evolutionary based optimisation of multivariable fuzzy...
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Evolutionary Based Optimisation of Multivariable FuzzyControl System of a Binary Distillation Column
Yousif Al-Dunainawi
Electronic and Computer Engineering Department
College of Engineering, Design and Physical Sciences
Brunel University London
Uxbridge, London, UK
Maysam F. Abbod
Electronic and Computer Engineering Department
College of Engineering, Design and Physical Sciences
Brunel University London
Uxbridge, London, UK
Abstract—Genetic Algorithms (GA), Simulated Annealing(SA) and Particle Swarm Optimisation (PSO) are population-based stochastic search algorithms that categorised into thetaxonomy of evolutionary optimisation. These methods havebeen employed independently to tune a fuzzy controller formaintaining the product compositions of a binary distillationcolumn. An analytical investigation has been conducted todistinguish the optimal tuning approach of the controlleramong these techniques. Based on simulation results, particleswarm optimisation approach combined with the fuzzy logiccontroller is identified as a comparatively better configurationregarding to its performance index as well as computationalefficiency.
Keywords–Fuzzy Logic Control; MIMO; Distillation; Evolu-tionary Optimisation;
I. INTRODUCTION
The pioneering studies of Zadeh on the theory of fuzzy
set, logic and approaches [1]–[3], have motivated many
researchers to establish a new discipline of the modern
control system. Thus, Mamdani and his co-workers had
proposed an innovative fuzzy control system for various
applications to model and control dynamic, nonlinear, ill-
defined and complex processes, based on fuzzy logic theory
[4], [5]Later, the conception of fuzzy logic control FLC has been
investigated and applied widely to the most of the engineer-
ing and applied science realms [6]–[9]. Additionally, hy-
bridisation of the various of evolutionary-based algorithms,
providing intelligent techniques that gives FLC system a step
ahead to produce powerful and more efficient solutions for
different applications [10]–[12]. Employing these algorithms
have been applied recently to both conventional and modern
control system to find the optimal tuning parameters of
the different configuration controllers [13], [14]. Instead
of the traditional emphasis on accuracy and certainty, soft
computing techniques can deal greatly with imprecision
and uncertainty to allow reasoning and computation usually
required for practical applications [11], as Zadeh stated
“Fuzzy logic is not fuzzy. Basically, fuzzy logic is a preciselogic of imprecision and approximate reasoning” [15].
This paper proposes an evolutionary-based multi-input
multi-output fuzzy control system MIMO-FLC to maintain
the product compositions of a binary distillation column
as near as to desired requirements. The distillation process
itself is considered a high nonlinear and characterised by
uncertainty and the ill-defined relationship between the
inputs and the outputs [16], [17]. The most motivated aim
to introduce a new control configuration of the column is
trying to find more robustness and effectiveness against the
process perturbations, therefore, energy efficient columns.
II. DISTILLATION COLUMNS
It is well known that distillation columns are the most
unit that used in oil refineries, chemical and petrochemical
plants . These columns are mainly used to separate mixtures
into their individuals components depending, basically, on
the difference of boiling points. Distillation is reported as
a highly demanding energy process. A report from the US
Department of Energy has indicated that distillation column
unit is the largest consumer of energy in the chemical indus-
try; typically, it accounts for 40% of the energy consumed
by petrochemical plant [18]. Regardless of its “hunger” for
energy, distillation continues to be a widely used process
for separation and purification. Therefore, efficiently oper-
ating these columns necessitates a high degree of automatic
control [19].
A. Process Description
The column has a number of trays (plates) which are
employed to enrich the components separation process. The
mixture is usually fed in the middle (or around) in the
column. Vapour is produced by a reboiler, which is supplied
by enough heat. The steam travels up through trays inside the
column to reach the top and, then, comes out to be liquefied
in a condenser. Liquid from the condenser, at that point,
enters into the reflux drum. As a final point, the distillate
product is removed from this drum as a pure product. In
addition, some liquid is fed back (reflux) close to the top,
2016 UKSim-AMSS 18th International Conference on Computer Modelling and Simulation
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2016 UKSim-AMSS 18th International Conference on Computer Modelling and Simulation
978-1-5090-0888-9/16 $31.00 © 2016 IEEE
DOI 10.1109/UKSim.2016.9
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2016 UKSim-AMSS 18th International Conference on Computer Modelling and Simulation
978-1-5090-0888-9/16 $31.00 © 2016 IEEE
DOI 10.1109/UKSim.2016.9
127
while the impure product is produced at the bottom outlet.
The distillation column diagram is depicted in Fig. 1.
Figure 1. Schematic representation of a binary distillation column
B. Model Representation
The model of a binary distillation column simulated in
this research is considered under the following assumptions:
1) No chemical reactions occur inside the column
2) Constant pressure
3) Binary mixture
4) Constant relative volatility
5) No vapour hold-up occurs at all stages
6) Constant hold-up liquid at all trays
7) Perfect mixing and equilibrium for vapour-liquid on
all stages
Hence, the mathematical expression of the model can be
represented by the following equations:
• On each tray (excluding reboiler, feed and condenser
stages):
Midxi
t= Li+1xi+1 + Vi−1yi−1 − Lixi − Viyi (1)
• Above the feed stage i = NF + 1:
Midxi
t= Li+1xi+1+Vi−1yi−1−Lixi−Viyi+FV yF
(2)
• Below the feed stage i = NF :
Midxi
t= Li+1xi+1+Vi−1yi−1−Lixi−Viyi+FLXF
(3)
• In the reboiler and column base i = 1, xi = xB:
MBdxi
t= Li+1xi+1 − Viyi +BxB (4)
• In the condenser, i = N + 1, xD = xN + 1:
MDdxi
t= Vi−1yi−1 − LixD −DxD (5)
• Vapour-liquid equilibrium relationship for each tray
[20]:
yi =αxi
1 + (α− 1)xi(6)
• The flow rate at constant molar flow:
Li = L, V i = V + FV (7)
since
FL = qF × F (8)
Fv = F + FL (9)
• The flowrate of both condenser and reboiler as: Re-
boiler:
B = L+ FL − V (10)
Condenser:
D = V + FV − L (11)
• The feed compositions xF and yF are found from the
flash equation as:
FzF = FL × xF − FV × yF (12)
The nominal and operation conditions of the column are
shown in the appendix in the end of this paper, and the
schematic diagram of a theoretical stage of the column is
shown in the Fig. 2.
Figure 2. Schematic diagram of ith stage of a binary distillation column
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III. CONTROL SYSTEM CONFIGURATION
In the present work, MIMO configuration is investigated
to control the product compositions of a binary distillation
column. One of the most common control loops of the binary
column is so-called (L− V ) configuration [19]. Where, the
reflux flow (L) is selected to control the mole fraction of
the top product (xD), while the reboiler steam flow (V ) is
chosen to control the composition of the bottom product, as
expressed in Eq. 13.[xDxB
]= GLV
[LV
](13)
where GLV is the column’s transfer function.
As it is known, the performance of any controller
depends as much on its design as on its tuning. Tuning
must be applied by operators to fit the controller to the
process. Therefore, there are many different approaches for
tuning, based on the particular performance criteria selected.
Therefore, evolutionary algorithms are employed as an
optimal tuner of the control parameters; genetic algorithm,
simulated annealing and particle swarm optimisation in this
paper for this purpose.
The control system aims to maintain the product compo-
sitions as close to the desired ones as possible despite the
expected disturbances.
A. Fuzzy logic control
A control system, based on fuzzy theory, simply trans-
forms a linguistic control strategy into automatic capabilities
for managing the nonlinearities and uncertainties of the
process. The proposed FLC structure has Mamdani infer-
ence system and the centroid defuzzification mechanisms.
The universe of discourse of the inputs and output were
normalised in the interval [1, 1]. Thus, actual system values
were converted through scaling parameters (gains). Gaus-
sian,the most common membership function was used to
defined the inputs and output of the fuzzy controller. the
relationship of the inputs as error and change in error, and
the output as control signal is shown in the surface viewer
of FLC in Fig. 3 as well as the if-then rules are detailed in
Table I .
TABLE IRULES BASED OF THE FLC.
ErrorNB NM NS SS PS PM PB
Ch
ang
ein
Err
or NB SS NS NM NM NB NB NB
NM PS SS NS NM NM NB NBNS PM PS SS NS NM NM NBSS PM PM PS SS NS NM NMPS PB PM PM PS SS NS NMPM PB PB PM PM PS SS NSPB PB PB PB PM PM PS SS
Linguistic expressions demonstrated to these fuzzy sets
are: PB: positive big, PM: positive medium, PS: positive
small, ZE: zero, NS: negatives small, NM: negative medium
and NB: negative big.
The Gaussian membership membership function is ex-
pressed as:
y(x) = e−(x−c)2
α (14)
where c and α are the mean and deviation of a Gaussian
membership function, respectively. The resulting fuzzy set
must be converted to a signal that can be sent to the process
as a control input. Centroid of the area has been used here
for the defuzzification process.
B. Genetic algorithms
Natural evolution inspired procedure as known genetic
algorithms GAs, can search for optimal or close-optimal
solutions for an optimization problem over the search space.
It generates an initially random population of candidate
solutions toward the optimal fitness (objective function) by
performing specific techniques, which are mimic the natural
selection processes, such as reproduction, crossover, and
mutation. The procedures are repeated until the prescribed
fitness is accepted, or the predetermined number of itera-
tions (generations) is implemented. The research topic of
tuning various control systems via GAs has already been
investigated in many researches [9], [21], [22].
C. Simulated Annealing
Simulated annealing is a heuristic optimisation method,
which is mimicking the process of metals annealing to
find the optimum solution via controlling the temperature.
SA initialises a candidate temperature, in optimization and
searches for optimal global fitness by slowly reducing the
temperature alike to the physical annealing process. Its
Figure 3. The relationship between inputs and output of the fuzzycontroller.
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advantages are reported as the considerable ability to find
the minimal fitness function in specific conditions as well
as it can deal with any objective function [23].
D. Particle Swarm Optimisation
Particle swarm optimisation (PSO) has been proposed by
Kennedy and Eberhart in 1995 [20] and 2001 [24], PSO
algorithm turned to be vastly successful. The several of
researchers have presented the merit of the implementation
of PSO as an optimiser for various applications [25], [26].
In PSO procedure, all particles are located randomly and
theoretical to move arbitrarily in a defined direction in
the search domain. Each particle direction is then changed
steadily to travel along the direction of its best previous
positions to discover a new better position according to
predefined objective function (fitness).
IV. SIMULATION AND RESULTS
In this paper, MIMO FLC has been designed of a binary
distillation column. EAs such as GA, SA and PSO were
employed to find the optimal scaling factors of the controller.
The integral of the time-weighted absolute error (ITAE) was
selected as the quantitative criterion for measuring control
performance. Minimisation of this index expressed in Eq.
15 is considered as fitness or objective function of EAs that
is used in this research.
ITAE =
∫ T
t=0
T × |E| dt (15)
where, E is the error between the desired value and output
of the product compositions of the column and T is a
simulation time, the schematic diagram of the designed
control system is depicted in Fig. 4.
To compare the performance of the various EAs for the
FLC controller design, three simulation experiments were
performed as follows:
1) Design of MIMO FLC controller without a compen-
sator
2) Design of MIMO FLC controller with a compensator
Figure 4. EA-based FLC design
3) Design of MIMO PID controller tuned by conventional
Ziegler-Nichols method [27]
Extensive simulations were carried out to find the optimal
initial parameters of EAs like the population size, the initial
condition, weight, etc.
Due to the randomness of EAs at initialisation stage,
20 times of runs had been done independently of each
algorithm. MATLAB R© and Simulink R© R2014b platform
were used for simulation via processor 3.6 GHz, with 8 GB
of RAM.
The FLC configuration with and without compensator
are shown in Fig. 5. The performance index of the different
controllers with various tuning method is given in Table II.
Clearly, all of the controllers designed using different
approaches pass the transient response requirements. Never-
theless, the performance of the PSO-base FLC with compen-
sator indicated better achievement regarding the performance
index and transit response. In addition, PSO outperformed
the other EAs techniques with minimum computation time.
(a)
(b)
Figure 5. MIMO FLC (a) without compensator, (b) with compensator
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TABLE IIPERFORMANCE INDEX OF CONTROLLERS TUNED BY VARIOUS
APPROACHES
Controller Tuning method ITAE Time (hour)PID Z-N 62.633 -
FLCGA 48.335 6.845SA 53.07 6.236
PSO 42.99032 4.5734FLC-compensator PSO 40.079 5.231
The compensator slightly improved the performance by
eliminating the interacting of loops, with more time cost due
to the number of parameters involved. For the convenience,
the comparisons of the time response behaviour of the
PID and PSO-based FLC with and without compensator is
presented in Fig. 6.
Time(min)0 50 100 150
xD
0
0.2
0.4
0.6
0.8
1
1.2
1.4PIDPSOFLC PSOFLC with Compensator
(a)
Time (min)0 50 100 150
xB
0
0.2
0.4
0.6
0.8
1
1.2
1.4PIDPSOFLC with CompensatorPSOFLC
(b)
Figure 6. Time Response of step setpoints of different control configura-tions (a) distillate and (b) bottoms product.
A. Robustness of the optimal controller
To check the robustness of the PSO-based FLC
with compensator against external disturbances, the
desired compositions of the column were set to change
asynchronously as follows; The desired compositions of
distillate and bottoms products are changing every 100
minutes for a thousand minutes. It can be observed that the
control actions of the controller were successfully adapted
to eliminate the effect of the external disturbances, where
the convergence of the desired responses was achieved after
the adaptation of the control output. The process output
responses to setpoints changes in the distillate and bottoms
compositions. Better performance is achieved with fuzzy
logic controller that tuned by PSO with a compensator to
eliminate the effect of inputs variance as shown in Fig. 7.
This result gives an indication that the proposed controller
can cope efficiently with disturbances.
(a)
(b)
Figure 7. Time response of changed-step setpoints of the product compo-sitions of the column (a) distillate and (b) bottoms product.
125131131
V. CONCLUSIONS
In this research, three of the common techniques of EA
were performed independently as a tuner to FLC. GA,
SA and PSO had been combined with FLC to control a
binary distillation column. The results showed that PSO
outperformed GA and SA by achieving improvement to
the performance of the controller as well as computational
efficiency. For comparison purposes, the conventional PID
controller was also simulated and applied to the same
column. PSO-based FLC with compensator proved its feasi-
bility and superiority by handling disturbances with minimal
ITAE performance index. Different control configurations
could be applied to distillation columns with various tuning
method like Gravitational Search Algorithm, which is to be
the subject of future work.
ACKNOWLEDGMENT
The corresponding author is grateful to the Iraqi Ministry
of Higher Education and Scientific Research for supporting
the current research.
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APPENDIX
Abbreviations, the operating conditions and technical as-
pects of the distillation column are detailed in following
table.
Symbol Description Value UnitN Number of trays 20 -NF Feed stage location 11 -F Typical inlet flow rate to the col-
umn1 kmol/min
D Typical distillate flow rate 0.5 kmol/minB Typical bottoms flow rate 0.5 kmol/minzF Light component in the feed (mole
fraction)0.5 -
qF Mole fraction of the liquid in thefeed
1 -
L Typical reflux flow rate 1.28 kmol/minV Typical boil-up flow rate 1.78 kmol/minα Relative volatility 2 -xD Distillate composition (mole frac-
tion)0.98 -
xB Bottoms composition (mole frac-tion)
0.02 -
i Stage number during distillation - -x Mole fraction of light component
in liquid- -
y Mole fraction of light componentin vapour
- -
M Tray hold-up liquid 0.5 kmolMD Condenser hold-up liquid 0.5 kmolMB Reboiler hold-up liquid 0.5 kmol
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