Fuzzy Optimization Approach for the Synthesis of Polyesters and

Article pubs.acs.org/IECR

Fuzzy Optimization Approach for the Synthesis of Polyesters and Their Nanocomposites in In-Situ Polycondensation Reactors Zahedi Ali Reza*,† and Rafizadeh Mehdi‡ †

School of New Technologies, Iran University of Science and Technology, Tehran, Iran Department of Polymer Engineering & Color Technology, Amirkabir University of Technology, Tehran, Iran

‡

ABSTRACT: A proportional-derivative (PD) fuzzy controller was presented to control the temperature of a polycondensation reactor. Synthesis of various polyesters and copolyesters were conducted using the devised controller. This controller uses reactor temperature error as well as its derivative. The desired jacket temperature had an uncertainty that was affected by noise and disturbance. This uncertainty was modeled using fuzzy numbers, and a fuzzy trajectory was achieved for the desired reactor temperature. Then, a generalized Takagi−Sugeno (GTS) fuzzy controller was designed. An adaptation algorithm was included in the controller. Compared to that of conventional proportional-integral-derivative (PID) controllers, experimental results presented a very good performance to control the 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 which could completely degrade the polymer. However, the fuzzy PD controller had no overshoot. The performance of the fuzzy PD controller to control a suitable temperature of the reactor was excellent with 0.2% accuracy without overshoot. The NMR results confirmed that the final polymers have been synthesized successfully. Moreover, the molecular weights of the samples, synthesized under fuzzy control, were generally higher and there was a better intercalation structure in such samples.

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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 results.7 As well, they progressed an experimental model as a process model in the control section. With the development of fuzzy logic theories by Zadeh8 and the emergence of successful control by Mamdani,9 fuzzy control has become 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 the past 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 a similar work, Asua et al.12 introduced a fuzzy system for optimizing the conditions of emulsion polymerization reaction; they also 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

INTRODUCTION In a polymerization reactor, monomers react to produce a certain high molecular weight polymer. To achieve desired final properties, process conditions during the polymerization must be well-controlled. On the other hand, 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 preplanned pattern. Polyester synthesis typically involves a premixing of required reactants (paste mixing) step, esterification among acid and hydroxyl groups, and a 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 the properties of the final product.2 The control of a 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 and it controlled monomer conversion successfully. In other works, Soroush and Kravaris4 and Muta et al.5 proposed a predictive controller based on a nonlinear model using a © 2017 American Chemical Society

Received: Revised: Accepted: Published: 11245

June 5, 2017 August 26, 2017 August 26, 2017 August 26, 2017 DOI: 10.1021/acs.iecr.7b02307 Ind. Eng. Chem. Res. 2017, 56, 11245−11256

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Industrial & Engineering Chemistry Research temperature of the polyester synthesis reactor. A PID controller, which was designed on the basis of an empirical model of reaction, was tuned on the basis of 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 microscale 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(1,3propanediol terephthalate) (PTT), and poly(bis(hydroxyethyl) terephthalate-co- maleic anhydride) (UPR).

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EXPERIMENTAL SECTION Materials. Terephthalic acid (TPA) and ethylene glycol (EG) were supplied by Shahid Toundgoyan Petrochemical Complex (Mahshahr, Iran). 1,3-Propanediol (PDO), 1,4-butanediol (BDO), was purchased from AppliChem GmbH (Darmstadt, Germany). 1,4-Cyclohexane dimethanol (CHDM) as comonomer of PETG and sodium 5-sulfoisophthalate acid (NaSIPA) as comonomer of PETNa were 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, o-dichlorobenzene, dichloroacetic, and 1,1,2,2,tetrachloroethane as solvents for intrinsic viscosity measurement were prepared from Merck Co (Darmstadt, Germany). For NMR spectrum, trifluoroacetic 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 (organically modified montmorillonite, OMMT) was purchased from Southern Clay Products (Gonzales, USA). 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 the polyesters and their nanocomposites were measured by dissolving them in a suitable solvent and using the Ubbelohde viscometer at 25 °C ± 0.1. 1H- and 13C NMR spectra were recorded on a Bruker DPX-500 Avance spectrometer operated at 500 MHz and 25 °C. Samples were dissolved in CHCl3, and a small amount of CDCl3 was added to lock the spectrometer; the spectra were internally referenced to tetramethylsilane. X-ray diffraction (XRD) profiles were recorded using aX’Pert MPD model (tube voltage, 40 kV, and tube current, 30 mA) with a monochromatic Co Kα radiation (λ = 1.789 Å). Samples were scanned from 2θ = 2° to 10° at a scanning rate of 1°/min using a reflection mode. Synthesis Setup. An overview of the reactor control system used and its accessories is shown in Figure 1, schematically. Three PT100 temperature sensors with an 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). A two-blade type mixer was used to mix a high viscous reactive mixture containing a 1500 W 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 the vacuum line. Sealing of the applied top reactor could tolerate 50 atm.

Figure 1. Schematic of the reactor.

The vacuum was created by a JB-85N-250 vacuum pump from FastVac Company (USA). Two chilled traps, in series, cooled in an isopropyl alcohol bath at −30 °C, 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. An I/O card model USB-4711A from AdvanTech (USA) was used for computer interfacing. An injection system was manufactured to add nanoclay during the polycondensation. Synthesis Procedure. Modification of OMMT. Like our previous work,14 the organoclay could be modified. Briefly, after drying nanoclay in a vacuum oven at 60 °C, 1 g of OMMT was added to 25 mL of ethanol/APS (95/5, v/v) and the mixture was refluxed for 6 h. Then the mixture was washed continuously by ethanol/deionized water (75/25, v/v) and finally was dried at 60 °C 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 premixed.14,15 In these experiments, the mixture was charged into the stirred reactor. Table 1 shows the reaction and process conditions of polyesters, copolyesters, and the synthesis of their nanocomposites. According to the table data, in all cases, the synthesis was carried out based on the following stages: 1. Paste mixing. The reactants are mixed at a given temperature and time as shown in Table 1. 2. Esterification. The temperature is brought to over 230 °C dependent on the product and pressures up to 3.5 bar until the water production stops. For synthesis of the polyester nanocomposites, nanoclay was sonicated in EG for an hour and added to the mixture after the pressure reached 1 bar. The mixing was continued for 30 min for better dispersion. 3. Polycondensation. 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 byproduct of the polycondensation reaction was removed over 3 hours by a vacuum pump. Finally, the pressure was adjusted to atmospheric pressure, and all materials were evacuated by nitrogen pressure. 11246

DOI: 10.1021/acs.iecr.7b02307 Ind. Eng. Chem. Res. 2017, 56, 11245−11256

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Industrial & Engineering Chemistry Research Table 1. Synthesis Conditions of Polyesters, Copolyesters, and Their Nanocompositesa

a

product

diol

diacid

catalyst

PET PETG PETNa PBT PTT UPR PET PETG PETNa PBT PTT

EG EG EG BDO PDO BHET EG EG EG BDO PDO

TPA TPA TPA TPA TPA MA TPA TPA TPA TPA TPA

ATO ATO ATO TBT TBT ATO ATO ATO TBT TBT

comonomer CHDM NaSIPA

CHDM NaSIPA

paste (°C/min)

ester. (°C)

polycond. (°C/min)

90/30 90/30 90/30 45−90/30 90/30 50/60 90/30 90/30 90/30 45−90/30 90/30

240 240 240 245 230 160 240 240 240 245 230

280/180 280/180 280/180 260/180 260/240 190/300 280/180 280/180 280/180 260/180 260/240

TMMT(%)

ref 21 15a

1 1 1 1 2

15d 15d 13 21 15a 15d 15d

Synthesis steps: paste; (ester.) esterification; (polycond) polycondensation.

Fuzzy Trajectory Idea. Clearly, the presented fuzzy controller uses the reactor temperature and its derivative. In addition to the reactor temperature error, a derivative of the temperature error is considered in order to avoid the instability that comes from a long delay time of heat transfer to the inside of the reactor. Also, this parameter could be helpful in making the reactor dynamic and faster in performance. Therefore, the error of reactor temperature is described as ereactor = Td,reactor − Treactor

Two significant methods to subtract two fuzzy numbers are the extension principle and α-cuts or intervals arithmetic. If Ã and B̃ are two fuzzy numbers, on the basis of the extension principle, Ã − B̃ fuzzy number is defined as μ Ã − B̃(z) = sup{T(μ Ã (x), μ B̃(y))|z = x − y}

(4)

where T is a T-norm. In the α-cuts method, α(Ã − B̃ ) is defined as

(1)

α

(Ã − B)̃ = α Ã − α B̃

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, generalized numbers and intervals could make a fuzzy number (Ñ ) which was a fuzzy set depend on a real numbers set (ℜ).16 Also, Ñ must examine as a normal fuzzy set (hgt(Ñ ) = supx ∈ℜ μ Ñ (x) = 1) and for ∀α ∈ (0,1], αÑ must be a closed interval and the support of Ñ (= 0+Ñ ) that should be bounded. Hence, any fuzzy number is a convex fuzzy set; however, the inverse relationship is not necessarily true. Figure 2

(5)

where the difference between [x,y] and [x′,y′] intervals is defined as [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 uniquely.16 Moreover, if singleton fuzzification is used, these two methods have the same result. Figure 3 shows the block diagram of the proposed controller with no adaptation mechanism. The fuzzy controller in this

Figure 3. Block diagram of proposed fuzzy controller. Figure 2. Desired jacket temperature as a fuzzy number.

research uses reactor temperature error, ereactor, and its derivative, ėreactor, as inputs, and power applied to the heater as output. An approach for fuzzy control of systems is developed by Takagi and Sugeno17 based on system linearization in some points. A Takagi−Sugeno fuzzy controller consists of NR fuzzy rules as follows:

illustrates the fuzzy trajectory idea of reactor temperature. In Figure 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 the α parameter being assumed constant during polymerization. In this experiment, the sampling time was one second and the parameters of the reactor temperature fuzzy number are a = 0.5 °C; b = 0.5 °C and α = 0.3 °C. To calculate the derivative of the temperature error, a fuzzy subtraction should be used as follows.

ereactor = Tn − Tn − 5 ̇

R j: if x1 is Ã(j) and ... and xn is Ã n(j) then u = ajT X + bj(1 ≤ j ≤ NR )

(8)

where X = [x1, x2, ..., xn] is known as a system state vector, Ã (j) i (1 ≤ i ≤ n,1 ≤ j ≤ NR) are fuzzy sets defined on a system case, u is the controller output, and in the equation aj and bj are constants. T

(3) 11247


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

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 N

∑ j =R1 w(j)(ajT X* + bj)

u* =

N ∑ j =R 1 w(j)

tv(X̃ ≤ Ã ) = sup{T(μ X̃ (x), μ Ã (a))|x ≤ a}

(15)

tv(X̃ ≥ Ã ) = sup{T(μ X̃ (x), μ Ã (a))|x ≥ a}

(16)

By substituting eqs 15 and 16 in eq 14 the following equation is derived:

(9)

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

tv(X̃ is Ã ) = T(sup{T (μ X̃ (x), μ Ã (a))|x ≤ a} sup{T(μ X̃ (x), μ Ã (a))|x ≥ a}

n (j)

w = ∏ μ Ã (j)xn* i

i=1

(17)

If X̃ is a generalized fuzzy number and Ã is a fuzzy pseudonumber, according to the definition of eq 17 then the true value of (X̃ is Ã ) will be equal to the height of X̃ ↓∩ Ã . In the other words:

(10)

Here, the fuzzy controller inputs were fuzzy numbers. The fuzzy set X̃ on ℜ is a generalized fuzzy number if Core(X̃ ) ≠ ⌀ and also ∀α and αX̃ are a closed interval. The usefulness of this definition despite the classical definition of fuzzy numbers16 is the inclusion of Gaussian fuzzification of crisp numbers or other methods of fuzzification that leads to fuzzy sets with plenty of benefits. A set of all generalized fuzzy numbers has been provided by ℜ̃G . On the other hand, the fuzzy set Ã on ℜ is a fuzzy pseudonumber if Core(Ã ) ≠ ⌀ and ∀α ∈ (0,1], αÃ is a closed interval or ∀α ∈ (0,1], αÃ is a semiopened interval. Therefore, saturated fuzzy sets used in the fuzzy rule are fuzzy pseudonumbers. These fuzzy sets are considered as linguistic variables and are presented by ℜ̃P . Assume that a fuzzy controller consists of NR fuzzy rules as follows:

tv(X̃ is Ã ) = hgt(X̃ ∩ Ã )

(18)

If X̃ is a singleton fuzzy number, it could be written: ⎧ 1 x = x* μ X ̃ (x )= ⎨ ⎩ 0 x ≠ x* ⎪

⎪

(19)

and Ã is a fuzzy pseudonumber, then: tv(X̃ is Ã ) = μ Ã (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

R j: if X1̃ is A1̃ (j) and ... and X̃ n is Ã n(j)

i=1

then u = c(j)

w(j) = T hgt(X̃i ∩ Ã i(j))

(11)

(21)

n

where X̃ 1, X̃ 2, ..., and X̃ n are generalized fuzzy numbers as the inputs of the controller, Ã (j) i (1 ≤ i ≤ n, 1 ≤ j ≤ NR) fuzzy sets are fuzzy pseudonumbers defined on inputs of the system, u is the controller output, and c(j) represents constants. The inference mechanism is similar to Takagi−Sugeno fuzzy controller inference mechanism as follows:

ereactor and ėreactor are inputs of the proposed fuzzy controller. Rule base of this controller includes rules with the general form ̃ then u = c(j) if ereactor is R̃ (j) and ereactor is J (j) ̇

(22)

Then the controller output is N

N

u=

∑ j =R 1 w(j)c(j) N ∑ j =R 1 w(j)

u= (12)

∑ j =R 1 w(j)c(j) N

∑ j =R 1 w(j)

(23)

(j)

where w could be calculated as follows: The calculations of antecedent satisfaction are the main difference as follows:

w(j) = tv[(ereactor is R̃ (j)) and (ereactor is J (̃ j) )] ̇ = T[(tvreactor is R̃ (j)), tv(ereactor is J (̃ j) )] ̇

w(j) = tv(X1̃ is A1̃ (j) and ... and X̃ n is Ã n(j)) i=1

= T tv(X̃i is n

Ã n(j))

= T[μ Ã(j)(ereactor , hgt(ereactor ∩ J (̃ j) )] ̇

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

(13)

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

w(j) = μ Ã(j)(ereactor)hgt(ereactor ∩ J (̃ j) ) ̇

(25)

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

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RESULTS AND DISCUSSION The Reactor Dynamics and Controller Design. To study the dynamic behavior of the process, an input step was utilized by a heater (200 W) at t = 0, and the reactor and jacket temperatures

tv(X̃ is Ã ) = tv(X̃ ≈ Ã ) = T(tv(X̃ ≤ Ã ), tv(X̃ ≥ Ã ))

(24)

(14) 11248


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Figure 4. Reactor temperature step response.

Figure 5. Performance of PI controller for reactor temperature.

where kp, T ,and Td are the gain, time constant, and dead time, respectively. The numerical values of parameters were determined by the curve fitting method. The area between step responses (ABC method19) of experimental data and transfer function was minimized (see Figure 4). This minimization was performed based on the Nelder−Mead method.20 However, the

were recorded, simultaneously. Figure 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 is as follows: G̃(s) =

kpe−Td Ts + 1

(26) 11249


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Figure 6. Diagram of command to the heater: (a) general view, (b) magnification view.

numerical values are kp = 239.55,

T = 5259.40,

controller, the calculated parameters are Td = 19.37

kc = 1.0206,

(27)

τI = 0.640559

(28)

and similarly, for the PID controller:

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 the PI

kc = 1.5124,

τI = 47.60,

τD = 7.04

(29)

Figure 5 shows the typical behavior of a PI controller for the synthesis of PET. In this experiment, the reference temperature 11250


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Figure 7. Performance of PID controller for reactor temperature.

Figure 8. Fuzzy sets defined on temperature error.

is 240 °C. Although the PI controller finally controlled the temperature with an accuracy of ±6 °C, the temperature overshoot was around 50 °C, which can completely degrade the polymer due to uncontrollable and high temperatures (around 290 °C). A small sampling time (one second) caused a thick curve as shown in Figure 6a. A closer look at the curve of Figure 6a could be seen in Figure 6b. Also Figure 7 shows the results for the PID controller application. It is observed that the controlled variable has the presence of offset integral action despite the controller structure. The long delay of heat transfer from the heater and 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 led to an increase of temperature up to 280 °C, which is not a suitable temperature. The behavior of other aromatic polyesters studied in this report were controlled similarly to that of PET as the most commercial aromatic polyesters. Therefore, the graphs of PET were only shown in brief. 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 Figure 8 and Figure 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 11251


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Figure 9. Fuzzy sets defined on the derivative of temperature error.

Table 2. Interface linguistic rulesa ereactor ėreactor

PB

PM

PS

Z

NS

NM

NB

NVB

NVB NB NS Z PS PB PVB

NB2B NV2B NV2B NV2B NVB NGB NVS

NV2B NV2B NV2B NGB NM NVS PS

NV2B NB NGB NS PS PS PV3B

NV2B NB Z PS PM PB PV6B

NV2B NGB PVS PGB PVB PV2B PV6B

NV2B NM PM PVB PV3B PV5B PV6B

NB Z PVB PV3B PV5B PV6B PV6B

NS PVS PV4B PV5B PV6B PV6B PV6B

a

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

Figure 10. Fuzzy controller performance at 200 °C. 11252


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Figure 11. Reactor temperature during the polymerization.

Figure 12. Jacket temperature during the polymerization.

inference engine is based on the T-norm defined by Zadeh8 as follows:

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

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 s. 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.

(30)

The error and its derivative are fuzzified in this controller and unified to the fuzzy inference engine. The fuzzy inference engine 11253


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Figure 13. Heat applied to the reactor.

This control system can handle the reactor temperature from 200 to 300 °C with high-precision. Figure 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 Figure 11 shows the reactor temperature controlled using the fuzzy controller. As seen in Figure 11, the fuzzy controller was very successful in controlling the reactor temperature in all three stages of paste mixing, esterification, and polycondensation. The esterification reaction is partially exothermic, and the polycondensation reaction is moderately endothermic. Moreover, in the case of in situ polymerization systems, a 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 also be able to control the temperature under disturbance. Figure 12 shows the jacket temperature during the polymerization. The applied heat during the reaction is shown in Figure 13. The intrinsic viscosities obtained from the polyesters synthesized via PID 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.

Table 3. Polyester and Polyester Nanocomposite Molecular Weight Synthesized via PID Temperature Control samples

clay concn (%)

[η] (dL/g)

Mn (g mol−1)

ref

PET PET/TMMT PETG PETG/TMMT PETNa PETNa/TMMT PBT PBT/TMMT PTT PTT/TMMT UPR

0 1 0 1 0 1 0 1 0 2 0

0.28 0.35 0.43 0.52 0.47 0.49 0.39 0.36 0.4 0.42

2800

21 21 15a 15a

17000 21900 22500 12400

15d 15d 15c 15c 13

15900 16800 1800

Table 4. Polyester and Polyester Nanocomposite Molecular Weight Synthesized via Fuzzy Logic Temperature Control

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samples

clay concn (%)

[η] (dL/g)

Mn (g mol−1)

PET PET/TMMT PETG PETG/TMMT PETNa PETNa/TMMT PBT PBT/TMMT PTT PTT/TMMT UPR

0 1 0 1 0 1 0 1 0 2 0

0.55 0.53 0.45 0.56 0.53 0.55 0.75 0.66 0.42 0.43

24000 22500 18100 24300 23500 23900 23200 20500 17000 17200 2600



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Table 5. D001 of Polyester Nanocomposites Synthesized via PID Temperature Control samples TMMT PET/TMMT PETG/TMMT PETNa/TMMT PBT/TMMT PTT/TMMT a

clay concn (%)

2θ (deg)a

D-Spacing (Å)

1 1 1 1 2

4.4 2.1 2.2 2.5 2.4 1.98

19.53 40.93 39.06 34.38 35.81 43.4

Δd 21.4 19.53 14.85 16.28 23.87

ref

15d 15c

Dominant peak.

Table 6. D001 of Polyester Nanocomposites Synthesized via Fuzzy Logic Temperature Control clay concn (%)

2θ (deg)

d-spacing (Å)

Δd

TMMT PET/TMMT PETG/TMMT PETNa/TMMT PBT/TMMT PTT/TMMT

1 1 1 1 2

4.4 2.00 1.96 1.96 2.3 1.35

19.53 42.97 43.85 43.85 37.36 64.13

23.44 24.32 24.32 17.83 44.6

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CONCLUSIONS Polyesters and copolyesters, as well as their nanocomposites, were synthesized in a homemade reactor. The process was performed in three stages, premixing around 40−90 °C, 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. A control setting via the Cohen−Cohn method was obtained, but the PI and PID controllers were unsuccessful. Although the PI controller finally controlled the temperature with an accuracy of ±6 °C, the temperature overshoot was around 50 °C, which can completely degrade the polymer. The PID controller performance indicated that the temperature was controlled with the accuracy of ±4 °C, and the temperature overshoot was about 40 °C. Efforts to improve reactor performance were not successful and led to an increase of temperature up to 300 °C. Fuzzy logic was applied to control the reactor temperature. Its result shows a 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 d-spacing of organoclay in both systems and there is a better intercalation structure in samples synthesized through fuzzy logic control.

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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. Polym. React. Eng. 2002, 10 (3), 121−133. (3) Tzouanas, V. K.; Shah, S. L. Adaptive pole-assignment control of a batch polymerization reactor. Chem. Eng. Sci. 1989, 44 (5), 1183−1193. (4) Soroush, M.; Kravaris, C. Nonlinear control of a batch polymerization reactor: An experimental study. AIChE J. 1992, 38 (9), 1429−1448. (5) Mutha, R. K.; Cluett, W. R.; Penlidis, A. On-Line Nonlinear ModelBased Estimation and Control of a Polymer Reactor. AIChE J. 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 J. 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. Proc. Inst. Electr. Eng. 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. J. 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. Chem. Eng. Res. Des. 2014, 92 (5), 903− 916. (e) Gao, S.-z.; Wang, J.-s.; Zhao, N. Fault diagnosis method of polymerization kettle equipment based on rough sets and BP neural network. Math. Probl. Eng. 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. J. Taiwan Inst. Chem. Eng. 2014, 45 (5), 2246−2257. (g) Ç etinkaya, S.; Zeybek, Z.; Hapoğlu, H.; Alpbaz, M. Optimal temperature control in a batch polymerization reactor using fuzzyrelational models-dynamics matrix control. Comput. Chem. Eng. 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. Polym.-Plast. Technol. Eng. 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. Chem. Eng. Sci. 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). Polym. Int. 2009, 58 (9), 1084−1091. (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 Perform. Polym. 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). J. Appl. Polym. Sci. 2009, 113 (6), 3520−3532. (b) Shirali, H.;

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Zahedi Ali Reza: 0000-0001-5451-9666 Notes

The authors declare no competing financial interest. 11255


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Industrial & Engineering Chemistry Research 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. J. Compos. Mater. 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. J. Thermoplast. Compos. Mater. 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 succinateco-fumarate) copolymer networks synthesized by polycondensation of pre-homopolyesters. 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.

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Fuzzy Optimization Approach for the Synthesis of Polyesters and

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