This document summarizes a study that compares different control methods for HVAC systems. It presents a mathematical model of an air conditioning system including a heat exchanger and conditioned space. It then describes a PID-cascade control system designed for the HVAC system, which combines a traditional PID controller for the inner loop with a PID controller for the outer loop. Simulations showed the PID-cascade controller had better performance in rejecting disturbances compared to traditional PID or compensator controllers alone.

1. The Second International Conference on Control, Instrumentation and Mechatronic Engineering (CIM09)
Malacca, Malaysia, June 2-3, 2009
PID-Cascade for HVAC System Control
Raad Z. Homod, T. M. I. Mahlia, Haider A. F. Mohamed
Center for research in Applied Electronics (CRAE)
University of Malaya, 50603 Kuala Lumpur, Malaysia
Tel: +60133353502 Email: raadahmood@yahoo.com
1
Department of Electrical & Electronic Engineering
The University of Nottingham Malaysia Campus
Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan, Malaysia
E-mail: haider.abbas@nottingham.edu.my
Abstract
The primitive controller used in the early version
for the HVAC, like the on-off (Bang-Bang)
controller, which is inefficient, inaccurate, instable,
and high-level mechanical wear. While the PID,
compensator, cascade controllers overcoming to these
disadvantages but when the offset response
(inaccurate), occur; the power consumption will
increase. In order to acquire better performance in
the central air-conditioning system, the PID-cascade
control was studied through comparing the
traditional PID, industrial PID (Ziegler-Nichols
tuning) and compensator controllers in simulation
and experiments. The output of system was predicted
through indoor, outdoor disturbance, at last based on
the mathematical model of air-conditioning space,
the simulations have found that PID- cascade
controller has the capability of self-studying and self-
adapting and obtain faster response and better
performance.
Keywords- PID, compensator, PID-cascade, HVAC
system, disturbance rejection.
NOMENCLATURE
Symbols
Mh The quality of heat exchanger, (kg)
AHU Air handling unit
Mr Air quality of air-conditioning room, (kg)
Ga Supply air flows ,(kg/s)
Gw Cold water (or hot water) flows,(kg/s)
Ca Specific heat capacities of air, (kj/kg Co
)
Cw Specific heat capacities of water(kj/kg Co
)
Ch Specific heat capacities of heat exchanger
(kj/kg Co
)
Tm The temperature of mix fresh air, (Co
)
Tl The temperature after heat exchanger,
(Co
)
Th Surface temperature of heat
exchanger,(Co
)
Twin The temperature of supply water, (Co
)
Tw out Back-water from heat exchanger, (Co
)
Qroom Perturbations inside thermal load, (kj)
Tout Uncontrolled outside temperature (Co
)
K1 the amplify coefficient of heat exchanger,
(Co
.s /kg)
T1 Heat exchanger time constant, (s)
Gr(s) the disturbance of heat exchanger, (kg/s)
K2 the amplify coefficient of room, (Co
.s/kg);
is; is Here,
T2 Conditioning space time constant, (s)
Tf (s) the disturbance to room, which include
the disturbances from outdoor and indoor,
(Co
).
Subscripts
h Heat exchanger
r Room
a Air
w Water
m Mixed fresh and return air
l Leaving
W in Water input
W out Water output
room Inside room
out Outside room
1,2 Heat exchanger, room region
f Indoor and outdoor
598

2. The Secon
Malacca, M
1. Introd
Heating,
systems are
Current HV
different c
components
these system
of air in b
occupants. T
satisfy the c
inertia, dela
disturbance
the dissatis
dissatisfying
different run
traditional P
Cascade
effect of a
control syst
reducing th
the cascade
frequency o
effect of cas
In this
conditionin
Then the
which com
cascade. T
in terms of
specificatio
Throug
found that
rejects the
response s
system.
2. Math
There a
mathemati
known law
the process
F
nd International
Malaysia, June
duction
Ventilation a
e widely used
VAC systems
ontrol schem
s, etc. Operati
ms have to kee
buildings, to m
Traditional PID
control purpos
ay and nonline
factor, like the
faction of tun
g performanc
nning medium
PID control, we
control is esp
load disturba
tem slowly. Th
e lag in the o
system respon
of oscillation.
scade control [
s study, the
ng space in the
PID-cascade
mbines the t
The cascade int
f the robust co
on.
gh the simulati
the PID contro
e disturbance a
speed and con
hematical M
are basically
cal model of
ws of nature o
s.
igure (1) Room-
l Conference o
2-3, 2009
and Air-Condit
d in different
are complex
mes, instrumen
ing twenty fou
ep the quality
maintain the
D controller som
e to the object
ar characterist
e tall and big sp
ning parameter
ce and the
m. To overcomi
e will add casc
pecially useful
ance that mov
he inner loop h
uter loop, with
nds more quick
Simulation wi
2-3].
heat excha
e HVAC syste
control system
traditional PI
ternal loop con
ontrol H2 optim
ion in the HVA
oller enhances
and the cascad
ntrol precision
Model for HV
two ways of
f a system: by
or through exp
-air conditioning
on Control, Inst
tioning (HVAC
t environment
x and integra
nts, mechanic
ur hours a da
and temperatu
comfort of th
metimes doesn
t, which is larg
tic and uncerta
pace, because
rs, the effect
adaptability
ng the failing
cade [1].
in reducing th
ves through th
has the effect
h the result th
kly with a high
ill illustrate th
anger and ai
em are modele
m is presente
D control an
ntrol is designe
mal performanc
AC system, it
the stability an
de increases th
n in the HVA
VAC System
f determining
y implementin
perimentation o
g system
trumentation an
C)
ts.
ate
cal
ay,
ure
he
n’t
ge
ain
of
of
to
of
he
he
of
hat
her
his
ir-
ed.
ed,
nd
ed
ce
is
nd
he
AC
m
a
ng
on
The fir
model
the air
the sec
parts a
2.1 He
Bas
therma
The tra
got fro
Wh
T1 is ti
contro
exchan
2.2 Co
Here
model
the sp
exchan
temper
heat ca
the spa
similar
Here th
air tem
that th
room
and C
space t
nd Mechatroni
rst one will tak
for HVAC wh
-processing un
cond part is the
are illustrated in
eat Exchanger
sed on the law
al balance equa
ansfer function
om (1).
here K1 is the c
ime constant, (
lled object, (s
nger, (kg/s). He
,
onditioning sp
e the supposi
of air-conditio
ace is airtight
nge between In
rature in the s
apacity of the
ace is ignored
r to the heat ex
he supply air te
mperature after
he specific heat
is equal to sp
Cr = Ca. The
temperature ca
ic Engineering
ke to obtain the
hich contain fro
nit (heating/coo
e air-conditioni
n figure (1).
r model
conservation o
ation [4] is sho
.....................
n of handled air
.
coefficient of
(s); τ1 is the pu
s); Gr is the
ere,
,
ace model
ition for the
oning space is
t and there is
ndoors and ou
space is almos
door, window
d. The thermal
xchanger [4].
emperature to r
r AHU and T
t capacity of ai
pecific heat cap
transfer funct
an be got from
(CIM09)
e mathematical
om the first par
oling system) a
ing room. Thes
of energy, the
wn as followin
.....................(
r temperature c
.....................(2
amplify, (Co
.s
ure time delay
disturbance o
temperature c
s followed as:
not the direc
utdoors; second
st equal; third
ws and the go
balance equat
.....
room is the han
Ts= Tl. Here a
ir in air-condit
pacity of supp
tion of condit
(3).
rt is
and
se two
ng:
1)
can be
2)
s /kg);
of the
f heat
control
firstly
ct heat
dly the
dly the
ods in
tion is
(3)
ndling
assume
ioning
ply air
ioning
599

3. The Secon
Malacca, M
Where K2
/kg); T2 is
of the con
room, whic
indoor, (Co
The transfe
conditionin
3. Co
An air-
consists of
deliver he
conditione
on/off type
the temper
valve on th
mixed with
ratio of ou
requiremen
In normal
job of m
However,
the outsid
rapidly. W
as does the
causes a dr
senses and
volume of
recover to
We can
problem,
which is u
encompass
Therefo
steam flow
a steam-flo
(steam flo
(change in
nd International
Malaysia, June
is the amplif
time constant
ntrolled object
ch include the
o
). Here,
,
er function of h
ng space can b
ontrol Syste
-handling unit
f a fan, heating
eated/cooled
d space, a thro
e common in r
rature and cont
he heating coil
h outdoor air a
utdoor air to r
nts for ventilati
l operation, the
maintaining a
in the particul
de air temper
When it does, th
e discharge air
rop in the spac
d corrects for
f space, it take
the desired tem
n improve the c
by adding a
used in an inne
s the disturbanc
ore the possibl
w and cascade t
ow controller.
ow) does not
outdoor air tem
l Conference o
2-3, 2009
.........
fy coefficient
t, (s); τ2 is the
t, Tf (s) is the
disturbances fr
,
heat exchanger
e got from (2)
em Design
t for a comm
g coil, and disch
air to the
ottling-type the
residential app
trols a steam (o
l. Return air fr
at the inlet to th
return air is u
ion (see Figure
e thermostat d
a stable spac
lar climate of
rature sometim
e mixed air tem
r temperature.
ce temperature
this, but becau
es an excessive
mperature.
control system
n intermediat
er feedback lo
ce.
le solution is
the output of t
But the flaw i
t encompass
mperature).
on Control, Inst
................(4)
of room, (Co
.
pure time dela
e disturbance
from outdoor an
r and
and (4)
.......(5)
mercial buildin
harge air duct
space. In th
ermostat (not th
lications) sens
or chilled wate
rom the space
he fan. The fixe
used to meet th
e 2).
does an adequa
ce temperatur
this applicatio
mes drops ve
mperature drop
This eventual
. The thermost
use of the larg
ely long time
m to alleviate th
te measureme
op and that w
to measure th
the thermostat
in the inner loo
the disturban
trumentation an
s
ay
to
nd
ng
to
he
he
es
er)
is
ed
he
ate
re.
on,
ry
ps,
lly
tat
ge
to
his
ent
will
he
to
op
ce
Fig
The
temper
shown
drops,
discha
discha
compa
Hence
approx
3.1 Ar
There
design
system
Here w
air-con
G1 and
heat e
G2m ar
setpoin
loop c
outside
3.2 PID
There
contro
Figu
nd Mechatroni
gure (2) A Casca
e possible solu
rature and let
n in Figure (2).
and consequen
arge temperatu
arge temperatu
arison with the
, the discharg
ximately consta
rchitecture of
are some resea
n and tuning rul
m [4].
we designed th
nditioning syst
d G2 are respe
exchanger and
re respectively
nt response co
controller, Qro
e load disturba
D tuning
are a large num
ller.
ure (3) Block di
C
ic Engineering
ade Control App
ution is to me
that control
. When the out
ntly the mixed
ure controller w
ure control loo
e space tempe
ge temperature
ant at its set po
the PID-casca
arches to study
le of traditiona
he cascade con
tem, which is s
ectively the co
d air-condition
y identification
ontroller and F
oom internal lo
ance.
mber of method
agram of propos
Cascade control
(CIM09)
plication in the H
easure the disc
the steam val
tside air tempe
d air temperatu
will sense this
op will be rap
erature control
will be main
oint [6-7].
ade
y simple contro
al cascade contr
ntrol system f
shown in Figu
ontrolled proc
ning room; G1
n models, PID
F (s) is the in
oad disturbanc
ds of tuning a P
sed model based
HVAC
charge
lve, as
erature
re, the
s. The
pid, in
l loop.
ntained
oller
rol
for the
ure (3).
ess of
1m and
is the
nternal
ce, Ta
PID
d on
600

4. The Secon
Malacca, M
The mo
reaction cu
referred to
From the Z
traditional
Kp=0.199,
3.2 Intern
As F
function of
Where Ts i
Then the
function is
Where f in
In the i
disturbance
loop contro
time delay
isoparamet
it is consid
and the er
robust con
actual des
function is
where λf is
λf is
practical a
then be tu
control per
The F(s) ca
To carry ou
can be is sh
nd International
Malaysia, June
ost popular one
urve method an
as the Ziegler–
Ziegler-Nichol
single PID con
, Ki= 0.0006 an
al loop contro
Figure.3 show
f middle proce
is the output of
e closed-loop
obtained as fo
nner (miner) fee
deal condition
, which
e inputs to the
oller F should
y. Then the c
tric signal to re
dered that the
rror is gradual
ntrol H2 optim
ired closed-lo
designed as th
s a control para
needed to tu
application, λf
uned monotoni
rformance.
an be solved fr
.
ut conveniently
hown as follow
l Conference o
2-3, 2009
s amongst them
nd instability m
–Nichols tunin
ls rules the par
ntrol are tuned
nd Kd= 7.063.
oller
ws, the distu
ss is shown as
.................
f G1(s).
complement
ollowing:
.................
edback
n, Td(s) should
means that
e middle proc
detect the err
ontroller F ou
eject the distur
output of cont
lly offset. Her
mal performanc
op complemen
he following:
......................
ameter.
uning in con
can be initial
ically on-line
rom (7) and is s
.......................
y, (9) is transfe
wing:
on Control, Inst
m are the
method. Both ar
ng method.
rameters of the
as following:
[8]
urbance transf
following:
................(6)
tary sensitivi
................(7)
be as the form
when the T
ess, the intern
ror of Ts after
utputs a rever
rbance. Actual
troller is limite
re based on th
ce objective, th
ntary sensitivi
................(8)
ntrol system.
ized to (τ
1
) an
to obtain bett
shown in (9).
................(9)
erred and F(s)
trumentation an
re
fer
ity
m:
Ta
nal
τ1
rse
lly
ed
he
he
ity
In
nd
ter
where
So the
Figure
Wh
system
disturb
robust
disturb
robust
consid
applica
P1, τ1.
also be
λf is tu
perform
5. Sim
To
techniq
simula
Th
tuning
Ziegle
Fo
design
plottin
system
nd Mechatroni
F1(s) can be ex
configuration
e 4.
Figure (4) Co
hen λf is relati
m is relatively
bance rejection
of control
bance rejection
and disturb
dered to be
ation, λf can be
If the process
e initialized ne
uned automatica
mance.
mulation
evaluate th
ques, impleme
ation is present
e PID parame
method [5].
r-Nichols meth
or compensator
n the compens
ng of the freq
matized and sim
ic Engineering
..................
xpressed as fol
....
of observer F
onfiguration of o
ively large, th
strong, but a
n will be weak
system is re
n will be relat
bance rejection
the tuning o
e initialized ne
P1 has not pu
ear to the time
ally on-line to
he goodness
ented on the
ted below.
eters are tuned
While PID in
hod [7, 11].
r used bode pl
sator [2, 9]. T
quency transfe
mplified by usin
(CIM09)
.......................
llowing:
.......................
can be shown
observer F [4]
he robust of c
at the meantim
k. When lessen
elatively weak
tively strong. S
n should be
of λf. In pra
ear the time de
ure time delay,
constant of P1
obtain better c
of the pro
HVAC system
d in the robus
dustrial tuning
lot and root-lo
The bode plo
fer function c
ng logarithmic
(10)
(11)
in
control
me the
ing λf,
k, the
So the
both
actical
elay of
λf can
. Then
control
oposed
m, the
st PID
g used
ocus to
ot is a
an be
plots.
601

5. The Secon
Malacca, M
The par
air conditi
4.5m heigh
kJ/kg.Co
, t
criterion in
field, the n
room and
Ga=1.08kg
1/R=0.2kw
cold-water
summer is
middle pr
following:
The pa
calculated
the contro
[10]
and the dis
expressed
Simula
controllers
setpoint re
has accurat
and the PID
Figure
nd International
Malaysia, June
rameters of the
oning room is
ht, the air spe
the air density
n the heating, v
number of takin
d the calcula
g/s, the hea
w/Co
and the
r and back-wa
Twin-Twout= -
rocess, heat e
K1= -19.35Co
.
arameters of
as following:
lled object G1
.
.
sturbances from
as:
0.052
0.81 0.
tion (1) the co
s are shown in F
sponse of the P
te response wh
D-cascade cont
(5) The simulat
l Conference o
2-3, 2009
e HVAC system
s 10 m length,
ecific heat cap
y is 1.2 kg/m3
ventilation and
ng a breath in
ation of the
at resistance
temperature e
ater to the hea
5Co
. At last th
exchanger, are
. s /kg, T1=30s
air-condition
K2=0.4Co s /k
1(s) and G2(s)
.
1
m outdoor and
926
mparison curv
Figure 5, it is s
PID-cascade co
hile the others a
trol responses
ion results of fou
on Control, Inst
m: the volume
8m width an
pacity is Ca=1
3
, Based on th
air-conditionin
air-conditionin
supply air
of wall
error of supp
at exchanger
he parameters
e calculated
.
ning room a
kg, T2=338s. S
can express a
.........(12)
.
...(13)
1
indoors can be
ves of four
seen that the
ontrol system
all have offset
quicker.
ur controllers
trumentation an
of
nd
.0
he
ng
ng
is
is
ply
in
of
as
are
So
as:
)
)
e
Sim
disturb
system
in ste
parame
simula
Ziegle
are sho
contro
is near
the dis
contro
contro
Fig
Sim
contro
parame
contro
proces
K1=-2
increas
4. it is
simula
PID c
simula
contro
Figu
6-
The
adaptiv
forwar
air-con
perform
Throug
nd Mechatroni
mulation (2)
bances of PID
m, the input of d
ep at 4000th
eters are kept
ation results o
r-Nichols PID
own in Figure
l is less that ot
r to the traditio
sturbances of
llers is simil
ller was respon
gure (6) The resp
disturbanc
mulation (3) to
l in the HVA
eters are ch
llers are kept u
ss, K1=-19.35 C
1.3 CO
s/Kg,
se 10%. The si
s seen that the
ation 1. Howe
control is grea
ation 3 can pro
l system.
ure 4 The step re
parameter
Conclusion
e PID-cascade
vely adjusting
rd, is adopted
nditioning sys
mance than
gh simulation
ic Engineering
To validate t
D-cascade con
disturbance in
second wh
t as same as
of traditional
tune and PID
e 6. The oversh
ther controllers
onal PID contr
traditional PI
lar. Moreover
nses quicker.
ponse for four co
ce is input at 400
o certify the rob
AC system, the
hanged to si
unchanged. Th
CO
s/Kg, K2=0
K2=0.924 CO
imulation resul
setpoint respo
ever, the over
ater than the
ove the robust
sponse for four c
rs of process are
controller, wh
the PID gains
the constant
stem. It has
traditional PI
n and experi
(CIM09)
the rejection t
ntrol in the H
ncreased from 0
ile the contr
Simulation 1
PID, compen
D-cascade contr
hoot of PID-ca
s, its governing
rol. The reject
ID and PID-ca
r, the PID-ca
ontrollers when t
00 seconds
bust of PID-Ca
e controlled p
imulate while
he gain of cont
.8 CO
s/Kg, be
O
s/Kg, which
lts are shown i
onse is similar
rshoot of trad
simulation 1
of the PID-Ca
controllers when
e changed
hich is a meth
s using cascad
temperature c
shown the
ID control sy
iment, PID-ca
to the
HVAC
0 to 50
rollers
1. The
nsator,
rollers
ascade
g time
tion to
ascade
ascade
the
ascade
process
e the
trolled
comes
both
in Fig.
to the
itional
. The
ascade
n the
od for
de feed
central
good
ystem.
ascade
602

6. The Second International Conference on Control, Instrumentation and Mechatronic Engineering (CIM09)
Malacca, Malaysia, June 2-3, 2009
control has better robust and adaptability to nonlinear
object. The air-condition system, which is controlled
by PID-cascade controller, in central air-conditioning
system, the control system has fast response and better
performance even if the seasonal outdoor heat
disturbance and uncertain indoor heat disturbance. The
PID-cascade control also applies the object which has
large inertia, pure lag, nonlinear characteristic and
uncertain disturb factor.
7. References
[1] Cheng-Ching Yu (2006) “Autotuning of PID
Controllers” 2nd Edition chp. 1, Pp. 17. London Springer
Verlag.
[2] Donald R. Coughanowr (1991) “Process Systems
Analysis and Control” Second Edition Chap. 15 Pp. 177,
New York publisher McGraw-Hill Inc.
[3]Antonio Visioli (2006)”Advances in Industrial
Control” 2nd
edition London publisher Springer-Verlag
[4]Wang, Jiang-Jiang; Zhang, Chun-Fa; Jing, You-Yin;
(2007) “Research of Cascade Control with an Application to
Central Air-Conditioning System” International Conference
on Machine Learning and Cybernetics, Vol 1, Pp.498 – 503
19-22 Aug. (2007)
[5] Q. Li, G. Zeng, X. Zhu and P. Sun, “A comparative
study of PID tuning methods,” Techniques of Automation
and Application, vol. 24, no. 11, pp 28-31, November 2005.
[6] Harold L. Wade (2004)”Basic and Advanced
Regulatory Control: System Design and Application” 2nd
Edition, the United States of America. ISA-The
Instrumentation, Systems, and Automation Society.
[7] Jairo Espinosa, Joos Vandewalle and Vincent Wertz
(2005) “Advances in Industrial Control” Part 1 pp 21-22
[8] Graham C. Goodwin, Stefan F. Graebe and Mario E.
Salgado, (2000) “Control System Design” ch. 3 pp 69-70.
Australia, Valpara´ıso.
[9] John J. D’Azzo and Constantine H. Houpis(2003)
“Linear Control System Analysis And Design With Matlab”
Fifth Edition chap.10 Pp. 37 , New York, Marceld Dekkerin
Inc.
[10] Wang, Jiangjiang; Zhang, Chunfa; Jing, Youyin;
(2007)”Hybrid CMAC-PID Controller in Heating Ventilating
and Air-Conditioning System” International Conference on
Mechatronics and Automation, Pp.3706 – 3711, 5-8 Aug.
2007
[11] Brian Roffel and Ben Betlem (2006) “Process
Dynamics and Control” chp. 32, Pp.463, West Sussex,
England, publisher John Wiley & Sons Ltd.
8. BIOGRAPHIES
Mr. Raad Z. Homod He
graduated with a B.Eng. in
Mechanical Engineering from the
University of Basrah, Iraq in
1991. He worked as engineer for
five years in General
Establishment of Steel & Iron
(Iraq) and then he worked ten years as HVAC
engineering in Al-Tomoh Al-Kabir Company (Libya).
Currently, he is perusing his Master in HVAC Systems
and Control at the Department of Mechanical
Engineering in University of Malaya.
DR. T.M. Indra Mahlia
received B.Eng from the
University of Syiah Kuala,
Indonesia, and M.Eng.Sc and
PhD from the University of
Malaya. He is currently an
Associate Professor at the
Department of Mechanical
Engineering, University of Malaya, Kuala Lumpur,
Malaysia.
Dr. Haider A. F. Mohamed
received his PhD in Electrical
Engineering from the
University of Malaya,
Malaysia in 2006. He worked
as a computer engineer for
two years and as a researcher
for four years before he
became a lecturer in the
Department of Electrical
Engineering in University of Malaya, Malaysia, in
2000. His main research fields are identification and
nonlinear intelligent control of various systems such as
robot arms, automated guided vehicles, and electric
drives.
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