 Open Access
 Total Downloads : 170
 Authors : Trinh Luong Mien
 Paper ID : IJERTV6IS110213
 Volume & Issue : Volume 06, Issue 11 (November 2017)
 Published (First Online): 28112017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Liquid Level Control of CoupledTank System Using FuzzyPid Controller
Trinh Luong Mien
Falculty of Electrical and Electronic Engineering University of Transport and Communications
No. 3 Cau Giay, Lang Thuong, Dong Da, Hanoi, Vietnam
Abstract: Liquid level control of coupledtank is widely used in the chemical industry – the environment is often affected by noise. The article deals with the fuzzyPID controller applied to the nonlinear dynamic model of the liquid level of the coupled tank system, taking into account the effects of noise. FuzzyPID controller is designed based on PID initial parameters (determined based on the linear model) and fuzzy logic calculator for tunning PID parameters (suitable for nonlinear models and noise). The study results are caried out throught simulation model on Matlab using the coupledtank nonlinear model with noise, applying the fuzzyPID proposed controller, PID based on Ziegler Nichols.
Keywords: PID, Fuzzy, Level control, Coupledtank

INTRODUCTION
Liquid level control is always in great demand in the chemical industry, petrochemical refining, water treatment, power generation and construction material production. In these technological processes, the fluid is pumped, stored in a tank, and then pumped to another tank. Over the liquid is processed by chemical reaction and/or agitation in the tank, where the liquid level in the tank is controlled [1,2,14]. The coupled tank systems are commonly used in industries and the master of controlling the level of liquid in the tank, the flow control between the tanks is an important of all technological process control systems. Today's chemicals – the field has a tremendous impact on our economy [1,13,14]. Improving the quality of control and increasing the efficiency of the processing/production process is always required in this field, in order to reduce production/processing cost and lower production cost.
Nonlinearity, associated kinetic and uncertainty are the major challenges posed by controlling the liquid level in the coupledtank. Most of the coupledtank object in published studies use a linear mathematical model when designing the controller, such as PID controlller [10,12], fuzzy controlller [9], fuzzyPID [8], LQR, state feedback controller, model reference adaptive control [4,13].
A number of recent studies have also addressed the nonlinear model of coupled tank using nonlinear control strategies such as sliding mode control [5,7,11], backstepping
coupledtank in the recently published works is good, but the implementation of these controllers is complex, the disturbance factor is not really considered.
This article proposes a control approach: combining between the fuzzy logic calculator and traditional PID controller for a nonlinear model with noise of the liquid level coupledtank control system. Firstly, the article presents a nonlinear model of the liquid level coupledtank control system. Then, the PID controller is designed based on a linear model of the coupledtank according to the method Ziegler Nichols; designing the fuzzy logic calculator for tunning PID parameters applied in the nonlinear model with noise of the coupledtank system. Finally, the study results is caried out throught simulation model on Matlab, showing the efiectiveness of the proposed control strategy.

DYNAMIC MODEL OF COUPLEDTANK SYSTEM This article deals with the coupled tanks with the two
separate vertical tanks (see Fig. 1). Both tanks are interconnected by a flow channel where a rotary valve will be used to vary the sectional area of the channel by changing the discharge coefficient of the valve B. The liquid is fed into the first tank through the DCmotor controlled electric valve. Then the liquid flows to the second tank through the manual valve B, the liquid flows out of the tanks through the manual valve A or/and the manual valve C by adjusting the discharge coefficient of the valve A, C. The liquid level in the second tank is measured by the liquid level untrasonic sensor that converts the real physical level in the second tank l2 [cm] to an electrical voltage signal y [V].
y ksl2 (1)
where ks [V/cm] is gain of level untrasonic sensor.
The control objective is to control the height of the liquid level in the second tank by manipulating the flow rate of the liquid into the first tank by means of the electric valve voltage. Assume that the valves output volume flow rate fi [cm3/s] is proportional to the manipulating voltage applied to electric valve u [V] as below equation:
control [3], passivity based control [6], fuzzy logic controller [1], neurofuzzysliding mode controller [2]. It can be seen
fi kvu
(2)
that the quality of the liquid level control system of the
where kv is gain of the electric valve [cm3/s/V].
Inlet
u y
MV,
liquidkv
Electric valve
AC
volltage signal
Tank 1
fi
l1
b, Cb
CV,
k
voltage signal
s
Tank 2
l
Level untrasonic sensor
Ve fi
LC
101
LT
l2SP
LR
101
LAH
101
LI
motor A1
Pump
fb
Valve B
2 A2
l1
A1 fb
101
A2
l2
101
LAL
101
a, Ca
Valve A Valve C
fa fc
c, Cc
Va 1
fa
Vb 2 Vc
fc
Level Sensor
Coupled Tank
(a). Schematic diagram of the coupledtank apparatus
(b). P&ID of the coupledtank liquid level control system
Electric Valve
Level controller
r u fi
l2 y
Voltage –
Voltage
Flow rate
Level Voltage
c). The block diagram of the coupledtank control system
Fig. 1. Description of the coupled tank liquid level control system
The liquid used in the coupled tank is assumed to be
dw1 w w w A dl1 f f f
A dl1 f f f
(6)
steady, nonviscous, incompressible type of liquid. Applying Bernoulli's principle for the liquid at point 1 (before valve B)
dt i a b
1 dt
i a b
1 dt
i a b
and point 2 (after valve B) with corresponding pressure p1 and
p2 (Fig. 1b), we have 2 cases:
dw2 w w A dl2 f f dt b c 2 dt b c
A dl2 f f
2 dt b c
(7)
Case 1: when the liquid level in tank 1 is higher or equal the liquid level in tank 2, l1l2, the liquid flows from tank 1 into tank 2, we obtain the balance equation:
where wi, wa, wb, wc are mass flowrate; A1, A2 [cm2] are respectively section area of the first tank and second tank.
p v2 p g(l l ) f bC 2
Using above equations (2), (3c), (4), (5), thus we obtain
1 2 2 1 2 b b f
bC
2g l l
(3a)
2
2 b b 1 2
dl 1
where g=981[cm2/s] is acceleration of gravity; l
[cm] is level1
(kbu aCa
2g l1 sign(l1 l2 )bCb
2g  l1 l2 )
(8)
3 1 3 dt A1
in the first tank; [g/cm ] is liquid density; fb [cm /s] is volume flow rate through valve B, v2 [cm/s] is liquid velocity at point 2; b [cm2] is section area of valve B, Cb [%] is percentage of opening valve B
dl2 1 (sign(l l )bC dt A 1 2 b
2
2g  l1 l2  cCc
2g l2 )
(9)
Case 2: when the height of the liquid level in tank 1 is less than in tank 2, such as l1<l2, the liquid flows from tank 2 into tank 1, we obtain the balance equation:
The equations (8) and () represent a nonlinear dynamic relationship of the liquid level (l1 and l2) in the two tanks with the ideal equations for the valves. In general applications, the square root law is only an approximation by solving directly
fb bCb
2g l2 l1
(3b)
the nolinear equations (8) & (9). But if the operating point is known and does not change quite often then it is convenient to
Combining the above equations, we have flowrate equation through the valve B as follows
linearize the system obtained by first principles around the desired operating point. This makes the process significantly simpler and the model works well in a region around the
fb sign(l1 l2 )bCb
2g  l1 l2 
(3c)
chosen operating point. This allows us to easily use linear control theory to design linear controller for the linear model of
Similarly, we obtain the volume flowrate equations
through the valve A, C as:
the coupledtank, such as PID controller.
fa aCa 2g l1
f cC 2g l
(4)
(5)
The linear model of the coupledtank: At the desired operating point of the fluid level in the second tank L2s, the control system is at steady state, so on:
c c 2
where a, c [cm2] are respectively section area of valve A, C;
dL1s 0 1 (k U aC
2g L

sign(L

L )bC
2g  L L )
(10)
and Ca, Cc [%] are percentage of opening valve A, C
dt A1
b s a 1s
1s 2s b
1s 2s
respectively.
dL2s 0 1 (sign(L

L )bC
2g  L L
) cC
2g L )
(11)
The coupled tank dynamics are based on the principle of
dt A2
1s 2s b
1s 2s c 2s
mass balance which states that the rate of change of liquid mass in each tank equals the net of liquid mass flows into the tank. Here it assumes that the liquid density and cross area of tanks are constant
where L1s is height at steady state, Us is pump voltage at at steady state.
DA
Inner diameter of valve A
0.5
cm
DB
Inner diameter of valve B
0.7
cm
DC
Inner diameter of valve C
0.5
cm
Hmax
Max. height of liquid level in tank 1, 2
30
cm
Considering a small incremental change in the control input, u in Us, which subsequently cause an incremental change in height in the two tanks, l1 in L1s and l2 in L2s. Hence, equations (8) and (9), assuming that the fluid always flows from tank 1 to tank 2, can be rewritten as:
d(l1 L1s ) 1 [k (u U ) aC
2g l L bC
2g l l L L ]
(12)
Assume that the desired height of fluid level in the second
dt A1
b s a
1 1s b
1 2 1s 2s
tank L2s
=15[cm], from equations (10), (11) and (20), we obtain
d(l L ) 1
the linear model of the liquid level process of the coupledtank
2 2s
(bC
2g l l L L

cC
2g l L )
(13)
system as below:
b
dt A2
1 2 1s
2s c
2 2s
G (s) l2 (s) 0.0176
L2
(21)
Following Newton's binomial generalized theorem, if x<<1 then we can approximate:
u(s)
s2 0.362s 0.007
(1 x) 1 x
(14)


THE FUZZYPID CONTROLLER DESIGN FOR
Applying the above approximation (14), we obtain the below equations:
LIQUID LEVEL PROCESS OF THE COUPLED TANKS SYSTEM
l1 L1s
L (1 l1 )
1s
L1s
l
L (1 l1 )
1s
2L1s
l
l1
L
2 L
1s
1s
l
(15)
The structure of the fuzzyPID controller for the liquid
level process of the coupledtank system is proposed as in Fig.
2. The fuzzyPID controller is a combination of the basic PID and the fuzzy logic calculator. The initial parametters
l2 L2s
L2s (1 2 )
L2s (1 2 )
L2s 2
(16)
kP0 , kI 0 , kD0
of the basic PID are definited based on the
L2s
2L2s
2 L2s
common methods, such as Ziegler Nichols (PIDZN), Chien
l l L L
(L L )(1 l1 l2 )
L L
l1 l2
(17)
Hrones Reswick (PIDCHR). The
kPF , kIF , kDF
are seft
1 2 1s 2s
1s 2s
L1s L2s
1s 2s
2 L1s L2s
tunning parametters of PID based on fuzzy logic calcutalor (FuzzyCal block in Fig.2) for the nonlinear model of coupled
Substitute these approximation equations (1517) into
(1213) and in combination with equations (1011), we obtain:
dl1 (k k )l k l kb u (18)
dt 1 2 1 2 2 A
1
dl2 k l (k k )l (19)
tank with the noise.

Designing the basic PID controller
The basic PID is designed based on the linear model of the liquid level process of the coupledtank system. Using the Ziegler Nichols method, we can determine the initial
dt 3 1 3 4 2
paramaters kP0
, kI 0
, kD0 .
k aCa g ; k bCb
g ; k bCb g ; k cCc g
The transfer function of the level control object as:
1 A 2L
2 A 2(L L ) 3 A 2(L L ) 4 A 2L
1 1s

1s 2s

1s 2s
2 2s
The equations (18) and (19) describe the linear model of the coupledtank system, where input is the incremetal pump voltage u(t) , and output is the incremetal fuild level in the
Gobj (s) ksGL2
(s)
0.1074 K
1 2
s2 0.362s 0.007 (T s 1)(T s 1)
(22)
second tank l2 (t) . By taking the Laplace transform of equations (1819) the following transfer function is obtained:
where K=15.372, T1=2.93, T2=48.78
Arcoding to the Ziegler Nichols 1st method, the parameters kP0 , kI 0 , kD0 can be determined as follows:
GL2
(s) l2 (s)
u(s)
s2 (k k
k3kb / A1

k k )s (k k

k k

k k )
(20)
G s k

kI 0 k s

(23)
1 2 3 4 1 3 1 4 2 4
In this paper, we design a fuzzyPID controller applied for coupledtank system with following parameters [15].
where:
C P0 s D0
Tab 1. Constants involved in coupledtank system of Fig. 1
kP0
1.2T2
KT1
1.2 * 48.78
15.372 * 2.93
1.31
Parameter
Desctiption
Value
Unit
kv
Gain of DCmotor electric valve
3.3
cm3/s/V
ks
Gain of level untrasonic sensor
6.1
cm/s
Ca
Percentage of opening valve A
60
%
Cb
Percentage of opening valve B
80
%
Cc
Percentage of opening valve C
60
%
D1, D2
Inner diameter of tank 1, 2
6
cm
k kP0
I 0 2T
1
0.22
T1
kD0 kP0 2 1.92
Howerver with the nonlinear model of the coupledtank, the acceptable pamameters are kP0 = 15, kI 0 = 0.3, kD0 = 11.
kP0
kPF
kI0
kIF
kD0
de kDF
dt
Fuzzy Cal
e
1
s
r u
FuzzyPID controller
de
–
y
Level Sensor
Coupled Tank
Electric Valve
p/>
Level process of coupledtank
dt
Fig. 2. Structure of fuzzyPID for liquid level process of coupledtank


Designing the fuzzy logic calculator
The fuzzy logic calculations block (FC) have: two inputs – level error in the second tank (EL), derivative of level error (DEL) corresponding to input voltage error signal e=yr (r level setpoint, y level in tank 2) and de/dt; three output is PL, IL, DL corresponding to the output value kPF, kIF, kDF.
Using membership functions are shaped triangular for all variables, fuzzied for all input variables by 5 fuzzy sets
{NL (Negative Large), NS (Negative Small), ZE (ZEro), PS (Positive Small), PL (Positive Large)}, fuzzied for all output variables by 5 fuzzy sets {SM (SMall), ME (MEdium), LA (LArge), QL (Quite Large), VL (Very Large)}. The physical
Tab.3. The basic fuzzy rule of kPL, kIL, kDL
PL IL
DL
EL
NL
NS
ZE
PS
PL
DEL
NL
SM
SM
SM
SM
SM
NS
SM
ME
SM
SM
SM
ZE
SM
SM
LA
LA
QL
PS
SM
SM
LA
QL
VL
PL
SM
SM
QL
VL
VL
Using the MaxMin composition rule and the cetroid defuzzification method, we can obtain the clear output value of FC: kPF, kIF, kDF for level control loop. Thus, the fuzzy PID controller can be calculated by equations:
I I 0
D D0
domain of the input & output variables are determined as: EL[20,20], DEL[2,2], PL[0,20], IL[0,1],
*
k = k
P P0
+ kPF
, k* = k
+ kIF
, k* = k
+ kDF
(24)
DL[0,15].
Depending on the characteristics of the level control proces of the coupledtank and the PID control principle in order to improve quality control for this system (see Tab.2),


SIMULATION RESULT
The simulated diagram of the fluid level process of coupledtank system is described as Fig. 3. The fuzzyPID controller is a combination of the FuzzyCal block with the VariablePID. The selftunning parameters of fuzzyPID is
we define the 25 basic fuzzy rules as Tab.3.
determine on equation (24), here
kP0 , kI 0 , kD0
are initial
Closedloop
respond
Rise time
Steady time
Over
shoot
Steady
error
Stability
Increasing kP
Decrease
Small
change
Increase
Decrease
Degrade
Increasing kI
Small
decrease
Decrease
Increase
Eliminate
Degrade
Increasing kD
Small
decrease
Decrease
Small
decrease
Small
change
Increase
Tab.2. The effect of kP, kI, kD tunning
parmaters of PID and kPF , kIF , kDF
are the clear output value
of the FuzzyCal block. The fluid level process of coupled tank is used as nonlinear model, using equations (8) and (9).
The simulation is carried out with three controllers: FuzzyPID, PIDZN1, PIDCHR. The quality control system is evaluated through four indexes (overshoot, rise time, steady time, steady error) in two circumstances: (a). varying setpoint level; (b). as impacted by the bound noise with small margin.
Fig. 3. Simulation of the fluid level coupledtank control system using fuzzyPID
30
L2 [cm]
25
20
15 Setpoint
PIDZN1
PIDCHR
10 FuzzyPID
5
0
0 20 40 60 80 100 120 140 160 180 200
Fig. 4. Response curves of the level controllers as varying setpoint level
Fig. 5. Response curves of the level controllers as having noise with small margin
The simulation results, as using PIDZN1, PIDCHR and FuzzyPID controller, is presented in Tab. 4.
Tab. 4. Performance of FuzzyPID controller & others
Controller
Index
FuzzyPID
PIDZN1
PIDCHR
Rise time
Small, ~1.5s
Large, ~4.1s
Very large, ~8.4s
Steady time
Small, ~3.1s
Large, ~11.2s
Very large, ~8.4s
Overshoot
Not
Large, ~19.4%
Small, ~12.3%
Steady error
Eliminate, or very small
with noise
Very small, but large swing
with noise
Very small, but swing with noise
The simulating results show that fuzzyPID has the best control quality: not overshoot, eliminating steady error, the smallest steady time and eliminating neraly the effect of the disturbaces, when it was compared to traditional PID controllers.

CONCLUSION
This paper has presented a case study where the basic PID controller is combined with the fuzzy logic calculator for the nonlinear model of the liquid level of coupledtank system. The simulation results suggest that the fuzzyPID proposed controller can be applied to the liquid level control process in the chemical industry, where noise is always presented. The fuzzyPID controller can improve quality of the liquid level coupledtank control system, increase the process efficiency and bring economic benefit to enduser. However, we need to study in more detail about dynamics of actuator & sensor, according to the actual device to obtain a more realistic control object model, which helps to control the fluid level in coupledtank better.
REFERENCES
[1]. Abdelelah Kidher Mahmood, Hussam Hamad Taha, Design Fuzzy Logic Controller for Liquid Level Control, International Journal of Emerging Science and Engineering (IJESE), Volume1, Issue11,September 2013
[2]. Ahcene Boubakir, Fares Boudjema, Salim Labiod, A Neurofuzzy sliding Mode Controller Using Nonlinear Sliding Surface Applied to the Coupled Tanks System, International Journal of Automation and Computing, 06 (1), February 2009, 7280. [3]. Vasile CALOFIR, Valentin TANASA, Ioana FAGARASAN, A backstepping control method for a nonlinear process – two coupled tanks, International conference on energy and environment (CIEM) 2013 [4]. MUHAMMAD NASIRUDDIN MAHYUDDIN, MOHD RIZALARSHAD, Performance Evaluation of Direct Model Reference Adaptive Control on a Coupledtank Liquid Level System,
ELEKTRIKA, 10(2), 2008, 917
[5]. Parvat B. J., Jadhav V. K., Lokhande N. N., Design and Implementation of Sliding Mode Controller for Level Control, Journal of Electronics and Communication Engineering (IOSRJECE) [6]. N. Kottenstette, J. Porter, G. Karsai, and J. Sztipanovits. Discretetime idapassivity based control of coupled tank processes subject to actuator saturation. In Resilient Control Systems (ISRCS), The 3rd International Symposium on, pages 115120, aug. 2010. [7]. N.B. Almutairi and M. Zribi, Sliding mode control of coupled tanks, Mechatronics, 16(7):427 441, 2006. [8]. Pawan Kumar Kushwaha and Vinod Kumar Giri, Control Strategies for Water Level Control of Two Tank System, IJBSTR RESEARCH PAPER VOL 1 [ISSUE 8] AUGUST 2013 [9]. Himanshu Gupa, Om Prakash Verma, Intelligent Controller for Coupled Tank System, International Journal of Advanced Research in Computer Science and Software Engineering, Volume 2, Issue 4, April 2012. [10]. Pawan Kumar Kushwaha and Vinod Kumar Giri, PID controllers for water level control of two tank system, International Journal of Electrical, Electronics & Communication Engineering, Vol. III Issue VIII August 2013 [11]. Mohd Tabrej Alam, Piyush Charan, Qamar Alam, Shubhi Purwar, Sliding Mode Control of Coupled Tanks System: Theory and an Application, International Journal of Emerging Technology and Advanced Engineering, Volume 3, Issue 8, August 2013. [12]. Messaouda AZZOUZI1, F. HALAL, Two liquid tanks control, U.P.B. Sci. Bull., Series C, Vol. 70, No. 1, 2008. [13]. Muhammad Nasiruddin Mahyuddin, Mohd. Rizal Arshad, Zaharuddin Mohamed, Simulation of Direct Model Reference Adaptive Control on a CoupledTank System using Nonlinear Plant Model, International Conference on Control, Instrumentation and Mechatronics Engineering (CIM07), Malaysia, May 2829, 2007. [14]. Carlos A. Smith, Automated continuous process control, John Wiley & Sons, 2002. [15]. Technical documentation of the PVD01 coupledtank system in the chemical laboratory, Petrovietnam, 2005.Trinh Luong Mien obtained his PhD degree in automation and control of technological processes and manufactures at Moscow State University of Railway Engineering (MIIT) in Russia Federation in 2012. Trinh Luong Mien is a lecturer at Faculty of Electrical and Electronic Engineering, University Transport
and Communications in Vietnam since 2004. His main research is the development of intelligent control algorithms for the technological and manufacturing processes in industry and transportation based on fuzzy logic, neuron network, adaptive & optimal theory; study algorithms controlling & ensuring the safe movement of the electrical train in ATP/ATO/ATS/ATC system of the urban railway; design the supervisory control system based on IoT platform.