Design and Implementation of Optimized Fuzzy Logic Controller for a

Article pubs.acs.org/IECR

Design and Implementation of Optimized Fuzzy Logic Controller for a Nonlinear Dynamic Industrial Plant Using Hysys and Matlab Simulation Packages Mehdi Mehrpooya*,†,‡ and Sima Hejazi§ †

Renewable Energies and Environment Department, Faculty of New Science and Technologies, ‡Hydrogen and Fuel Cell Laboratory, Faculty of New Science and Technologies, and §School of Chemical Engineering, University College of Engineering, University of Tehran, Tehran, Iran ABSTRACT: A fuzzy logic controller (FLC) is appropriate for systems with high complexity and nonlinearity. FLC is implemented directly on a chemical process simulator in dynamic mode to handle some uncertainty of the system. Also because accurate tuning of the fuzzy membership functions (MFs) is difficult and has an important effect on FLC performance, particle swarm optimization (PSO) is utilized. To display capability of this method, FLC is optimized with PSO. Next PSO-FLC is used to control pressure of a distillation column in an ethane plus recovery process in dynamic mode. Results show that the proposed method can use PSO-FLC in the Hysys dynamic efficiently.

1. INTRODUCTION Chemical engineers use simulators to design and analyze processes to understand their characteristics and behavior against effective parameters. Steady-state simulation is used for analyzing a system to ensure process operability and improve product quality and quantity.1 Next the dynamic behavior of a plant must be analyzed to design a profitable control strategy. But the main challenge in performance of the control system is when uncertainty and nonlinearity behavior of the process increases.2,3 For example a fixed-gain PID controller which is widely used for simple systems is not suitable for processes with high nonlinearity. FLC which uses a new control method based on human knowledge is inherently nonlinear and can handle the complex systems with nonlinear behavior.4 The concept of fuzzy at first is presented by Zadeh5 and then numerous theoretical and practical studies proved the rigorous fuzzy performance.5,6 The fundamental difference between fuzzy control and conventional control is that conventional control starts with a mathematical model of the process and controllers are designed for the model; whereas fuzzy control starts with heuristics and human expertise (in terms of fuzzy IF−THEN rules) and controllers are designed by synthesizing these rules. So if the mathematical model of the process is uncertain, we can use fuzzy controllers instead of conventional controllers. For many industrial processes it is difficult to obtain an accurate and simple mathematical model, whereas there are knowledge and experience of human experts who can provide a collection of knowledge based IF−THEN rules that are very useful for controlling the process.6 Also a fuzzy controller has more adjustable parameters and so is more flexible and more adaptable to the conditions of the nonlinear problem. Experimental results confirm that a fuzzy controller is able to perform better than the conventional PID controller.7 Several fuzzy control strategies have been reported in literature for process control and have confirmed this reality. Fuzzy logic controller (FLC) is used to control the steam temperature in steam-distillation for oil extraction.8 FLC gives better results © XXXX American Chemical Society

compared to the PID controller considering the set point tracking. But before implementing FLC on an industrial process its parameters such as fuzzy MF must be adjusted precisely. So a simulation environment is required to make sure about good performance of adjusted FLC. Accurately adjusting membership function parameters is difficult, so genetic algorithms9−12 and particle swarm optimization11,13−15 are used for adjusting fuzzy membership functions.16 Particle swarm optimization (PSO) has simple implementation and fast convergence,11 so in this paper, it is used to tune fuzzy MFs. Matlab is used as a simulation environment, and the plant is modeled by mathematical equations.17 Two fuzzy logic controllers are developed for control of top and bottom composition of a binary distillation column.17 Modeling and control of a continuous distillation tower through fuzzy technique is investigated in matlab.18 For complex and nonlinear chemical processes, a complicated set of mathematical equations that are obtained by applying the laws of mass, energy, and momentum conservation should be solved. Also these equations represent the overall behavior of the system, but cannot simulate details of the unit.19 In this study a new approach which implements FLC on an industrial nonlinear process simulated in Hysys is proposed. It is done by a connection between Matlab and Hysys in dynamic mode. Hysys is used in the Matlab as a block in a Simulink model. Also because the produced simulation is a rigorous and nonlinear dynamic model of the process, it is the best choice as a block to test and determine performance of the designed PSO-FLC. Without this interface, PSO-FLC can only be implemented on a linear dynamic model within Matlab, whereas this model can handle real and nonlinear behavior of the process. So by using Hysys as plant environment in Matlab, Received: March 23, 2015 Revised: October 20, 2015 Accepted: October 24, 2015

A

DOI: 10.1021/acs.iecr.5b02076 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

concentration of i-butane in the top stream at 0.152% (as heavy key) are defined as column specs. Also the reflux ratio is 5. Table 1 presents composition and typical operating condition

it is possible to examine PSO-FLC performance as a controller. Figure 1 illustrates the structure of the system. To verify

Table 1. Composition and Operating Condition of Column separator liquid product N2 H2S CO2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 H2O

Figure 1. Schematic of the connection between Matlab and Hysys.

performance of this method, FLC is used to control top pressure of the distillation column in a hydrocarbon recovery process in dynamic mode.

2. PROCESS DESCRIPTION AND CONTROL STRATEGY Figure 2 illustrates process flow diagram of a direct refrigeration process for partial recovery of C2+ fractions. Refrigeration and separation is one of the most conventional methods for hydrocarbon recovery from natural gas.20,21 Distillation column in this process is chosen as case study to prove the capability of the proposed method. The feed gas enters the inlet separator, and a portion of the heavier hydrocarbons are removed. A separator vapor product follows to a gas−gas heat exchanger and cools down to −10.1 °C. Next it enters a chiller and its temperature reaches to −20.7 °C. Chiller outlet follows to the low temperature separator (LTS) to separate a portion of heavy hydrocarbons as liquid product. LTS controls the dew point of the outlet gas to the desired value. Outlet gas from LTS provides the required cooling in the gas−gas heat exchanger and its temperature reaches to around −5 °C. LTS liquid product enters T-100 distillation column after passing through an expansion valve. In this column light ends are separated and liquid product is stabilized. The Peng−Robinson equation of state is used to calculate thermodynamic properties of the mixture. The column operates at about 20 bar and has 15 stages, and feed stream enters at stage 7. Concentration of propane in the bottom stream at 0.5% (as light key) and

temp, °C pressure, kPa molar flow, kmol/h

lights

Composition 0.0022 0.0034 0.0005 0.0005 0.0003 0.0004 0.4681 0.6784 0.2918 0.2669 0.1307 0.0489 0.0290 0.0015 0.0467 0.0001 0.0143 0.0000 0.0138 0.0000 0.0026 0.0000 0.0000 0.0000 Operating Conditions −45.88 −31.27 2053 2050 73.62 106.5

condensor drain

heavies

0.0002 0.0008 0.0002 0.1481 0.4487 0.3664 0.0309 0.0047 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0015 0.2143 0.4584 0.1513 0.1464 0.0280 0.0000

−31.27 2050 46.60

125.6 2059 16

Table 2. Information of Column Sizing type of tray diameter, m tray space, m hold up, m

sieve 3.964 0.609 0.133

of the column, and Table 2 reports information about the column sizing. Also specifications of the other important streams are shown in Table 3. Heat exchanger tube side pressure drop and shell side pressure drop are 35 and 5 kPa,

Figure 2. Plant P&ID with a distillation column. B


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Industrial & Engineering Chemistry Research Table 3. Composition and Operating Condition of the Streams to gas plant

inlet separator vapor

N2 H2S CO2 C1 C2 C3 iC4 nC4 iC5 nC5 C6 H2O

0.0066 0.0003 0.0003 0.7576 0.1709 0.0413 0.0068 0.0101 0.0028 0.0027 0.0006 0.0000

0.0067 0.0003 0.0003 0.7638 0.1695 0.0396 0.0062 0.0090 0.0022 0.0020 0.0003 0.0000

temp, °C Pressure, Kpa Molar flow, kmol/h

0 6200 1464

−0.1323 6174 1443

inlet separator liquid Composition 0.0013 0.0005 0.0003 0.3417 0.2656 0.1548 0.0460 0.0860 0.0403 0.0460 0.0175 0.0000 Operating Conditions −0.1323 6174 47.04

Table 4. Information of Gas−gas Heat Exchanger 1.239 × 106 1.669 × 105 7.422 1

Table 5. Information of Chiller duty, kj/h delta P, kPa

Gas to LTS

sales gas

LTS liq

0.0067 0.0003 0.0003 0.7638 0.1695 0.0396 0.0062 0.0090 0.0022 0.0020 0.0003 0.0000

0.0067 0.0003 0.0003 0.7638 0.1695 0.0396 0.0062 0.0090 0.0022 0.0020 0.0003 0.0000

0.0073 0.0003 0.0003 0.8031 0.1533 0.0275 0.0032 0.0039 0.0006 0.0005 0.0000 0.0000

0.0022 0.0005 0.0003 0.4681 0.2918 0.1307 0.0290 0.0467 0.0143 0.0138 0.0026 0.0000

−10.12 6138 1443

−20.67 6099 1443

−5.531 6094 1274

−20.67 6099 169.1

point and consequently product composition.25 So this parameter must be controlled and because in this case, vapor product rate is always positive so it is the best manipulating variable for pressure control.28 Also the level of the condenser and bottom of the column due to their influence on time response are assumed to be controlled using the distillate and bottom rates. So the following control loops are defined: (1) pressure controller by directly changing the flow rate of the vapor phase of the overhead; (2) bottom level control through the bottom product flow rate adjustment; (3) accumulator level control by manipulating the top product liquid flow rate; (4) last tray temperature control by means of the manipulation of the reboiler heat duty.

respectively. Tables 4 and 5 present specifications of the gas− gas heat exchanger and chiller. After steady state simulation,

duty, Kj/h UA, Kj/C-h mean temp driving force, C Ft factor

gas to chiller

1.476 × 106 38.86

dynamic mode must be used for selecting the efficient control strategy.22 Distillation columns are one of the most important devices in the chemical processes and any of them have their special control structure.23,24 Control of product purity in the distillation column is essential purpose in business point of view. The selection criteria of the desired tray is described.25,26 The best method for indirect composition control is temperature control of a tray.27 Figure 3 shows the temperature profile

3. PARTICLE SWARM OPTIMIZATION PSO is a search algorithm that is initialized with a random set of particles.29,30 The PSO algorithm is simple and easily implemented, and few parameters are required to be tuned.31 Each particle in this algorithm is presented by its current velocity Vi and current position Xi. Also its individual velocity is updated according to the current velocity Vi, personal best position Pib, and the global best position Pgb, where particle i presents the smallest fitness function, assuming as Pib and the position yielding the lowest fitness function among all the Pib is Pgb, during the iteration.32 The PSO algorithm can be explained as follows: Step 1: It starts with a random population of particles Xi(k) = (xi1(k), xi2(k), ..., xid(k))

i = 1, 2, ..., n

k = 1, 2, ..., itr

Figure 3. Temperature profile along the column trays in the steady state mode.

(1)

where n is number of particles, d is number of particle’s dimensions, itr is the maximum number of iterations of optimization, and k is the current number of iteration, and velocities:

along the column trays. Temperature profile is approximately smooth except the segment near the feed stage. This is due to effect of the entering the feed, so this stage is not suitable for temperature control. The bottom stage shows the amount of vapor moving up from the reboiler, its duty is used to as control variable. Also column pressure affects the components boiling

Vi (k) = (vi1(k), vi2(k), ..., vid(k)) k = 1, 2, ..., itr C

i = 1, 2, ..., n (2)


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Industrial & Engineering Chemistry Research Step 2: Mean Absolute Error (MAE) is used to evaluate the merit of each particle as follows: t

f (Xi(k)) =

∑time = 1 |etime(Xi(k))| tn

i = 1, 2, ..., n

k = 1, 2, ..., itr

(3)

where e is the difference between the set point and the actual value which is output at the tth run time of the process. Step 3: So for each particle the best position is identified as follows: Pi b(0) = Pgb(0) = Xi(0)

Pib(k) = Xi ∈ min f (Xi(k), Xi(k − 1))

Figure 4. Closed-loop control system with components of a traditional fuzzy logic system.

4.1. Fuzzification. In the fuzzification process numerical inputs are converted into variables that are recognizable for a fuzzy set. Each numerical input is defined by two or more membership functions that describe the degree of membership value in a range of [0, 1]. There are many different types of MF and here the fuzzy set is a triangular shape that is represented by three parameters {a, b, c} as follows (Figure 5):37

(4)

for i = 1, 2, ..., n (5)

Step 4: The best global position Pgd is identified as follow: Pgb(k) = Xi ∈ min f (Pi b(k))

⎧0 ⎪ ⎪u − a ⎪b − a TriangleMF(u ; a , b , c) = ⎨ ⎪c − u ⎪c − b ⎪ ⎩0

(6)

Step 5: Then the positions of individual particles update as Xi(k + 1) = Xi(k) + Vi (k + 1)

(7)

for which the velocity is calculated as Vi (k + 1) = w·Vi (k) + c1·r1·(Pi b(k) − Xi(k)) + c 2·r2·(Pgb(k) − Xi(k))

if u ≤ a if a ≤ u ≤ b if b ≤ u ≤ c if c ≤ u

(10)

where a, b, and c show the center and the left and right deviations from the center of a triangle membership.

(8)

Vi(k + 1) and Vi(k) are the updated and current particles velocities, Xi(k + 1) and Xi(k) are the updated and current particles positions, c1 and c2 are two positive constants, which control the effect of the local and global search abilities of PSO and usually are equal to 2.33 r1 and r2 are random numbers in the range of [0, l], and w is the inertia weight which is used to control the velocity and plays a very important role in PSO convergence behavior.34 If the inertia weight is reduced linearly from 0.9 to 0.4 by the following equation, the performance of PSO will be improved.35 w − wmin wi = wmax − max ·k (9) itr

Figure 5. Triangular MF.

4.2. Rule Base. The fuzzy rule base consists of a group of fuzzy IF−THEN rules that are extracted from experience and knowledge of the experts.3,36 Tagaki−Sugeno and Mamdani are two types of expressions for the fuzzy model. In Tagaki− Sugeno type FLCs, a linguistic IF−THEN FLC rule is expressed as below:37

where wmax and wmin are 0.9 and 0.4. Step 6: Transfer to step 2 until sufficient good fitness is achieved. The PSO algorithm is used for the optimum design of the parameters of membership functions of FLC which is described in the following section.

IF a1 is d1 AND.....AND am is dm THEN u1 = g1(a1 , ..., am), ...AND um = gm(a1 , ..., am)

(11)

where di , i = 1,2,..., m are input fuzzy sets and gj() can be any linear function. The form of a linguistic IF−THEN rule in Mamdani type can be defined as follows;

4. FUZZY LOGIC CONTROLLER Fuzzy logic control uses a new control strategy that can formulate engineer knowledge into a mathematical model to control a system.3 Figure 4 illustrates the basic configuration of a fuzzy inference system in a closed-loop control system. A typical fuzzy system consists of four components: fuzzification, rule base, inference engine, and defuzzification. Two inputs, error and error difference, enter fuzzy block and by fuzzification, numerical values of them are converted to fuzzy sets. Next the inference engine, by using linguistic IF−THEN rules that are expressed in fuzzy rule base, makes the decision in order to map fuzzy sets at input into fuzzy sets at output. Finally defuzzification converts fuzzy sets values at output into the crisp values that enter the process.

IF a1 is d1 AND.....AND am is dm THEN u1 is S1......AND um is Sm

(12)

where di, i = 1,2,...,m are input fuzzy sets and Sj, j = 1,2,...,m are output fuzzy sets. On the other hand, in a Mamdani-type of FLC, consequent is stated by MFs. In this work, Mamdani-type of FLC is used and the rule base consists of 15 IF−THEN rules. 4.3. Inference Engine. The inference engine is the kernel of FLC that, according to IF−THEN rules, implement fuzzy D


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Industrial & Engineering Chemistry Research inference for mapping fuzzy sets at input into fuzzy sets at output. Max-Min composition and Max-Product composition are two of the most common methods used in the inference mechanism of fuzzy control:36,37 In this paper, Mamdani Max-Min inference method and 2 inputs and 1 output is used. A fuzzy system with two inputs a1 and a2 and a single output u is described by r linguistic IF− THEN rules in the Mamdani form: IF a1 is d1m and a 2 is d 2 m THEN um is Sm for m = 1, 2, ... ,r

Figure 7. Defuzzification centroid technique.

(13)

where d1m and d2m are mth antecedent fuzzy sets and Sm is the mth consequent fuzzy set. Aggregated output for r rules and two-input is given by

u* = (

∫u

+

u5

∫u

∫u

μ(u4)·u du +

4

2

for m = 1, 2, ..., r

μ(u1)·u du +

1

ηSm(u) = max[min[ηa m(input(i)), ηa m(input (j))]] 1

u2

/(

(14)

μ(u1)du +

1

+

max in the above formula represents the union of sets, also an example of graphical Mamdani (max−min) inference method is shown in Figure 6.

∫u

μ(u 2)·u du +

2

∫u

u4

μ(u3)·u du

3

∫u

u6

μ(u5)·u du)

5

u2

∫u

u3

u5

μ(u4) du +

4

∫u

u3

μ(u 2) du +

2

∫u

∫u

u4

μ(u3) du

3

u6

5

μ(u5) du)

(16)

5. THE PROPOSED PSO-FLC Performance of the designed PSO-FLC is studied on the control of column top pressure by adjusting vapor phase stream of the overhead. Matlab fuzzy logic toolbox is used to design FLC structures. Also PSO algorithm is implemented in Matlab. Here FLC determines its output according to the error and error difference as follows: e(t ) = SP(t ) − PV(t )

(17)

Δe(t ) = e(t ) − e(t − 1)

(18)

where SP is set-point variable and PV is process variable; e(t) is the error and Δe(t) is the error difference at time t. Figure 8

Figure 6. Graphical Mamdani (max−min) inference method. Figure 8. . Structure of FLC for column pressure control with two inputs and one output.

4.4. Defuzzification. Defuzzification converts the fuzzy sets derived by the inference mechanism into the numerical values as inputs to the plant.38 Task of the defuzzifier is to specify a best point that represents the fuzzy set Sm (the output of the fuzzy inference engine). This is similar to the mean value of a random variable. The centroid (center of gravity) technique that is used in this paper is the most common defuzzification method (Figure 7).39 This defuzzifier specifies the u* as the center of the area covered by the membership function of Sm, the relation of this method is as follows: u* =

∫ μ(u)·u du ∫ μ(u) du

illustrates the overall configuration of FLC with two inputs: error and error difference, and one output: change in VLV-104 opening percentage before optimization with PSO. Also Figure 9 shows membership functions of the FLC variables before optimization in which present values of the error and error difference are composed of five and three linguistic terms between −100 and 100 and the output is partitioned into five fuzzy sets between −50 and 50. Linguistic terms assigned to these fuzzy sets are BN, N, Z, P, BP, BIG DEC, DEC, HOLD, INC, BIG INC meaning big negative, negative, zero, positive, big positive, big decrease, decrease, increase, hold, big increase. Table 6 presents the empirical fuzzy rule-base for this problem. Triangular shape MFs is represented by three parameters, so PSO searches all of the input and output membership function

(15)

This method is shown in Figure 7 (eq 16) E


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set of MF parameters and then a fitness function is calculated to determine pib and pgb. Next according to eqs 7 and (8), particles reach to the new positions and parameters being updated. These parameters will be used to check the performance of the FLC. This procedure is repeated until the goal is achieved. The last values will be considered as optimized MF parameters. Figure 11 illustrates the convergence and evolution of PSO by

Figure 9. Membership functions of FLC before optimization.

Table 6. Rule Base for the FLC e:

BN

N

Z

P

BP

BIG INC BIG INC INC

INC INC DEC

INC HOLD DEC

INC DEC DEC

DEC BIG DEC BIG DEC

Δe N Z P

Figure 11. Convergence and evolution of PSO.

the MAE objective function. According to this figure the value of MAE, before implementation of PSO is 10.43, and after that MAE reduces to 1.37. Table 8 shows MF parameters before and after optimization. Figure 12 shows the tuned membership functions by using PSO.

parameters in 39 dimensional spaces ((8 input MFs + 5 output MFs) × 3 = 39). There are 50 particles in a swarm, and the total searching iterations are set to be 100. Table 7 presents Table 7. PSO Parameters parameter

value

c1 c2 wmax wmin number of particle (n) searching iterations (itr) fitness function

2 2 0.9 0.4 50 100 MAE

Table 8. MF Parameters before and after the PSO before PSO

parameters of the PSO. Figure 10 illustrates the optimization method for MF parameters. This approach starts with the initial

Figure 10. Flowchart of PSO to adjust fuzzy MF parameters.

MF values

input 1 error

aBN, aBDec bBN, bBDec cBN, cBDec aN, aDec bN, bDEC cN, cDEC aZ, aHOLD bZ, bHOLD cZ, cHOLD aN, aINC bN, bINC cN, cINC aN, aB INC bN, bB INC cN, cB INC

−150 −100 −50 −100 −50 0 −50 0 50 0 50 100 50 100 150

after PSO

input 2 delta error

output VLV104

input 1 error

−200 −100 0 −100 0 100 0 100 200

−75 −50 −25 −50 −25 0 −25 0 25 0 25 50 25 50 75

−430.2 −24.4 −16.6 −30.7 −15.4 0 −5.6 0 6.1 0 15.2 30.3 −430 −24.4 −16.6

input 2 delta error

iutput VLV104

−161.4 −99.5 0.5 −18.2 0 20.9 0 100.1 161.2

−75.2 −50.3 −2.5 −8.9 −4.4 0 −0.2 0 0.2 0 4.5 8.8 2.6 49.1 74.2

Figure 12. Tuned membership functions by using PSO algorithm. F


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6. RESULT AND DISCUSSION The main task of a properly designed controller is to set the process variable to the set point when disturbances happen. Changes in the feed gas pressure are considered as a disturbance which has a severe effect on the column feed stream. Figures 13, 14, 15, and 16 show the response in

Table 9. Parameters of PID Controllers PID controllers

Kc

Ti

Td

PIC101 LIC103 LIC102 TIC101

14.8 13.8 14 14.5

3.99 × 10−02 8.08 × 10−02 0.712 0.272

8.86 × 10−03 1.79 × 10−02 0.158 6.03 × 10−02

performs in its optimum point. Figure 17 shows the comparison between disturbance rejection with PID and

Figure 13. Change in composition of the column feed stream.

Figure 17. Disturbance rejection with PID and PSO-FLC controller for PIC101.

PSO-FLC controller when inlet pressure changes from 6200 to 10340 kPa at the time of 50 s. This figure illustrates that both controllers responded well to the disturbances and it is very clear that PSO-FLC performs better in accuracy, settling time, and overshoot. At rise time both controllers respond the same. In this paper accuracy is the amount of MAE. Settling time is the required time to get within a certain distance of a new equilibrium value (usually 5% or 2%) of the final value. Overshoot is the maximum peak value of the response curve measured from the desired response of the system. Table 10

Figure 14. Change in molar flow of the column feed stream.

Table 10. Comparison between PSO-FLC and PID maximum overshoot (%) settling time (s) mean absolute error

Figure 15. Change in pressure of the column feed stream.

PSO-FLC

PID

0.73 56 1.37

1.37 74 29

presents the comparison between these parameters for PID and PSO-FLC. Also because the control loops in the distillation column depend on other parameters, the performance of the other controllers after using PSO-FLC improves. Results from Figures 18, 19, and 20 suggest that implementation of PSOFLC for pressure control improves the performance of LIC103 and LIC102 and TIC, at accuracy, settling time, and overshoot.

7. CONCLUSION A new idea for direct implementation of optimal fuzzy logic controller on the Hysys dynamic environment is proposed and analyzed. Because of the nonlinear behavior of a system, a fuzzy logic controller can produce better results than the conventional controllers. A PSO-FLC is designed and applied on a Hysys dynamic mode environment to control the top pressure of an industrial distillation column used in a hydrocarbon recovery process. Results show that the proposed method can be efficiently applied for control of the chemical processes on

Figure 16. Change in temperature of the column feed stream.

compositions, flow rate, pressure, and temperature of the column feed stream in the condition that the inlet pressure changes from 6200 to 10340 kPa. Table 9 presents the tuning of the PID controller by using the Ziegler Nichols (ZN) tuning method in the Hysys environment. PID parameters are tuned with the Ziegler Nichols approach first. The optimum values of the parameters are selected and applied, so the PID controller G


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Figure 18. Disturbance rejection with PID controller for LIC103 before and after using PSO-FLC for PIC101.

Figure 19. Disturbance rejection with PID controller for LIC102 before and after using PSO-FLC for PIC101.

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REFERENCES

(1) Buckley, Ps.; Luyben, W.Aspen. HYSYS 3.2 Installation Guide; Aspen Technology: U.S.A, 2003. (2) Liu, D H F.; Abonyi, J. Software For Fuzzy Logic Control. In Instrument Engineers Handbook, Process Control And Optimization; Lipták B. G. Ed.; CRC Press: 2006; pp 360−374. (3) Vebruggen, H. B.; Bruijn, P. M. Fuzzy Control And Conventional Control: What Is (And Can. Be) The Real Contribution Of Fuzzy Sets Systems. Fuzzy Sets Syst. 1997, 90, 151. (4) Costas, P. P.; Siettos, I.C. Fuzzy Reasoning in Introductory Tutorials in Optimization and Search Methodologies; Springer US: 2005. (5) Zadeh, L. A. Fuzzy Sets. Information and Control. 1965, 8, 3. (6) Wang, L. A Course in Fuzzy Systems and Control; Prentice Hall PTR: 1997. (7) Natsheh, E.; Buragga, K. A. Comparison between conventional and fuzzy logic PID controllers for controlling dc motors. Int. J. Comput. Sci. 2010, 7, 128. (8) Mohammad, N. N.; Kasuan, N.; Rahiman, M. H. F.; Taib, M. N. Steam temperature control using fuzzy logic for steam distillation essential oil extraction process. IEEE Digital Object Identifier 2011, 53. (9) Li, Z.; Yang, Y.; Gong, X.; Lin,Y.; Liu, G. Fuzzy control of the semi-active suspension with MR damper based on GA. In IEEE Vehicle Power and Propulsion Conference, September 3−5, 2008, Harbin, Hei Longjang, China. (10) Pekgokg, O.; Gurel, R.; Bilgehan, M. M.; K ysa, M. Active suspension of cars using fuzzy logic controller optimized by genetic algorithm. Int. J. Eng. Appl. Sci. 2010, 2 (4), 27.

Figure 20. Disturbance rejection with PID controller for TIC101 before and after using PSO-FLC for PIC101.

the Hysys dynamic environment. Also results prove that PSOFLC can perform better than a PID controller at accuracy, settling time, and overshoot for a distillation column.

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FLC = fuzzy logic controller MFs = membership functions W = inertia weight M = membership functions degree e(t) = error Δe(t) = change in error SP = set point PV = process variable LTS = low temperature separator P&ID = piping and instrumentation diagram PSO-FLC = combination of PSO and FLC Xid = current position in search pace Vid = current velocity Pid = personal best position in space Pgd = global best position in space min = minimum max = maximum BN = big negative N = negative Z = zero P = positive BP = big positive BIGDEC = big decrease DEC = decrease BIGINC = big increase INC = increase T = temperature (°C) MAE = mean absolute error t = time k = iteration m = number of rules ai = ith fuzzy input uj = jth fuzzy output di = ith input fuzzy sets Sj = jth output fuzzy sets uj = Defuzzifier value

AUTHOR INFORMATION

Corresponding Author

*Tel: +98 21 61118564. Fax: +98 21 88617087. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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NOMENCLATURE PSO = particle swarm optimization H


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Design and Implementation of Optimized Fuzzy Logic Controller for a

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