Soft Computing Technique and Conventional Controller for Conical Tank Level Control

Indonesian Journal of Electrical Engineering and Informatics (IJEEI)
Vol. 4, No. 1, March 2016, pp. 65~73
ISSN: 2089-3272, DOI: 10.11591/ijeei.v4i1.196  65
Received August 14, 2015; Revised January 5, 2016; Accepted January 20, 2016
Soft Computing Technique and Conventional Controller
for Conical Tank Level Control
Sudharsana Vijayan*
1
, Avinashe KK
2
PG scholar, Dept. of Electronics and Instrumentation, Asst. professor, Dept. of Electronics and
Instrumentation Vimal Jyothi Engineering College, Chemperi, Kannur, Kerala
*Corresponding author, e-mail: sudharsanavijayan@gmail.com
1
, Avinashe@vjec.ac.in
2
Abstract
In many process industries the control of liquid level is mandatory. But the control of nonlinear
process is difficult. Many process industries use conical tanks because of its non linear shape contributes
better drainage for solid mixtures, slurries and viscous liquids. So, control of conical tank level is a
challenging task due to its non-linearity and continually varying cross-section. This is due to relationship
between controlled variable level and manipulated variable flow rate, which has a square root relationship.
The main objective is to execute the suitable controller for conical tank system to maintain the desired
level. System identification of the non-linear process is done using black box modelling and found to be
first order plus dead time (FOPDT) model. In this paper it is proposed to obtain the mathematical modelling
of a conical tank system and to study the system using block diagram after that soft computing technique
like fuzzy and conventional controller is also used for the comparison.
Keywords: Matlab, Fuzzy, PID, Nonlinear System
1. Introduction
The control of nonlinear
[1]
systems has been an significant research topic and many
approaches have been proposed
[2]
. In most of the process industries controlling of level, flow,
temperature and pressure is a exigent one. They may be classified as linear and non-linear
processes based on the plant dynamics. Control of industrial processes is a challenging task for
several reasons due to their nonlinear behavior, uncertain and time varying parameters,
constraints on manipulated variable, interaction between manipulated and controlled variables,
unmeasured and frequent disturbances, dead time on input and measurements.
The control of liquid level in tanks and flow between the tank is a basic crisis in process
industries. In level control process, the tank systems like cylindrical, cubical are linear one, but
that type of tanks does not provides a complete drainage. For complete drainage of fluids, a
conical tank is used in some of the process industries, where its nonlinearity might be at the
bottom only in the case of conical bottom tank. The drainage efficiency can be improved further
if the tank is fully conical in shape. In many processes such as distillation columns, evaporators,
re-boilers and mixing tanks, the particular level of liquid in the vessel is of great significance in
process operation. A level that is too high may upset reaction equilibria, cause damage to
equipment or result in spillage of valuable or hazardous material. If the level is too low it may
have bad consequences for the sequential operations
[2]
.
So control of liquid level is an important and frequent task in process industries. Level of
liquid is desired to maintain at a constant value. This is achieved by controlling the input flow.
The control variable is the level in a tank and the manipulated variable is the inflow to the tank.
Conical tanks find wide applications in process industries, namely hydrometallurgical industries,
food process industries, concrete mixing industries and wastewater treatment industries.
The paper is organized as follows: Section I discusses about non linear level process, in
Section II and III discusses about experimental setup and modeling of the system and controller
design like conventional controller and fuzzy logic controller (FLC), respectively. The simulation
results are presented in Section IV. The conclusions are given in Section V.

 ISSN: 2089-3272
IJEEI Vol. 4, No. 1, March 2016 : 65 – 73
66
2. Proposed Work
2.1. Experimental Setup
The system used is a conical tank and is highly nonlinear due to the variation in area of
cross section. The controlling variable is inflow of the tank. The controlled variable is level of the
conical tank. Level sensor is used to sense the level in the process tank and fed into the signal
conditioning unit and the required signal is used for further processing.
Figure 1. Block diagram of process
The level process station used to perform the experiments and to collect the data
[11]
.
One of the computers used as a controller. It consists of the software which is used to control
the level process station. The Figure 1 consists of a process tank, reservoir tank, control valve, I
to P converter, level sensor and pneumatic signals from the compressor. When the set up is
switched on, level sensor senses the actual level, initially the signal is converted to current
signal in the range between 4 to 20mA.This signal is then given to the computer through data
acquisition cord.
Based on the controller parameters and the set point value, the computer will take
consequent control action and the signal is sent to the I/P converter. Then the signal is
converted to pressure signal using I to P converter and the pressure signal acts on a control
valve which controls the inlet flow of water in to the tank.
Capacitive type level sensor is used to senses the level from the process and converts
into electrical signal. Then the electrical signal is fed to the I/V converter which in turn produces
corresponding voltage signal to the computer. The actual water level storage tank sensed by the
level transmitter is feedback to the level controller & compared with a desired level to produce
the required control action that will position the level control as needed to maintain the desired
level. Now the controller decides the control action & it is given to the V/I converter and then to
I/P converter. The final control element (pneumatic control valve) is now controlled by the
resulting air pressure. This in turn control the inflow to the conical tank & the level is maintained.
The tank is made up of stainless steel body and is mounted over a stand vertically. Water enters
the tank from the top and leaves the bottom to the storage tank. The System specifications of
the tank are as follows chapter.
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2. Proposed Work
[11]
.
acquisition cord.
 ISSN: 2089-3272
66
2. Proposed Work
[11]
.
acquisition cord.

IJEEI ISSN: 2089-3272 
Soft Computing Technique and Conventional Controller for Conical … (Sudharsana Vijayan)
67
2.2. Mathematical Modelling
The dynamic behavior [11] of the liquid level h in the conical storage tank system shown
in Figure 2. From the figure,
})(2{
3
1 2
h
H
R
A
dt
dh
dt
dV

})(2{
3
1 22
h
H
R
A
dt
dh
FF outin 
Figure 2. Tank crossection
Output mass flow rate can be written in terms of the exit velocity, Ve
eeout VaF 
From mass balance eqn,
)()()
2
)(
()(0 21
21
2
21
21

pp
qzzqg
vv
quuq
dt
dme 



)()0()
2
()0(0 21
2
2

pp
qqg
v
qq


Finally,
YhUhYhF
dt
dy
sssis 2
5
23
2
3
2 
 
CUy
dt
dy
)(
2
12
shC


 and 2
52
sh

 
Taking Laplace transform,
]1[)(
)(


S
C
sU
sy

IJEEI ISSN: 2089-3272 
67
})(2{
3
1 2
h
H
R
A
dt
dh
dt
dV

})(2{
3
1 22
h
H
R
A
dt
dh
eeout VaF 
)()()
2
)(
()(0 21
21
2
21
21

pp
qzzqg
vv
quuq
dt
dme 



)()0()
2
()0(0 21
2
2

pp
qqg
v
qq


Finally,
YhUhYhF
dt
dy
sssis 2
5
23
2
3
2 
 
CUy
dt
dy
)(
2
12
shC


 and 2
52
sh

 
]1[)(
)(


S
C
sU
sy

IJEEI ISSN: 2089-3272 
67
})(2{
3
1 2
h
H
R
A
dt
dh
dt
dV

})(2{
3
1 22
h
H
R
A
dt
dh
eeout VaF 
)()()
2
)(
()(0 21
21
2
21
21

pp
qzzqg
vv
quuq
dt
dme 



)()0()
2
()0(0 21
2
2

pp
qqg
v
qq


Finally,
YhUhYhF
dt
dy
sssis 2
5
23
2
3
2 
 
CUy
dt
dy
)(
2
12
shC


 and 2
52
sh

 
]1[)(
)(


S
C
sU
sy


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68
2.3. Tank Specification
Height of the tank, H = 70cm
Top diameter of the tank, D = 35.2cm
Bottom diameter of the tank, d = 4cm
Valve coefficient. K = 2
From above data calculate the process gain (C) and time constant (τ)
Where,
α = 5.035
β = 10.7
steady state value ℎ =10 (model 1)
process gain C=3.184 and time constant τ = 62.81
so, model 1 =
3.184
62.81 + 1
so, model 2 =
4.472
355.28 + 1
3. Controller Design
3.1. Controller Tunning
A proportional-integral-derivative controller (PID controller) is a generic control loop
feedback mechanism (controller) widely used in many control systems [5]. A PID controller
calculates an error value as the difference between a measured process variable and a desired
set point. The controller attempts to minimize the error by adjusting the process control inputs.
The PID controller is simple and robust and hence widely used in most of the process
industries.
The controller parameters can be tuned using Cohen and Coon method or Ziegler
Nichol’s method. Cohen [6] and Coon method is commonly referred to as open loop response
method for tuning the parameters of conventional controllers.
3.2. Conventional Controllers
A PI controller as Figure 3 is commonly used in engineering control system. PI
controller calculation involves two separate constant parameters, Proportional and Integral
denoted by KP and KI. P depends on present error and I on the accumulation of past errors [5].
By tuning these two parameters in PI control algorithm the controller can provide desired action
designed for specific process requirement. Different tuning rules used for achieving by properly
selecting the tuning parameters and τ for a PI controller [7].
Figure 3. Block diagram of PID controller
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Where,
α = 5.035
β = 10.7
so, model 1 =
3.184
62.81 + 1
so, model 2 =
4.472
355.28 + 1
industries.
 ISSN: 2089-3272
68
Where,
α = 5.035
β = 10.7
so, model 1 =
3.184
62.81 + 1
so, model 2 =
4.472
355.28 + 1
industries.

IJEEI ISSN: 2089-3272 
69
A Proportional Integral Derivative controller (PID) is a generic control loop feedback
mechanism widely used in industrial control systems. It is robust due to its strategy to give
bounded errors. It was an essential element of early governors and it became the standard tool
when process control emerged in the 1940s. In process control today, more than 95% of the
control loops are of PID type, most loops are actually PI control.PID controllers can these days
be found in all areas where control is needed.
3.3. Fuzzy Controller
MATLAB is a high-performance language for technical computing integrates
computation, visualization, and programming in an easy-to-use environment where problems [9]
and solutions are expressed in familiar mathematical notation.
This paper presents a simple approach to design fuzzy logic based controller for
MATLAB/Simulink environment [10]. It provides tools to create and edit fuzzy inference systems
within the framework of MATLAB, and it is also possible to integrate the fuzzy systems into
simulations with Simulink. (U) is defined as the output for fuzzy controller. They are fuzzy
linguistic variable represent the level error (e), change of level error (Δe) and the output control
effort (u) respectively. A fuzzy logic system (FLS) [12] can be defined as the nonlinear mapping
of an input data set to a scalar output data.
Figure 4. Fuzzy logic system
A FLS consists of four main parts
[13]
:
 Fuzzifier
 Rules
 Inference engine
 Defuzzifier
These components and the general architecture of a FLS are shown in Figure. The
process of fuzzy logic is explained in Algorithm 1: Firstly, a crisp set of input data are gathered
and converted to a fuzzy set using fuzzy linguistic variables, fuzzy linguistic terms and
membership functions. This step is known as fuzzification. Afterwards, an inference is made
based on a set of rules. Lastly, the resulting fuzzy output is mapped to a crisp output using the
membership functions, in the defuzzification step [8]. The input and output of the fuzzy
controllers are designed below,

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Figure 5. Input variable “error”
Figure 6. Input variable “change error”
Figure 7. Output variable “output”
Generally fuzzy controller has two inputs like error and change in error. Figure 5 is the
membership function of error and Figure 6 is the membership function of change in error.
Figure 7 represents the controlling action of the valve.
A fuzzy inference system (FIS) essentially defines a nonlinear mapping of the input data
vector into a scalar output, using fuzzy rules. The mapping process involves input/output
membership functions, FL operators, fuzzy if–then rules, aggregation of output sets, and
defuzzification.
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defuzzification.
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defuzzification.

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Figure 8. Fuzzy controller system
An FIS with multiple outputs can be considered as a collection of independent multi-
input, single-output systems. FIS contains four components: the fuzzifier, inference engine, rule
base, and defuzzifier. The rule base contains linguistic rules that are provided by experts [10]. It
is also possible to extract rules from numeric data. Once the rules have been established, the
FIS can be viewed as a system that maps an input vector to an output vector.
4. Simulation Result
At first, the mathematical model of conical tank level process is derived in terms of
differential equation and an open loop response is obtained by performing step test in Matlab.
The process is identified and closed loop control performances of various PI and PID
controllers were studied and results are presented in figures for two regions. Response and
comparison of conventional controllers and fuzzy controllers are shown in Figure 9 and
Figure 10.
Figure 9. Response of model1 at setpoint 5cm
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Figure 10.
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Figure 10.

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From this response, fuzzy controller fastly tracks the set point than PI and PID
controllers. Comparison of controller action like settling time delay time and rise time and errors
are shown in Table 1.
Table 1. Comparison of control actions model1 at setpoint 5cm and model2 at setpoint 15cm
Model Controller Settling time (sec) Delay Time (sec) Rise Time (sec)
1
PI 13.89 0.6328 1.6799
PID 13.37 0.3012 1.5136
FUZZY 1.215 0.2352 1.4895
2
PI 4.69 0.2021 0.5316
PID 4.2195 0.0915 0.5746
FUZZY 0.873 0.0751 0.4631
Analysis shows in Table 2, the design of fuzzy controller gives a better performance by
means of minimum delay time, minimum settling time, minimum rise time and satisfactory over a
wide range of process operations.
Table 2. Comparison of errors model1 at setpoint 5cm and model2 at setpoint 15cm
Model Controller ISE (sec) IAE (sec) ITAE (sec)
1
PI 13.44 7.152 17.76
PID 6.15 4.893 12.73
FUZZY 0.3614 0.1359 0.9207
2
PI 39.36 7.024 5.705
PID 18.01 4.79 4.094
FUZZY 17.82 2.18 2.4
The behavior of fuzzy controller is to provide better performance in the case of errors
and control actions.

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5. Conclusion
The controlling of nonlinear process is a challenging task. The nonlinearity of the
conical tank is analyzed. Modelling and transfer function of the system is done by using system
identification. Open loop step test method is used to find the proportional gain, delay time and
dead time. Here Taylor series approximation is used for the non linear approximation because
of accuracy compared to other non linear approximation technique. Conventional controllers like
PI & PID controllers are used as basic controllers; fuzzy controller is also used for obtaining
improved performance. Here, after analyzing both simulated response of models, the fuzzy
controller is superlative controller than PI and PID controllers.
References
[1] D Angeline, K Vivetha, K Gandhimathi T Praveena. ‘Model based Controller Design for Conical Tank
System’. International Journal of Computer Applications. 0975 – 8887. 2014; 85(12).
[2] Anna Joseph and Samson Isaac J. ‘Real Time Implementation of Model Reference Adaptive
Controller for a Conical Tank’. Proceedings of International Journal on Theoretical and Applied
Research in Mechanical Engineering. 2013; 2(1): 57-62.
[3] T Pushpaveni, S Srinivasulu Raju, N Archana, M Chandana. ‘Modeling and Controlling of Conical
tank system using adaptive controllers and performance comparison with conventional PID’.
International Journal of Scientific & Engineering Research, ISSN 2229-5518. 2013; 4(5): 629.
[4] K Sundaravadivu, K Saravanan and V Jeyakumar. “Design of Fractional Order PI controller for liquid
level control of spherical tank modeled as Fractional Order System”. IEEE, ICCSCE, Malaysia. 2011:
522 – 525.
[5] Marshiana D and Thirusakthimurugan P. ‘Design of Ziegler Nichols Tuning controller for a Non-linear
System’. Proceedings of International Conference on Computing and Control Engineering. 2012:
121-124.
[6] Abhishek Sharma and Nithya Venkatesan. ‘Comparing PI controller Performance for Non Linear
Process Model’. Proceedings of International Journal of Engineering Trends and Technology. 2013;
4(3): 242-245.
[7] H Kiren Vedi, K Ghousiya Begum, D Mercy, E Kalaiselvan. “A Comparative Novel Method of
Enhanced Tuning of Controllers for Non-Linear Process”. National System Conference. 2012.
[8] A Short Fuzzy Logic Tutorial April 8, 2010
[9] Fuzzy control programming. Technical report, International Electrotechnical Commision. 1997.
[10] J Mendel. Fuzzy logic systems for engineering: a tutorial. Proceedings of the IEEE. 1995; 83(3): 345-
377.
[11] Rajesh T, Arun Jayakar, Siddharth SG. “Design and implementation of IMC based PID controller for
conical tank level control process”. International Journal of Innovative Research in Electrical,
Electronics and Instrumentation and control Engineering. 2014; 2(9).
[12] Tutorial on fuzzy Logic.
[13] Marcelo Godoy Simoes, Colorado School of Mines Engineering Division 1610 Illinois Street Golden,
Colorado 80401-1887 USA “Introduction to fuzzy control”.

Soft Computing Technique and Conventional Controller for Conical Tank Level Control

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Soft Computing Technique and Conventional Controller for Conical Tank Level Control