Fuzzy Optimization Approach for the Synthesis of Polyesters and Their

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Fuzzy Optimization Approach for the Synthesis of Polyesters and Their Nanocomposites in In-Situ Polycondensation Reactors Ali Reza Zahedi, and Mehdi Rafizadeh Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b02307 • Publication Date (Web): 26 Aug 2017 Downloaded from http://pubs.acs.org on August 28, 2017

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Industrial & Engineering Chemistry Research is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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Industrial & Engineering Chemistry Research

FIG. 1. Schematic of the reactor. 133x215mm (300 x 300 DPI)

ACS Paragon Plus Environment


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FIG. 2. Desired jacket temperature as a fuzzy number. 52x33mm (300 x 300 DPI)


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FIG. 3. Block diagram of proposed fuzzy controller. 35x15mm (300 x 300 DPI)



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FIG. 4. Reactor temperature step response. 64x51mm (300 x 300 DPI)


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FIG. 5. The performance of PI controller for reactor temperature. 64x50mm (300 x 300 DPI)



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FIG. 6.The diagram of command to the heater: a) general view, b) magnification view. 128x200mm (300 x 300 DPI)


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FIG. 7. The performance of PID controller for reactor temperature. 65x52mm (300 x 300 DPI)



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FIG. 8. Fuzzy sets defined on temperature error. 45x24mm (300 x 300 DPI)


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FIG. 9. Fuzzy sets defined on the derivative of temperature error. 35x15mm (300 x 300 DPI)



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FIG. 10. The fuzzy controller performance at 200 °C. 65x51mm (300 x 300 DPI)


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FIG. 11. Reactor temperature during the polymerization. 65x52mm (300 x 300 DPI)



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FIG. 12. The jacket temperature during the polymerization. 65x52mm (300 x 300 DPI)


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Fuzzy Optimization Approach for the Synthesis of Polyesters and Their Nanocomposites in In-Situ Polycondensation Reactors Zahedi Ali Reza1,∗∗, Rafizadeh Mehdi2 1

School of New Technologies, Iran University of Science and Technology, Tehran, Iran 2

Department of Polymer Engineering & Color Technology, Amirkabir University of Technology, Tehran, Iran

Abstract A proportional-derivative (PD) fuzzy controller was presented to temperature control of a polycondensation reactor. Synthesis of various polyesters and copolyesters were conducted using devised controller. This controller uses reactor temperature error as well as its derivative. The desired jacket temperature had uncertainty due to be affected by noise and disturbance. This uncertainty is modeled using fuzzy numbers, and a fuzzy trajectory was achieved for desired reactor temperature. Then, a generalized Takagi-Sugeno (GTS) fuzzy controller was designed. An adaptation algorithm was included in the controller. Compared to conventional

proportional-integral-derivative

(PID)

controllers,

experimental

results

presented a very good performance to control reactor temperature of in-situ polymerization of polyesters. Although the PID controller finally controlled the temperature with an accuracy of ±6 °C, the temperature overshoot was around 20°C that could completely degrade the polymer. However, fuzzy PD controller had no overshoot. The performance of fuzzy PD controller to control the temperature of the reactor at suitable was excellent with 0.2% accuracy without overshoot. The NMR results confirmed that the final polymers have been synthesized successfully. Moreover, molecular weights of samples, synthesized under fuzzy control, were generally higher and there was a better intercalation structure in such samples.

Keyword: Fuzzy control; Fuzzy trajectory; In-situ polycondensation; reactor control; Aromatic polyesters

∗

To whom all correspondence should be addressed, [email protected]

1



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INTRODUCTION In polymerization reactor, monomers react to produce a certain high molecular weight polymer. In order to achieve desired final properties, process conditions during the polymerization must be well-controlled. On the other hands, most of the ultimate polymer properties such as molecular weight and its distribution, the rate of monomer conversion, the degree of branching, and copolymer composition during the course of polymerization are not measurable. Therefore, some other measurable and estimable parameters should be selected to be used in closed-loop control 1. Temperature, density, pressure, flow rate, and so forth are some examples of control variables. A batch polymerization is usually performed based on a pre-planned pattern. Polyester synthesis typically involves pre-mixing of required reactants (paste mixing) step, esterification among acid and hydroxyl groups, and polycondensation step that results in the final polymer. Each step has its own process conditions. Temperature control of the reactive mixture is one of the most common control strategies. Because the temperature of polymerization can effect on the final product properties 2. The Control of polymerization reactor is an interesting field developed by many researchers, during the last decades. In 1989, the pole placement control technique as an experimental transfer function using the autoregressive-moving average (ARMA) model for the temperature control of batch polymerization reactor was exerted by Tzouanas and Shah

3

which controlled monomer

conversion successfully. In other works, Soroush and Kravaris 4 and Muta et al. 5 proposed a predictive controller based on a nonlinear model using a Kalman filter estimator for controlling the reactor temperature of polymerization. In this regard, Alamir et al. 6 designed a nonlinear controller included the one-step Newton strategy to estimate the state variables. Recently, Aumi and Mhaskar reviewed the modeling of the batch process and obtained the model parameters using the published results7. As well as, they progressed an experimental model as a process model in the control section. It could be resulted, upon the development of fuzzy logic theories by Zadeh 8 and the emergence of successful control by Mamdani 9, fuzzy control has been a significant approach in the polymer synthesis industry. It was known that Fuzzy controllers could be classified into two families: fuzzy model and fuzzy rules. In recent two decades, many manuscripts have been published about fuzzy theory applications in the controlling of the polymer chemical and its production process 10. Abony et al. 11 designed an adaptive Takagi-Sugeno fuzzy model as a process control for controlling the polymerization reaction which performed better than conventional controllers. In similar work, Asua et al. 12 2


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introduced a fuzzy system for optimizing the conditions of emulsion polymerization reaction; also they developed a model-based fuzzy controller for controlling such reactors. In this study, for the first time, conventional PI and PID controller and fuzzy PD controller were applied to control the temperature of polyester synthesis reactor. PID controller, which was designed based on an empirical model of reaction, was tuned based on the Cohen-Cohn formulation. PI and PID controllers were unable to present acceptable performance and the structure of fuzzy PD controller was the GTS fuzzy one. For scrutiny, the controller performance was investigated for reactor temperature trajectory. It is clear that this fuzzy controller could successfully control the reactor temperature in different micro or nanoscale polymers. This PD fuzzy controller was utilized to control the temperatures of polyesters and their nanocomposites including: poly(ethylene terephthalate) (PET), poly(ethylene

terephthalate-co-1,4-cyclohexane

dimethanol)

(PETG),

poly(ethylene

terephthalate-co-5-sulfoisophthalate acid) (PETNa), poly(1,4-butanediol terephthalate) (PBT), poly(1,3-propanediol terephthalate) (PTT), and poly(bis(hydroxyethyl) terephthalateco- maleic anhydride) (UPR).

EXPERIMENTAL Materials Terephthalic acid (TPA) and ethylene glycol (EG) was supplied by Shahid Toundgoyan Petrochemical Complex (Mahshahr, Iran). 1,3-propanediol (PDO), 1,4butanediol (BDO), was purchased from AppliChem GmbH (Darmstadt, Germany). 1,4cyclohexane dimethanol (CHDM) as comonomer of PETG and sodium 5-sulfoisophthalate acid (NaSIPA) as comonomer of PETNa was purchased from Sigma–Aldrich Co (London, England). Ethanol as a solvent, antimony oxide (ATO) and tetrabutyltitanate (TBT), as polycondensation catalysts, 3-aminopropyltriethoxysilane (APS) as nanoclay modifier, odichlorobenzene, dichloroacetic and 1,1,2,2,tetrachloroethane as solvents for intrinsic viscosity measurement were prepared from Merck Co (Darmstadt, Germany). For NMR spectrum, triflouroacetic acid (TFA) as a solvent was used from Scharlau Co (Barcelona, Spain). Also, phenol as a solvent for intrinsic viscosity measurement was applied from Scharlau Co (Barcelona, Spain). Cloisite 30B (OMMT) was purchased from Southern Clay 3



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Products (Gonzales, USA). In order to synthesize UPR, bis(hydroxyethyl) terephthalate (BHET) was prepared based on our previous work

13

, and maleic anhydride (MA) was

purchased from Merck Co (Darmstadt, Germany).

Measurements Intrinsic viscosities of polyesters and their nanocomposites were measured with dissolving them in a suitable solvent and using Ubbelohde viscometer at 25oC ±0.1. 1H- and 13

C-NMR spectra were recorded on a Brucker DPX-500 advance spectrometer operated at

500 MHz and 25oC. Samples were dissolved in CHCl3, and a small amount of CDCl3 was added to lock the spectrometer; the spectra were internally referenced to tetramethylsilane. Xray diffraction (XRD) profiles were recorded using aX’Pert MPD model (tube voltage: 40 kV and tube current: 30 mA) with a monochromatic Co-Karadiation (λ=1.789 Å). Samples were scanned from 2θ= 2o to 10o at a scanning rate of 1o/min using a reflection mode.

Synthesis Setup Overview of the used reactor control system and its accessories is shown in FIG. 1, schematically. Three PT100 temperature sensors with the accuracy of ±0.2 °C were mounted inside the reactor, jacket, and condenser. The reactor pressure was measured by a pressure transducer (Ashcroft Inc model KM-11 USA). Two blades type mixer was used to mix high viscous reactive mixture containing a 1500 watts electrical heater around the reactor. On top of the reactor, there are five connections to conjoin temperature and pressure sensors, apply pressure by nitrogen, and connect vacuum line. Sealing of the applied top reactor could tolerate 50 atm. The vacuum was created by a JB-85N-250 vacuum pump from FastVac Company (USA). Two chilled traps, in series, cooled in iso-propanol bath at -30 oC, were used to prevent the entry of organic materials into the vacuum pump. All data acquisition and control tasks were performed with home-written Visual C#.net code. I/O card model USB4711A from AdvanTech (USA) had the responsibility of computer interfacing. An injection system was manufactured to add nanoclay during polycondensation.

4


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Synthesis Procedure Modification of OMMT Like our previous work14, the organoclay could be modified. Briefly, after drying nanoclay in a vacuum oven at 60oC, 1g OMMT was added to 25 mL ethanol/APS (95/5, v/v) and the mixture was refluxed for six hours. Then the mixture was washed continuously by ethanol/deionized water (75/25, v/v) and finally was dried at 60oC overnight. The obtained modified organoclays were designated as TMMT. Synthesis of polyesters, copolyesters, and their nanocomposites It was reported that the diol and diacid with a hydroxyl group/acid group molar ratio of 1.7 were premixed14-15. In these works, the mixture was charged into the stirred reactor. Table 1 shows the reaction and process conditions of polyesters, copolyesters, and their nanocomposites synthesis. According to the table data, in all cases, the synthesis was carried out based on the following stages: 1- The paste mixing in which the reactants are mixed at given temperature and time shown in Table 1. 2- The esterification in which the temperature is brought over 230°C dependent on product and pressures up to 3.5 bars continued until the water production stops. For synthesizing of polyester nanocomposites, nanoclay was sonicated in EG for an hour and added to the mixture after pressure reached to one bar. The mixing was continued for 30 minutes in order to better dispersion. 3- The polycondensation in which the reaction temperature over 270°C and pressures up to 0.01 bar is set. In this step, polycondensation was the predominant reaction and dialcohol as a by-product of the polycondensation reaction was removed by a vacuum pump during three hours. Finally, the pressure was adjusted to atmospheric pressure and all materials were evacuated by nitrogen pressure.

Fuzzy Trajectory Idea Clearly, the presented fuzzy controller uses reactor temperature and its derivative. In addition to reactor temperature error, a derivative of temperature error is considered in order to avoid instability that comes from long delay time of heat transfer to the inside of the 5



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reactor. Also, considering this parameter could be helpful in making reactor dynamic and faster in performance. Therefore, the error of reactor temperature is described as: eReactor = Td,Reactor − TReactor

(1)

where Td,Reactor and TReactor are desired and measured reactor temperature, respectively. Certainly, the errors of reactor temperature could be known as a crisp real number. Like other works, a generalized numbers and intervals could make a fuzzy number ( N% ) which was a fuzzy set depend on a real numbers set ( ℜ )

. Also, N% must examine as a normal fuzzy

16

set ( hgt( N% ) = supx∈ℜ µ N% ( x ) = 1 ) and for ∀α ∈ ( 0,1] , α N% must be a closed interval and the support of N% ( =

0+

N% ) that should be bounded. Hence, any fuzzy number is a convex fuzzy

set; however, the inverse relationship is not necessarily true. FIG. 2 illustrates the fuzzy trajectory idea of reactor temperature. In FIG. 2, the uncertainty parts are represented by a and b parameters. Likewise, the environmental disturbance and the rate of the process heat transfer could result in α parameter assumed constant during polymerization. In this experiment, sampling time was one second and the parameters of the reactor temperature fuzzy number are a= 0.5oC; b= 0.5oC and α= 0.3oC. In order to calculate the derivative of the temperature error, a fuzzy subtraction should be used as follows. e&Re actor = Tn − Tn −5

(3)

Two significant methods to subtract two fuzzy numbers are including extension principle, and α -cuts or intervals arithmetic. If A% and B% are two fuzzy numbers, based on the former, A% − B% fuzzy number is defined as:

µ A% − B% ( z ) = sup {T ( µ A% ( x ), µ B% ( y )) z = x − y}

(4)

where T is a T-norm. In the latter, α ( A% − B% ) is defined as: α

( A% − B% ) = α A% − α B%

(5)

where the difference between [ x , y ] and [ x′, y′ ] intervals is defined as:

6


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[ x , y ] − [ x′, y ′ ] = [ x − x′, y − y ′ ]

(6)

It could be assumed obviously that the set of all α -cuts represent every fuzzy set 16

uniquely

. Moreover, if singleton fuzzification is used, these two methods result in the

same. FIG. 3 shows the block diagram of the proposed controller with no adaptation mechanism. The fuzzy controller in this research uses reactor temperature error, eReactor , and its derivative, e&Reactor , as inputs, and power applied to the heater as output. An approach for fuzzy control of systems is developed by Takagi and Sugeno 17 based on system linearization in some points. A Takagi-Sugeno fuzzy controller consists of N R fuzzy rules as follows: % ( j ) and . . . and x is A % ( j) Rj : if x1 is A 1 n n

(8)

then u = a j T X+ b j (1 ≤ j ≤ NR )

where X = [x1 ; x2 ; . . . ; xn ] T is known as a system state vector, A%i( j ) ( 1 ≤ i ≤ n ,1 ≤ j ≤ N R ) are fuzzy sets defined on system case, u is the controller output, and in the equation a j and b j are constants. The fuzzy controller output is a convex combination of the results of its rules and each result weight is commensurate to prior satisfaction. By considering the current state of the system as X* = [x1* ; x2* ; . . . ; xn* ] T the output of controller could be resulted by: NR

∑w u* =

( j)

( a j T X* + b j )

j =1

NR

(9)

∑w

( j)

j =1

where w( j ) is the antecedent satisfaction of the jth rule, as follows: n

w( j ) = ∏ µ A% ( j ) x*n i =1

(10)

i

Here, the fuzzy controller inputs were fuzzy numbers. The fuzzy set X% on ℜ is a generalized fuzzy number if Core( X% ) ≠ ∅ and also ∀α and

α

X% are a closed interval. The

usefulness of this definition despite the classical definition of fuzzy numbers

16

is the

inclusion of Gaussian fuzzification of crisp numbers or other methods of fuzzification that 7



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leads to fuzzy sets with plenty of benefits. A set of all generalized fuzzy numbers has been % . On the other hand, the fuzzy set A% on ℜ is a fuzzy pseudo-number provided by ℜ G

if Core( A% ) ≠ ∅ and ∀α ∈ ( 0,1] ,

α

A% is a closed interval or ∀α ∈ ( 0,1] ,

α

A% is a semi-

opened interval. Therefore, saturated fuzzy sets used in the fuzzy rule are fuzzy pseudo-

% . numbers. These fuzzy sets are considered as linguistic variables and are presented by ℜ P Assume that a fuzzy controller consists of N R fuzzy rules as follows:

Rj : if X% 1 is A%1( j ) and . . . and X% n is A% n( j )

(11)

then u = c(j) where X% 1 , X% 2 ,... and X% n are generalized fuzzy numbers as the inputs of the controller,

A%i( j ) (1 ≤ i ≤ n, 1 ≤ j ≤ NR ) fuzzy sets are fuzzy pseudo-numbers defined on inputs of the system, u is the controller output, and c( j ) are constants. The inference mechanism is similar to Takagi-Sugeno fuzzy controller inference mechanism as follows: NR

∑w

( j) ( j)

j =1 NR

u=

c

(12)

∑w

( j)

j =1

The calculations of antecedent satisfaction are the main difference as follows: w( j ) = tv( X% 1 is A%1( j ) and . . . and X% n is A% n( j ) )

(13)

n

= Τ tv( X% i is A%i( j ) ) i =1

where tv( X% ) is a real number in [0,1] as the truth value operator, and T is a T-norm. tv( X% ) maps each statement to its true value. In order to evaluate w( j ) , the true value of linguistic terms should be determined in a GTS fuzzy controller. It could be assumed X% equal to A% , approximately. Therefore, its true value is:

tv( X% is A% ) = tv( X% ≈ A% ) = T( tv( X% ≤ A% ),tv( X% ≥ A% ))

(14)

8


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As reported before 18, the following definitions could be used alternatively in order to obtain the true value of X% ≥ A% and X% ≤ A% :

tv( X% ≤ A% ) = sup {T( µ X% ( x ), µ A% ( a ))| x ≤ a}

(15)

tv( X% ≥ A% ) = sup {T( µ X% ( x ), µ A% ( a ))| x ≥ a}

(16)

By substituting Eqs. (15) and (16) in Eq. (14) the following equation is derived:

tv( X% is A% ) = T(sup {T( µ X% ( x ), µ A% ( a ))| x ≤ a} ,

(17)

sup {T( µ X% ( x ), µ A% ( a ))| x ≥ a} )

If X% is a generalized fuzzy number and A% is a fuzzy pseudo-number, according to the definition of Eq. (17) then the true value of ( X% is A% ) will be equal to the height of X% I A% . In the other words:

tv( X% is A% ) = hgt( X% I A% )

(18)

If X% is a singleton fuzzy number, it could be written: 1 x = x* * 0 x ≠ x

µ X% ( x ) = 

(19)

and A% is a fuzzy pseudo-number, then:

tv( X% is A% ) = µ A% ( x* )

(20)

This proposition shows that if the inputs of GTS fuzzy controller are singleton fuzzy sets, then the GTS fuzzy controller will be reduced to a TS fuzzy controller. Therefore, Eq. (13) can be rewritten as: n

w( j ) = T hgt( X% i I A%i( j ) )

(21)

i =1

eReactor and e&Reactor are inputs of the proposed fuzzy controller. Rule base of this controller includes rules with the general form:

9



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if eReactor is R% (j) and e&Reactor is J% (j) then u= c(j)

Page 22 of 35

(22)

Then the controller output is: NR

∑w u=

( j) ( j)

j =1 NR

c

(23)

∑w

( j)

j =1

where w( j ) could be calculated as follows: w( j ) = tv [( eRe actor is R% ( j ) ) and ( e&Reactor is J% ( j ) )] = T [ tv( e is R% ( j ) ),tv( e& is J% ( j ) )] Re actor

Reactor

= T [ µ A% ( j ) ( eRe actor ), hgt( e&Reactor I J%

( j)

(24)

)]

and if the algebraic product applied as the T-norm, it could be simplified as follows:

w( j ) = µ A% ( j ) ( eReactor )hgt( e&Reactor I J% ( j ) )

(25)

Hence, a generalization is performed on the TS fuzzy controllers that could be compared with further experimental results.

RESULTS AND DISCUSSION The Reactor Dynamics and Controller Design In order to study the dynamic behavior of the process, an input step was utilized by a heater (200 watts) at t=0 and the reactor and jacket temperatures were recorded, simultaneously. FIG. 4 shows the reactor temperature variations according to the time. A first-order system plus dead time (FOPDT) was fitted to the data. The formula of FOPDT as follows: k e −Td G% ( s ) = p Ts + 1

(26)

where k p ,T and Td are the gain, time constant and dead time, respectively. The numerical values of parameters were determined by curve fitting method. The area between step 10


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responses (ABC method

19

) of experimental data and transfer function was minimized (see

FIG. 4). This minimization was performed based on the Nelder-Mead method

20

. However,

the numerical values are: k p = 239.55,

T = 5259.40,

Td = 19.37;

(27)

Hence, the overall behavior of relay, process and the sensor is FOPDT; then the Cohen-Coon method was used to tune PI and PID controllers. Consequently, the Cohen-Coon relationships were applied to calculate controller parameters. For PI controller, the calculated parameters are: k c = 1.0206, τ I = 0.640559

(28)

And similarly, for PID controller: k c = 1.5124, τ I = 47.60, τ D = 7.04

(29)

FIG. 5 shows the typical behavior of PI controller for the synthesis of PET. In this experiment, the reference temperature is 240°C. Although the PI controller finally controlled the temperature with an accuracy of ±6 °C, the temperature overshoot was around 50°C that can completely degrade the polymer due to uncontrollable and high temperature (around 290°C). Small sampling time (one second) caused a thick curve as shown in FIG. 6a. The close look at the curve of FIG. 6a could be seen in FIG. 6b. As well as FIG. 7 shows the results for the PID controller application. It is observed that controlled variable has offset integral action presence despite in controller structure. The long delay of heat transfer from the heater, jacket into the reactor is believed to be responsible for this offset. However, it is not possible to decrease this delay time. The controller performance indicates that temperature controlled with an accuracy of ±4°C, and the temperature overshoot was about 40°C. Efforts to improve reactor performance were not successful and lead to increase the temperature up to 280°C which is not a suitable temperature. It is necessary that the behavior of other aromatic polyesters studied in this report were controlled similarly to PET as the most commercial aromatic polyesters. Therefore, the graphs of PET were only shown in brief.

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Fuzzy Controller Design As the temperature path of reaction is an important issue, in addition to the reactor temperature, the derivation of reactor temperature and its error was also put into the fuzzy algorithm (see FIG. 8 and FIG. 9). Linguistic rules and fuzzy sets to control the reactor temperature were defined. Then, the results of linguistic rules were set according to the Table 2 data. The table shows the applied power to the system based on the conditions of a skilled operator (The numbers on the table are in watt). The fuzzy inference engine is based on the T-norm defined by Zadeh 8 as follows:

T ( a ,b ) = min( a ,b )

(30)

The error and its derivative are fuzzified in this controller and unified to the fuzzy inference engine. The fuzzy inference engine can directly return a crisp value of heater power after defuzzification of the result. The reactor temperature error and its derivative obtained via the current temperature and the temperature mean value in the last 5 seconds. A suitable control with an accuracy of ±0.5 °C was obtained by applying this controller to the process at 200, 240, and 280°C. This control system can handle the reactor temperature from 200 to 300°C with high-precision. FIG. 10 shows the results of the fuzzy controller. As an important point, this controller has no overshoot with the control accuracy of ±0.5°C.

Temperature Control during Polymerization To ensure the controller performance, experiments were conducted during the course of polymerization of aromatic polyesters. The red graph in FIG. 11 shows the reactor temperature controlled using the fuzzy controller. As seen in FIG. 11, the fuzzy controller was very successful in control the reactor temperature in all three stages of paste mixing, esterification, and polycondensation. The esterification reaction is partially exothermic and polycondensation reaction is moderately endothermic. Moreover, in the case of in-situ polymerization systems, the similar result was observed despite the presence of nanoparticles that could cause instability in the reactor temperature. This means that the designed fuzzy controller will be able also to control the temperature under disturbance. FIG. 12 shows the jacket temperature during the polymerization. The applied heat during the reaction is shown in FIG. 13. The intrinsic viscosities obtained from the polyesters synthesized via PID 12


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temperature control and fuzzy logic temperature control (see Table 3 and Table 4) show that the molecular weights of those synthesized via the fuzzy approach were generally higher. It means that the temperature control of the polymerization process plays an important role. On the other hands, the results from XRD graphs for nanocomposites show that the precise temperature control can affect significantly on the d-spacing of organoclay in both systems (See Table 5 and Table 6) and there is a better intercalation structure in samples synthesized through fuzzy logic control.

CONCLUSIONS Polyesters and copolyesters, as well as their nanocomposites, were synthesized in a home-made reactor. The process was performed three stages, premixing around 40-90oC, esterification around 230-250°C and polycondensation around 260-280°C depending on reactants. In these reactions, the temperature overshoot can degrade the polymer. In the first step, conventional PI and PID controllers were applied. Control setting via Cohen-Cohn method was obtained, but the PI and PID controllers were unsuccessful. Although the PI controller finally controlled the temperature with the accuracy of ±6 °C, the temperature overshoot was around 50°C that can completely degrade the polymer. The PID controller performance indicated that temperature controlled with the accuracy of ±4°C, and the temperature overshoot was about 40°C. Efforts to improve reactor performance were not successful and lead to increase temperature up to 300°C. Fuzzy logic was applied to control the reactor temperature. Its result shows with 0.2% accuracy without overshoot. The NMR results confirmed that the final polymers have been synthesized successfully based on the molecular structure. The intrinsic viscosities obtained from the polyesters synthesized via PID controller and fuzzy logic controller showed that the molecular weights of those synthesized via the fuzzy approach were generally higher. Hence, temperature control of the polymerization plays an important role. On the other hands, the results from XRD graphs for nanocomposites show that the precise temperature control can affect significantly on the dspacing of organoclay in both systems and there is a better intercalation structure in samples synthesized through fuzzy logic control.

13



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REFERENCES 1. Schork, J., Framework of the Control Problem In Control of Polymerization Reactors, Taylor & Francis: 1993; pp 101-109. 2. Rafizadeh, M., Sequential linearization adaptive control of solution polymerization of methyl methacrylate in a batch reactor. Polymer Reaction Engineering 2002, 10 (3), 121-133. 3. Tzouanas, V. K.; Shah, S. L., Adaptive pole-assignment control of a batch polymerization reactor. Chemical Engineering Science 1989, 44 (5), 1183-1193. 4. Soroush, M.; Kravaris, C., Nonlinear control of a batch polymerization reactor: An experimental study. AIChE Journal 1992, 38 (9), 1429-1448. 5. Mutha, R. K.; Cluett, W. R.; Penlidis, A., On-Line Nonlinear Model-Based Estimation and Control of a Polymer Reactor. AIChE Journal 1997, 43 (11), 3042-3058. 6. Alamir, M.; Sheibat-Othman, N.; Othman, S., Constrained nonlinear predictive control for maximizing production in polymerization processes. IEEE Transactions on Control Systems Technology 2007, 15 (2), 315-323. 7. Aumi, S.; Mhaskar, P., Integrating data-based modeling and nonlinear control tools for batch process control. AIChE Journal 2012, 58 (7), 2105-2119. 8. Zadeh, L. A., Fuzzy sets. Information and Control 1965, 8 (3), 338-353. 9. Mamdani, E. H., Application of fuzzy algorithms for control of simple dynamic plant. Electrical Engineers, Proceedings of the Institution of 1974, 121 (12), 1585-1588. 10. (a) Abeykoon, C., A novel model-based controller for polymer extrusion. IEEE Transactions on Fuzzy Systems 2014, 22 (6), 1413-1430; (b) Aumi, S.; Corbett, B.; Mhaskar, P.; Clarke-Pringle, T., Data-based modeling and control of nylon-6, 6 batch polymerization. IEEE Transactions on Control Systems Technology 2013, 21 (1), 94-106; (c) Finkler, T. F.; Kawohl, M.; Piechottka, U.; Engell, S., Realization of online optimizing control in an industrial semi-batch polymerization. Journal of Process Control 2014, 24 (2), 399-414; (d) Hosen, M. A.; Hussain, M. A.; Mjalli, F. S.; Khosravi, A.; Creighton, D.; Nahavandi, S., Performance analysis of three advanced controllers for polymerization batch reactor: an experimental investigation. Chemical Engineering Research and Design 2014, 92 (5), 903916; (e) Gao, S.-z.; Wang, J.-s.; Zhao, N., Fault diagnosis method of polymerization kettle equipment based on rough sets and BP neural network. Mathematical Problems in Engineering 2013, 2013, 1-12; (f) Hosen, M. A.; Khosravi, A.; Creighton, D.; Nahavandi, S., Prediction interval-based modelling of polymerization reactor: a new modelling strategy for chemical reactors. Journal of the Taiwan Institute of Chemical Engineers 2014, 45 (5), 22462257; (g) Çetinkaya, S.; Zeybek, Z.; Hapoğlu, H.; Alpbaz, M., Optimal temperature control in a batch polymerization reactor using fuzzy-relational models-dynamics matrix control. Computers & Chemical Engineering 2006, 30 (9), 1315-1323; (h) Solgi, R.; Vosough, R.; Rafizadeh, M., Generalization of Takagi-Sugeno Fuzzy Controller and its Application to Control of MMA Batch Polymerization Reactor. Polymer-Plastics Technology and Engineering 2006, 45 (2), 243-249. 11. Abonyi, J.; Nagy, L.; Szeifert, F., Takagi-Sugeno fuzzy control of batch polymerization reactors. In Soft Computing in Engineering Design and Manufacturing, Springer: 1998; pp 420-429. 12. Vicente, M.; Leiza, J.; Asua, J., Maximizing production and polymer quality (MWD and composition) in emulsion polymerization reactors with limited capacity of heat removal. Chemical Engineering Science 2003, 58 (1), 215-222. 13. Zahedi, A. R.; Rafizadeh, M.; Ghafarian, S. R., Unsaturated polyester resin via chemical recycling of off-grade poly(ethylene terephthalate). Polymer International 2009, 58 (9), 1084-1091. 14


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14. Heidarzadeh, N.; Rafizadeh, M.; Taromi, F. A.; Bouhendi, H., Preparation of poly (butylene terephthalate)/modified organoclay nanocomposite via in-situ polymerization Characterization, thermal properties and flame retardancy. High Performance Polymers 2012, 24 (7), 589-602. 15. (a) Sepehri, S.; Rafizadeh, M.; Afshar-Taromi, F., Synthesis and characterization of copolymers of poly(ethylene terephthalate) and cyclohexane dimethanol in a semibatch reactor (including the process model). Journal of Applied Polymer Science 2009, 113 (6), 3520-3532; (b) Shirali, H.; Rafizadeh, M.; Taromi, F. A., Synthesis and characterization of amorphous and impermeable poly (ethylene-co-1, 4-cyclohexylenedimethylene terephthalate)/organoclay nanocomposite via in situ polymerization. Journal of Composite Materials 2014, 48 (3), 301-315; (c) Sheikholeslami, S. N.; Rafizadeh, M.; Taromi, F. A.; Bouhendi, H., Synthesis and characterization of poly(trimethylene terephthalate)/organoclay nanocomposite via in situ polymerization. Journal of Thermoplastic Composite Materials 2014, 27 (11), 1530-1552; (d) Heidarzadeh, N.; Rafizadeh, M.; Taromi, F. A.; del Valle, L. J.; Franco, L.; Puiggalí, J., Effect of Hydroxyapatite Nanoparticles on the Degradability of Random Poly (butylene terephthalate-co-aliphatic dicarboxylate) s Having a High Content of Terephthalic Units. Polymers 2016, 8 (7), 253-274; (e) Sheikholeslami, S. N.; Rafizadeh, M.; Taromi, F. A.; Shirali, H.; Jabbari, E., Material properties of degradable Poly (butylene succinate-co-fumarate) copolymer networks synthesized by polycondensation of prehomopolyesters. Polymer 2016, 98, 70-79. 16. Lilly, J. H., Basic Concepts of Fuzzy Sets. In Fuzzy Control and Identification, John Wiley & Sons, Inc.: 2010; pp 11-26. 17. Zhang, H.; Liu, D., Identification of the Takagi-Sugeno Fuzzy Model. In Fuzzy Modeling and Fuzzy Control, Birkhäuser Boston: 2006; pp 33-79. 18. Lilly, J. H., Takagi–Sugeno Fuzzy Systems. In Fuzzy Control and Identification, John Wiley & Sons, Inc.: 2010; pp 88-105. 19. Rafizadeh, M., Dynamics of 3 or higher-level systems, the approximation and identification of systems. In Process Dynamics and Control Applied approach in Chemical , Polymer and Metallurgical Engineering, Tehran Polytechnic Press: Tehran, 2011; pp 95-119. 20. Balu, K.; Padmanabhan, K., B Constrained Optimisation Methods In Modeling And Analysis Of Chemical Engineering Processes, I.K. International Publishing House Pvt. Ltd.: 2007; pp 372-386. 21. Mazloom, M.; Rafizadeh, M.; Haddadi-Asl, V.; Pakniat, M., Synthesis and mathematical modelling of polyethylene terephthalate via direct esterification in a laboratory scale unit. Iranian Polymer Journal (English Edition) 2007, 16 (9), 587-596.

15



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Figure Captions: FIG. 1. Schematic of the reactor. FIG. 2. Desired jacket temperature as a fuzzy number. FIG. 3. Block diagram of proposed fuzzy controller. FIG. 4. Reactor temperature step response. FIG. 5. The performance of PI controller for reactor temperature. FIG. 6.The diagram of command to the heater: a) general view, b) magnification view. FIG. 7. The performance of PID controller for reactor temperature. FIG. 8. Fuzzy sets defined on temperature error. FIG. 9. Fuzzy sets defined on the derivative of temperature error. FIG. 10. The fuzzy controller performance at 200 °C. FIG. 11. Reactor temperature during the polymerization. FIG. 12. The jacket temperature during the polymerization. FIG. 13. Heat applied to the reactor.

16


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Table 1. Synthesis conditions of polyesters, copolyesters and their nanocomposites Product Diol

Diacid Catalyst Comonomer

PET

EG

TPA

ATO

PETG

EG

TPA

PETNa

EG

TPA

Paste

Ester. Polycond.

o

TMMT(%) Ref.

( C/min) (oC)

(oC/min)

--

90/30

240

280/180

--

21

ATO

CHDM

90/30

240

280/180

--

15a

ATO

NaSIPA

90/30

240

280/180

--

--

PBT

BDO TPA

TBT

--

45-90/30 245

260/180

--

15d

PTT

PDO TPA

TBT

--

90/30

230

260/240

--

15d

UPR

BHET MA

--

--

50/60

160

190/300

--

13

PET

EG

TPA

ATO

--

90/30

240

280/180

1

21

PETG

EG

TPA

ATO

CHDM

90/30

240

280/180

1

15a

PETNa

EG

TPA

ATO

NaSIPA

90/30

240

280/180

1

--

PBT

BDO TPA

TBT

--

45-90/30 245

260/180

1

15d

PTT

PDO TPA

TBT

--

90/30

260/240

2

15d

230

17



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Table 2. Interface linguistic rules eReactor

PB

PM

PS

Z

NS

NM

NB

NVB

NVB

NB2B

NV2B

NV2B

NV2B

NV2B

NV2B

NB

NS

NB

NV2B

NV2B

NB

NB

NGB

NM

Z

PVS

NS

NV2B

NV2B

NGB

Z

PVS

PM

PVB

PV4B

Z

NV2B

NGB

NS

PS

PGB

PVB

PV3B

PV5B

PS

NVB

NM

PS

PM

PVB

PV3B

PV5B

PV6B

PB

NGB

NVS

PS

PB

PV2B

PV5B

PV6B

PV6B

PVB

NVS

PS

PV3B

PV6B

PV6B

PV6B

PV6B

PV6B

e&Re actor

PB: positive big; PM: positive medium; PS: positive small; Z: zero; NS: negative small; NM: negative medium; NB: negative big; NVB: negative very big

18


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Table 3. Polyester and polyester nanocomposite molecular weight synthesized via PID temperature control Samples

Clay Conc. (%)

[η] (dL/g)

Mn(gmol-1)

Ref.

2800

21

PET

0

0.28

PET/TMMT

1

0.35

PETG

0

0.43

PETG/TMMT

1

0.52

PETNa

0

0.47

21900

--

PETNa/TMMT

1

0.49

22500

--

PBT

0

0.39

12400

15d

PBT/TMMT

1

0.36

PTT

0

0.4

15900

15c

PTT/TMMT

2

0.42

16800

15c

UPR

0

--

1800

13

19


21

17000

15a 15a

15d


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Table 4. Polyester and polyester nanocomposite molecular weight synthesized via fuzzy logic temperature control Samples

Clay Conc. (%)

[η] (dL/g)

Mn (gmol-1)

PET

0

0.55

24000

PET/TMMT

1

0.53

22500

PETG

0

0.45

18100

PETG/TMMT

1

0.56

24300

PETNa

0

0.53

23500

PETNa/TMMT

1

0.55

23900

PBT

0

0.75

23200

PBT/TMMT

1

0.66

20500

PTT

0

0.42

17000

PTT/TMMT

2

0.43

17200

UPR

0

--

2600

20


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Table 5. The d001 of polyester nanocomposites synthesized via PID temperature control Samples

Clay Conc. (%)

2θ(°)*

d-spacing(Å)

∆d

Ref.

TMMT

--

4.4

19.53

--

15d

PET/TMMT

1

2.1

40.93

21.4

21

PETG/TMMT

1

2.2

39.06

19.53

15a

PETNa/TMMT

1

2.5

34.38

14.85

--

PBT/TMMT

1

2.4

35.81

16.28

15d

PTT/TMMT

2

1.98

43.4

23.87

15c

* Dominant Peak

21



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Table 6. The d001 of polyester nanocomposites synthesized via fuzzy logic temperature control Samples

Clay Conc. (%)

2θ(°)

d-spacing(Å)

∆d

TMMT

--

4.4

19.53

--

PET/TMMT

1

2.00

42.97

23.44

PETG/TMMT

1

1.96

43.85

24.32

PETNa/TMMT

1

1.96

43.85

24.32

PBT/TMMT

1

2.3

37.36

17.83

PTT/TMMT

2

1.35

64.13

44.6

22


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For Table of Contents Only

23


Fuzzy Optimization Approach for the Synthesis of Polyesters and Their

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