level control in horizontal tank

1. Level Control in Horizontal Tank by Fuzzy-PID
Cascade Controller
Satean Tunyasrirut, and Santi Wangnipparnto
Abstract—The paper describes the Fuzzy–PID cascade controller
to control the level of horizontal tank that has diameter 300 mm and
480 mm long. Interface card module PCI-6024E in computer and
Lab View software program is used for built the cascade controller.
Structure of its where the inner loop is a PID controller for regulating
flow rate of system and outer loop is a Fuzzy logic controller for
control the level. The response time, steady state error, load
disturbance, and control valve action of cascade are tested and
compared with the simple controller. The experimental shows that at
the same water level 50% set-point, the rising time to set-point of
cascade controller is less than the simple controller about 1750 ms,
and it has steady state error less than simple controller about ±1% .
The load disturbance on the plant has no affect when using the
cascade controller. The control valve action of the cascade controller
has operation high frequency than the simple controller so the water
level in horizontal tank is smoothly constant. Overshoot affect on
cascade and simple controller has not occurred. the cascade
controller that consist of the PID and the fuzzy logic control to
improve the dynamic characteristic of the level control in horizontal
tank. The performance of it will comparing with the simple loop or
fuzzy logic controller.
Keywords—Fuzzy PID, level control, horizontal tank.
I. INTRODUCTION
OWADAYS, the various parameters in the process of
industrial are controlled such as temperature, level, and
etc. Some process needs to keep the liquid level in the
horizontal tank such as oil, chemical liquid in its. The level
control is a type of control method for common in process
system. The level control system must be controlled by the
proper controller. The objective of the controller in the level
control is to maintain a level set point at a given value and be
able to accept new set point values dynamically. The
conventional proportional-integral-derivative (PID) is
commonly utilized in controlling the level, but the parameter
of those controllers must be turned by tuning method either in
time response of frequency response to meet their required
Manuscript received November 30, 2006. The research has been supported
in part by Faculty of Engineering, Pathumwan Institute of Technology,
Bangkok 10330, Thailand and Research Center for Communications and
Information Technology, King Mongkut's Institute of Technology
Ladkrabang (KMITL), Bangkok 10520, Thailand.
Satean Tunyasrirut is with Asst. Prof at Pathumwan Institute of
Technology, Thailand. His research interests include modern control,
intelligent control, Power Electronics, Electrical Machine, and Drives (e-
mail: satean2000@gmail.com).
Santi Wangnippranto is with Asst. Prof. at Department of Electrical
Engineering, Faculty of Engineering, Pathumwan Institute of Technology,
Bangkok 10330, Thailand. His research interests include sensor technology,
control system, enhance heat transfer, and energy conversion.
(e-mail:nipparnto@gmail.com).
performances [1,2]. On the other hand, the fuzzy controller is
also popularly implemented in many practical industrial
automation applications.
II. THEORY
A. Cylindrical Horizontal Tank System
The structure of the liquid volume in horizontal tank is
shown in Fig. 1.
H
Fig. 1 The horizontal tank model
The continuity equation is essentially the equation for the
conservation of mass as follows;
o
o
o
i Q
Q
dt
dm
ρ
ρ −
= (1)
Where
m = ρV = Mass of water, kg
,
o o
Q Q
i o = Volume flow rate, inlet and outlet respectively.
ρ = Water density = 1000 kg/m3
o
o
o
i Q
Q
dt
dV
−
= (2)
When dV = 2(Dh-h2
)dh and Dh = 2Rh are substituted in
Eq.(2) and given as;
)
(
2 2
h
Dh
Q
Q
dt
dh o
o
o
i
−
−
= (3)
Where h
Cv
Qo
o = and Cv = value constant are substituted
in Eq.(3) and given as;
)
,
(
)
(
2
)
(
2 2
2
o
i
o
i
Q
h
f
h
Dh
h
Cv
h
Dh
Q
dt
dh
=
−
−
−
= (4)
N
World Academy of Science, Engineering and Technology 25 2007
78

2. Taylor-series expansion and Laplace transform are used,
and we get:
1
1
)
((
2
1
)
(
)
(
2 +
=
⎟
⎠
⎞
⎜
⎝
⎛ +
−
−
−
=
s
K
A
s
h
Dh
A
s
Q
s
H
o
i ω
(5)
where K= -1/(2A(Dh-h2
)) and ω = -1/A.
From the transfer function shows that K and ω as a function
of nonlinear h.
III. PID, FUZZY, AND CASCADE CONTROLLER
A. PID Controller
The most industrial process can be controlled with PID
control (Proportional-Integral-Derivative) provided in
equation:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
+
= ∫
t
dt
t
de
Td
dt
t
e
Ti
t
e
K
t
u
0
)
(
)
(
1
)
(
)
( (6)
Where u is the control variable and e is the control error
(e=ysp-y). The parameters of its can be determined by ultimate
sensitivity method that using Kc=4.5 and received the data
from Fig. 2. All data is used for calculated the parameters of
PID controller as shown in Table I.
Fig. 2 Data result from the ultimate sensitivity method
TABLE I
PARAMETERS OF PID CONTROLLER
Type of control Kc Ti TD
P 2.25 ∞ 0
PI 2.045 0.1037 0
PID 2.647 0.0625 0.01562
B. Fuzzy Logic Controller
Fuzzy control uses a list of rules than complicated
mathematical expressions. These rules are modeled after
decisions previously made by humans through the process
control system. The inputs of fuzzy logic controller are the
level error between the actual level and target level of the
level in horizontal tank. The fuzzy logic controller consists of
fuzzification, control rule and defuzzification stages. To create
the membership function, Membership function editor is used
for expressing input and output variables. The input variable
is the level error. The number of membership functions for
each input variable is designated in seven ranges. The setting
level of the horizontal tank is defined as the fuzzy controller
output, which has 49 membership functions.
(a)
(b)
(c)
Fig. 3 Membership function of input and output variables for the
level control; (a) error, (b) CE, and (c) output assumption
The form of all input and output membership functions is
selected to be triangle-shaped functions for simplicity. In
fuzzification stages, the input variables, the level is converted
into fuzzy variables by using the membership function as
shown in Fig. 3 where e and ce of level is the fuzzy subsets in
the universe. The linguistic rules are shown in Table II.
Pu = 25 ms
DelayTime =300 ms
PBu =22.22
Kc=4.5
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79

3. TABLE II
CONTROL RULES FOR INPUT AND OUTPUT VARIABLES
ce
e NB NM NS ZE PS PM PB
NB DE0 DE0 DE0 DE0 DE0 DE0 DE0
NM DE1 DE1 DE1 DE1 DE1 DE1 DE1
NS DE2 DE2 DE2 DE2 DE2 DE2 DE2
ZE DE3 DE3 DE3 DE3 DE3 DE3 DE3
PS DE4 DE4 DE4 DE4 DE4 DE4 DE4
PM DE5 DE5 DE5 DE5 DE5 DE5 DE5
PB DE6 DE6 DE6 DE6 DE6 DE6 DE6
C. Cascade Control
Cascade control can be used for improved disturbance
rejection when there are several measurement signals and one
control variable. Cascade control is built up by two control
loop as shown in Fig. 4. The inner loop is called the secondary
loop that using the PID controller, the flow transmitter is used
for sending the feedback signal. The outer loop is called the
primary loop that using the fuzzy logic controller, the level
transmitter is used for sending the feedback signal.
Fig. 4 Plant model of cascade control system
IV. EXPERIMENTAL SETUP
The simplified of the level control system is shown in Fig.
5. It consists of a microcomputer, interface card, level
transmitter, Flow transmitter, and linear control valve. The
microcomputer is a cascade controller that used for controls
the level in horizontal tank. The outer loop, the fuzzy
controller is received the level signal, computation and
sending control signal as the set point of PID controller. The
inner loop, PID controller is received the flow signal,
computation and sending control signal to the control valve in
order to keep the water level at the set point in the horizontal
tank.
Fig. 5 Plant level control set up
V. EXPERIMENTAL RESULTS
In this paper shows level control from 10-90% of the
horizontal tank by cascade controller. There are three types of
the experimental as the response time, load disturbance, and
control valve action are investigated.
A. The Response Time
The process response or response time of the level control
system, when changing the step set point from 0 to 10, 25, 75
and 90 are tested. At the step set point from 0 to 50%, the
response time of the simple loop or fuzzy controller and
Cascade controller are compared and shown in Fig. 6.
(a)
(b)
Fig. 6 The process response result at the step set point 0-50% when
(a) the fuzzy logic controller only, (b) the cascade controller
I / V V / I SUPPLY TANK 1
TANK 2
LT
FT
PI
MOTOR PUMP
HV1
HV2
HV3
HV4
HV6
HV5
CV1
L
H
4-12mA
4-20mA
0 - 10V
0 - 10V
4-20mA
A/D D/A
Terminal
block
CB-68LP
Interface
card
PCI-6024E
Controller
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80

4. From the Fig. 6 shows that the response time of the
cascade controller is less than the fuzzy logic controller about
7.9% and it has steady state error less than the fuzzy logic
controller too.
B. Level Control with Interrupt Load
At water level 50%, interrupting load by decrease water to
level 25% and off valve quickly. The response time of the
fuzzy controller only and the cascade controller are compared
and shown in Fig. 7. It is seen from the Fig. 7 that the fast
responses can also be obtained, the response time of the
cascade controller is less than the fuzzy controller only about
4.6%.
(a)
(b)
Fig. 7 The process response result at interrupting load when (a) the
fuzzy logic controller only, (b) the cascade controller.
C. Control Valve Action
Control valve action of the fuzzy controller only and the
cascade controller are compared and shown in Fig. 8. It is
seen from the Fig. 8 that the control valve of the cascade
controller operates at high frequency and keep level nearly the
set point.
(a)
(b)
Fig. 8 The action of control valve at level set point 50% when (a) the
fuzzy logic controller only, (b) the cascade controller
VI. CONCLUSION
PID and fuzzy controller are used for built the cascade
controller in order to control the level in the horizontal tank. It
has been shown that the speed of responses of the level
control system with and without load interrupt in the tank are
fast. Hence, it can be conclusion that;
1. The response time of the cascade controller less than
the single loop or fuzzy logic controller about 7.9%
at the step level set point 0 to 50%.
2. Both of the fuzzy logic controller and the cascade
controller give the smallest state error.
3. The interrupt load has slightly effect to the fuzzy
logic controller and the cascade controller.
4. The control valve action of the cascade controller is
operated at high frequency than the single loop so the
water level in the tank is smoothly
ACKNOWLEDGMENT
The authors gratefully acknowledge the Mr. Kampol-
Prompornchai and Mr. Watee Kaewpet who work hardly and
testing this research.
REFERENCES
[1] J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic
controller,” ASME Trans. Vol64, 1942, pp.759-768.
World Academy of Science, Engineering and Technology 25 2007
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5. [2] W. K. Ho, C. C. Hang, and J. H. Zhou, “Performance and gain and
phase margins of well-known PI Tuning formulas,” accepted for
publication in IEEE Trans. Contr. Syst. Technol., 1995.
[3] Jacob, J.Michael., “Industrial Control Electronics”, New Jersey:
Prentice-Hall, 1988.
[4] Passino, Kevin M., and Yurkovich, Stephen., “Fuzzy Control”, Sydney:
Addison-Wesley, 1998.
Satean Tunyasrirut received in B.S.I.Ed. in Electrical Engineering
and M.S.Tech.Ed in Electrical Technology from King Mongkut’s
Institute of Technology North Bangkok(KMITNB),Thailand in 1986
and 1994, respectively. In 1995 he was awarded with the Japan
International Cooperation Agency (JICA) scholarship for training the
Industrial Robotics at Kumamoto National College of Technology,
Japan. Since 1995, he has been a Asst. Prof at Department of
Instrumentation Engineering, Pathumwan Institute of Technology, Thailand. His
research interests include adaptive control, intelligent control, electric drives.
Santi Wangnipparnto received in B.S.I.Ed. in Electrical
Engineering from King Mongkut’s Institute of Technology North
Bangkok(KMITNB) ,Thailand in 1988 and M.eng and D.eng in
Energy Technology from King Mongkut University of Technology
Thonburi (KMUTT),Thailand in 1994 and 2001, respectively. In
1995 he was awarded with the Japan International Cooperation Agency (JICA)
scholarship for training the Sensor Technology at Nara National College of Technology,
Japan. Since 2005, he has been a Asst. Prof at Department of Electrical Engineering,
Pathumwan Institute of Technology, Thailand.. His research interests include Sensors,
Control system, Energy conversion, and Enhance heat transfer .
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