mentioned above, the crucial part of
energy consumption in a building is connected
wi
th heating
and cooling devices.
For this reason, the first step would be the preparation of
mathematical model of a room. Then, the next step shows
the realisation of a thermal comfort model of this room. The
thermal comfort model can be used for the st
udy of HVAC
systems. The model is also useful for the studi
es of control
strategies (fuzzy
model predictive control) as well as for
finding the solutions for reducing the electrical energy
consumption and for maintaining acceptable indoor air
conditions re
lated to thermal comfort. Thus, in the paper
there are suggested control strategies for reducing energy
consumption and maintaining these acceptable indoor air
conditions related to thermal comfort.
AIR

CONDITIONING SYSTEMS
In a dynamic system, such as t
he air conditioning and air

conditioned room processes, heat and mass transfer occurs.
For a comprehensive analysis of the complex system that
provides the right climate inside the room it is necessary to
group the input and output signals, such as:
−
input
signals
from the out
door
environment (outdoor
temperature and humidity, outdoor airflow, wind speed
and direction, solar radiation, outdoor air pollution
);
−
input
signals from the indoor environment (internal heat
and moisture gains, airspeed, temperature
of internal
surface bulkhead
, pollution);
−
output signals (indoor temperature and humidity, exhaust
air temperature and humidity, indoor air quality
,
pressure
difference between indoor air and outdoor air
, air quality
index
and indicators of human therma
l comfort
PMV
–
Predictive Mean Vote
, PPD
–
Predicted Percentage
Dissatisfied
, DR
–
Draught Rate
(EN ISO 7730:1994;
ASHRAE 2003;
Jones 2001)
.
In this paper
we
presented
air conditioning system
which
consists of the following subsystems:
−
air preparation s
ubsystem
which
consists of devices that
perform appropriate air transformation
;
−
indoor environment subsystem
which
consists of air
conditioner room and devices affecting of parameters
indoor air
;
−
air
supply
subsystem
in building
which consist
s
of
a
devic
es implementing the air flow from the air
preparation subsystem for air distribution subsystem
;
−
control subsystem.
Air
supply
subsyste
m in building
is not taken into account
in this paper. The main task of the air conditioning system
is to provide the req
uired parameters indoor environment in
an air conditioned room, regardless of the disturbances. In
order to carry out the experiments, it was assumed input
parameters: the state of outside air, heat gains, moisture
gains, pollutions, air supply and air qua
lity in the room.
Control subsystem provides the correct operation of the air
conditioning system. The correct selection of the structure
of the system and the control algorithm, process variables
and set

points determine the quality of work of the air
co
nditioning system
, both in terms of observance of indoor
air parameters and the
energy and economic effects
. It is
therefore necessary to properly design control system with
subsequent fine

tuning to the actual working conditions.
An
additional problem, wh
ich meets during the design of the
control system in the air conditioning system is the absence
of sensors measuring indicators of human comfort.
To
evaluate human thermal comfort we used indirect
indicators that combines the environment parameters and
fee
lings
of comfort
.
P
arameters of environments and indirect indicators:
operating temperature, effective temperature
were used in
the simulation experimental
.
The PMV index, PPD index
and DR index were used in the simulation. The precise
characteristics of
indicators has been included in the
previous papers
(see Nowak and Urbaniak
2005; Nowak
and Urbaniak 2007;
Nowak 2008
;
Nowak and Urbaniak
20
10;
Nowak and Urbaniak 2011).
In air conditioning there are three groups of disturbances
which have a significant
impact on the operation of air
conditioning system: chang
ing
paramet
ers value of the
outdoor air, changing parameters value of
heating l
oad and
moisture in room, changing parameters value of the energy
factors. Described disturbances are included in the
si
mulation study.
ROOM CLIMATE CONTROL SYSTEM
In this paper there is presented the simulation model of
a
room in a building
witch
actuators
that have been
prepared in Matlab
&
Simulink software
(Fig. 1)
. The
simulation
model includes physical parameters and
parameters of the construction of walls, floor and roof. The
mathematical simulation model of a room requires the
definitions on the room geometry, specifies thermal
properties of the room materials, thermal resistance of the
room, heater characteristics
(temperature of hot air, flow

rate), air

conditioning characteristics and initial room
temperature. The room
’s model is presented in Matlab
&
Simulink as a subsystem that calculates room’s
temperature variations. It takes into consideration heat flow
from
a heater, cold flow from an air

conditioning system
and heat losses to the environment. Heat losses and
temperature time derivative are expressed by special
equation (
see
Nowak and Urbaniak 2005
;
Nowak and
Urbaniak 2010
).
Figure 1:
R
oom and actuator
m
odels
in Matlab
&
Simulink
SYNTHESIS OF CONTROL ALGORITHMS
An approach for control of thermal comfort has been
p
resented by Fanger (Fanger 1973;
Fanger 1982). The main
goal of this control is to obtain such values of microclimate
parameters that allow to a
chieve the demand
level of
general PMV index. U
sual, this demand is formulated
respect to optimum energy consumption. These two general
goals: PMV achievement (in an expected period) and
minimum energy consumption are the conflicting ones.
Thus, there is a
n option to formulate the optimization
problem with two conflicting criteria and to search
eventually for the compromise solution.
In the control system
the
model predictive controllers have
been used. The analysis of their basic implementation in
air

con
ditioner system was presented in previous
papers
(Nowak and Urbaniak 2007;
Nowak 2008
;
Nowak and
Urbaniak 2010).
In this paper there is presen
ted
modifications of predictive controllers.
The methodology is
related to controllers that present almost the sam
e structure
and characteristics as in the classic solution. Thus, MPC
algorithms are defined by the process model related to
control purposes. The design of the control system is
characterized by four main steps (
Burdais at al. 2010;
Freire
at al. 2008;
No
wak 2008
;
Tatjewski 2002
):

process modelling: The data from input (manipulated)
and output (controlled) signals are used to predict the
process behaviour (output prediction) in a future
horizon, defined as a prediction horizon
(N
y
).

cost function definitio
n: The system closed

loop
performance during the prediction horizon is specified.
It is defined by using the output prediction, the
reference signal and the control effort.

cost function optimization: The cost function is
optimized as a function of the set
of future control
s
ignals (within control horizon
–
N
u
)
to be applied to the
process during the prediction horizon. In this step,
constraints for the manipulated and controlled variables
can be added in order to deal with the system operation
constraints,
e.g.
, limits on the actuators of the HVAC
system.

redefined strategy horizon: Only the first control signal
computed from the cost function optimization is applied
to the real process and, in the next step time, the whole
algorithm is repeated.
The contro
l rule is given by the following general
optimization problem (1):
(1)
where: x(i)
–
i

th reference, y(i)
–
i

th measured outpu
t,
∆u(i)
–
i

th manipulated variable change, λ
–
weighting
coefficient penalizing relative big changes in ∆u, N
y
–
prediction horizon, N
u
–
control horizon.
In this paper there is described the consideration of the
constraint over the control signal, impo
sed by the HVAC
device.
In view of the fact that control objects are non

linear in the air

conditioning system, an attempt to
modelling of non

linear objects
a
n
d are designed non

linear
predictive controllers
–
FMPC (
Fuzzy Model Predictive
Control
).
Step r
esponse necessary for the synthesis of the
fuzzy predictive controller was obtained by modelling an
object using fuzzy logic and observation of the step
response for model object.
There has been undertaken
experimental research using predictive algorithms
with
fuzzy modelling of model FDMC (Fuzzy

Dynamic Matrix
Control).
Detail of the rule base for heater formed by
observing the results of simulations of the air

conditioning,
are listed below:
If (T
out
is cold) and (T
in
is cool) then heater is heating.
If (
T
out
is very cold) and (T
in
is cool) then heater is strong
heating.
If (T
out
is warm) and (T
in
is warm) then heater is turned off.
If (T
out
is very warm) and (T
in
is very warm) then heater is
turned off.
Other objects were modelled: a cooler with a fan,
a
humidifier and a heat exchanger. For each of the models
designed DMC control law which is shown the following
equations (2):
R
c
i
: IF y(k) is A
0
i
and y(k

1) is A
1
i
and …
…and y(k

n
R
) is
A
nR
i
and u(k

1) is
B
1
i
and
…
(2)
…and u(k

m
R
) is
B
mR
i
THEN
∆u
i
(k)=
(k
e
)
i
e(k)

∑(k
q
u
)
i
∆u(k

q)
where: i=1,…,r indexes rule or local laws DMC control,
e(k)=x(k)

y(k) is control error.
Control signal is represen
ted by the following formula
(
Tatjewski 2002
)
:
(3)
where:
are
the
normalized weights (
activatin
g
levels
of
the corresponding fuzzy rules), ∆u
i
(k)
is
the output of the
i

th local controller
.
The
analytic structure
of
FDMC is shown in
Fig. 2
. The
dashed line is selected fuzzy inference block.
Figure 2:
Analytic structure of FDMC
The performance results of the FDMC controller are
compared with the results obtained by using conventional
PID algorithm.
Setting the set points for
air conditioning control system is
realized by minimizing the obje
ctive function. In general,
the objective function consists of the cost of non

OB
JECT
T
w
1
(k)
DMC 1
w
2
(k)
w
r
(k)
DMC 2
DMC r
…
∆
u
1
(k)
∆
u
2
(k)
∆
u
r
(k)
e(k)
x(k)
∆
u(k)
z/(z

1)
y(k)
y(k)
u(k)
…
OBIEK
T
T
w
1
(k)
DMC 1
w
2
(k)
w
r
(k)
DMC 2
DMC r
…
∆
u
1
(k)
∆
u
2
(k)
∆
u
r
(k)
e(k
)
x(k)
∆
u(k)
z/(z

1)
y(k)
y(k)
u(k)
…
compliance with the parameters of comfort microclimate in
the room, cost of realization of air changes and cost of air
conveying.
For tuning the classic controller (PID) we def
ined the
transfer function of the heating elements, heat exchangers,
condenser with fan and valves.
PID c
ontroller parameters
were tuned using
Signal Constraint
block of
Simulink
Response
.
Details of the transfer function and
the values
of
the coefficients
are presented in detail in previous works of
authors (
Nowak and Urbaniak 2007;
Nowak 2008
; Nowak
and Urbaniak 2010;
Nowak and Urbaniak 2011).
SIMULATION RESULTS
The mathematical model of thermal comfort
has been
implemented in Matlab
&
Simulink together
with the use of
intelligent algorithms in simulation investigations. The
main task of the proposed intelligent control system is to
provide thermal comfort and minimize energy
consumption. Simulation studies have been conducted by
taking into account two c
onflicting criteria: optimization of
the PMV index value, and energy saving.
The problem of
energy saving was analyzed by assuming that the PMV
index value must be in
cluded in the limit:

0,5 < PMV
<
+0,5.
I
n the Fig.
3
there is shown the curve of PMV in
dex
change
s
during 24 hours for an office

room (continuous
line
–
for the priority d
emand to aspire the PMV index
value to zero; dashed line
–
with additional restriction
of
energy consuming).
Fig
ure
3
:
Changes PMV index
Results of research of energy
consumption (power
consumed by the heater, cooler with fan and humidifier) for
a system with predictive control algorithms with fuzzy
model and the system using only the traditional PID control
algorithms in a cascade configuration were compared.
The
cours
e of changes of power heater (Pn) is presented in Fig.
4. The course of changes of power cooler (Pc) is presented
in Fig. 5. The course of changes of power humidifier (Pnw)
is presented in Fig. 6. In all cases the dashed lines present
the result of effect
of classical algorithms
–
PID, the solid
lines present the result of effect of fuzzy predictive
algorithms, the
b
old solid line represents the
actuator
set

point
.
Fig
ure
4
:
Changes of heater power
–
set

point (bold solid
line), classical algorithms (das
hed line), nonlinear
predictive algorithms (solid line)
Fig
ure
5
:
Changes of cooler power
–
set

point (bold solid
line), classical algorithms (dashed line), nonlinear
predictive algorithms (solid line)
Fig
ure
6
:
Changes of humidifier power
–
set

poin
t (bold
solid line), classical algorithms (dashed line), nonlinear
predictive algorithms (solid line)
CONCLUSIONS
In the paper
the
several approaches for thermal comfort
optimization with a use of simulation tools
we
re compared
.
The classic approach to
the control was expanded in the
research concerning minimization of power consumption
with maintaining thermal comfort index level within the
specified limits. The results of computer simulations
presented in the paper shows that the compromise between
t
wo conflicting goals is possible thanks to implementation
of intelligent control algorithms.
Method
s
of calculating the
total costs of the process were presented in previous papers
of authors (Nowak and Urbaniak 2007; Nowak and
Urbaniak 2011).
For comparis
on algorithms we calculated the values: the
total cost of the process (the sum of
:
error control in the
room
, unit cost of poor air quality,
airstream ventilation,
enthalpy before and after the transformation of air, unit cost
of air transformation, the co
st of energy,
pressure drop air
in pipe
,
efficiency of actuators
), cost of control expressed
by the
integral of the
absolute
control signal
, control
accuracy described by the
integral of the
absolute
error
signal
.
The v
alues: the total cost of the process
(
C
T
), costs
of control
,
values
of the control accur
acy for classical
algorithms and
fuzzy
prediction
algorithm were
compared
(see Table
1).
Table 1: Comparison of algorithms

the costs and
indicators
Classical
algorithms
FMPC
FMPC to
classical
(per
centage)
C
T
125,0
108,4
86,72%
C
ontrol
c
ost
102,7
98,8
96,20%
Control
accuracy
99,3
96,9
2,42
%
Fuzzy model predictive control (FMPC) algorithms are
most effective
ones
,
what allows to
reduce energy cost.
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umur
,
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and
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P.
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WEB REFERENCES
Energy pr
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(
http://ec.europa.eu/europe2020/pdf/energy3_en.pdf
)
Accessed on 15/07/2013
BIOGRAPHIES
Mariusz NOWAK
was born in Poland and went to the
Poznan University of Technology (control engineering).
He
obtained the PhD degree in 2007.
From
September 2007
he
is an
Assistant Professor
at the Institute of Computing
Science
of
the
Poznan
University of Technology.
H
is
research interest include: computer simulation,
intelligent control system, computer control systems for
environmental engine
ering, intelligent building systems
,
comfort climate control.
Andrzej URBANIAK
was born in Poland and went to the
Poznan University of Technology (control engineering) and
Poznan University of A. Mickiewicz (mathematics). He
obtained the PhD degree in 197
9. From 1990 he is
a
professor of Institute of Computing Science. He is author
or co

author of 5 books and over 200 papers concerning the
computer control systems and application of computer
science in environmental engineering.
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