Optimization-Based Control Strategy with Wavelet ... - ACS Publications

Subscriber access provided by University of Florida | Smathers Libraries

Article

Optimization-based Control Strategy with Wavelet Network Input-Output Linearizing Constraint for an Ill-Conditioned High-Purity Distillation Column Pichak Tanakunmas, Chanin Panjapornpon, ATTHASIT TAWAI, and Tanawadee Dechakupt Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01135 • Publication Date (Web): 11 Jul 2017 Downloaded from http://pubs.acs.org on July 21, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

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.

Page 1 of 45

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

Industrial & Engineering Chemistry Research

Optimization-based Control Strategy with Wavelet Network Input-Output Linearizing Constraint for an Ill-Conditioned High-Purity Distillation Column Pichak Tanakunmas,†, ‡ Chanin Panjapornpon,*, †, ‡ Atthasit Tawai,§ and Tanawadee Dechakupt** †

Department of Chemical Engineering, Center of Excellence on Petrochemicals and Materials

Technology, Faculty of Engineering, Kasetsart University, Bangkok 10900, Thailand ‡

The Center for Advanced Studies in Industrial Technology, Kasetsart University, Bangkok

10900, Thailand §

Department of Mechanical and Process Engineering, The Sirindhorn International Thai-German

Graduate School of Engineering, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand **

Department of Industrial Chemistry, Faculty of Applied Science, King Mongkut’s University

of Technology North Bangkok, Bangkok 10800, Thailand July 7, 2017 Submitted for Publication in I&EC Research *

Corresponding author: Tel: +66 2 797 0999/1230; fax: +66 2 561 4621. E-mail: [email protected] (C. Panjapornpon)

ACS Paragon Plus Environment

1


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

Page 2 of 45

ABSTRACT

A new nonlinear optimization control strategy is developed for multivariable control of an illconditioned, high-purity distillation column. A high-gain directional effect resulting from illconditioned nature of the system causes difficulty in controllability and requires a higher performance control system. The developed optimal controller applies a minimization of energy consumption as the optimal objective function to treat ill-conditioning effect, while wavelet neural network input/output linearizing constraints force the outputs to reach the desired set points. In this paper, ethylene dichloride purification is used as a case study. The process dynamics are evaluated based on relevant thermodynamic properties in Aspen Plus Dynamics and are controlled by the proposed controller in the MATLAB/Simulink platform. Control performances are investigated in this co-simulation environment for set point tracking and regulatory problems. The simulation results demonstrate that robust tracking is attained, while compensation of the input disturbances is effectively improved compared with a model predictive controller.

KEYWORDS: Nonlinear optimization-based control; High-purity distillation column; Ethylene dichloride distillation; Input-output linearization; Wavelet neural network model


2

Page 3 of 45

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


1. INTRODUCTION Control of a high-purity distillation column is a well-known problem in controller design due to the inherently nonlinear behavior. The nonlinear behavior is mainly caused by the presence of a large number of stages and the internal material flow which exists so as to increase the product purification. A multivariable system with an ill-conditioning nature influences the behavior of the distillation column.

The closed-loop stability of the system is significantly affected by

disturbances (e.g., upsets in the feed flow or feed composition), particularly in the case of the high process gains by which the inputs are strongly amplified. Although there are many studies on the control of distillation columns, they focus only on columns of low to moderate purity.1–6 Multivariable control with a single-input, single-output (SISO) control structure was typically applied. Such control techniques may be not applicable for a high-purity distillation column that exhibits ill conditioning.7–9 Thus, an effective control strategy that provides strong robustness so as to achieve the desired high-purity product is needed. In recent years, investigation into optimal control for improving the controllability and operability of the high-purity distillation column has been reported.1,8,10–20 Model predictive control (MPC) is one of the successful implementations of needed control strategy. A model described as an ordinary differential equation,10,11,20 a transfer function, or a state-space model12– 14

is typically used in the controller formulation. However, the physical-based models have some

practical drawbacks. A large number of equations for increasing model precision results in a burdensome computational load. Accordingly, an approach of MPC formulation by a nonlinear neural network model has received more attention.1,8,15 In a development of the nonlinear MPC for a binary distillation system, Shaw and Doyle8 applied a multi-input, multi-output (MIMO), recurrent dynamic neural network model. This nonlinear MPC achieves robust closed-loop


3


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

Page 4 of 45

performance, but it requires a complex model to consider input/output interactions. Ou and Rhinehart1 applied a terminal cost constraint MPC for dual composition control of a laboratoryscale distillation column by using a grouped neural network model to express the relation between input-output pairs. Waller and Böling15, meanwhile, proposed a quasi-autoregressivemoving-average model with exogenous input (ARMAX) for the dual composition control of an ill-conditioned distillation column. A nonlinear autoregressive exogenous (NARX) model is an attractive neural model of the time series type that provides more flexibility to capture the nonlinear process behavior using various supporting nonlinear estimators such as sigmoid, neural, tree-partitioning and wavelet networks. Sriniwas et al.16 proposed a one-step-ahead-prediction nonlinear MPC with a multi-input, singleoutput, wavelet NARX (WNARX) model in a polynomial form for dual composition control. The wavelet structure has drawn much interest due to fast convergence and remarkably good prediction.16,17 Following on Sriniwas et al.,16 Nazaruddin and Cahyadi17 applied a seriesparallel WNARX model to an adaptive global predictive controller. Despite there being much literature on neural-based MPC for a high-purity distillation column, there is little work addressing the ill-conditioned problem and/or the influence of the feed disturbances. The MPC may give the minimal solution based on the optimization, but it does not guarantee the closedloop stability at the desired set point due to the input/output gain effect of the ill-conditioned process. Also, there is some concern about the tuning parameter selection of MPC for stabilizing the closed-loop system with a large set of state variables. In this study, a new optimal control strategy for a high-purity distillation column is proposed by combining the advantages of input/output (I/O) linearization with a WNARX model. The control objective is to minimize energy consumption of the column subject to the constraints of


4

Page 5 of 45

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


the closed-loop output tracking formulated by the WNARX-based I/O linearization. Performance of the proposed method of control is evaluated through servo and regulatory tests and compared with proportional-integral (PI) and MPC controllers using the co-simulation environments of ASPEN Plus Dynamics® (Aspentech, Inc.) and MATLAB/SIMULINK software (Mathworks, Inc.); with a high-purity ethylene dichloride (EDC) distillation column being used as a case study. The paper is structured as follows. The development of the WNARX-based optimal controller with I/O linearizing constraints is explained in Section 2, followed by a description of a highpurity EDC distillation column in Section 3. The modeling of the EDC distillation column is presented in Section 4, followed by the implementation of the control system in Section 5. The servo and regulatory tests to demonstrate the control performance are given in Section 6. 2. DEVELOPMENT OF NONLINEAR OPTIMAL CONTROL STRATEGY 2.1 Wavelet-Nonlinear Autoregressive Exogenous Model In this study, a feedforward WNARX network for one-step-ahead prediction is applied for estimating output dynamics and developing a nonlinear optimization function. Its structure is simple and suitable for I/O linearization. The wavelet structure provides a fast convergence with the data training and has fewer nodes, compared to other nonlinear estimators achieving the same approximation quality. A simple block diagram of the network is shown in Figure 1.


5


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

Page 6 of 45

Figure 1. A feedforward WNARX model structure for one-step-ahead output prediction. The network consists of hidden and output layers with a series-parallel structure. The sets of inputs, outputs, and measured disturbances are fed to tapped delay lines (TDL) in the hidden layer and mapped as regressor variables for the wavelet network function. The wavelet network outputs can be expressed by following equations: yˆ (k + 1) = yˆ l + yˆ nl yˆl = (θ − R ) ⋅ P ⋅ L + D

(1)

yˆ nl = as ⋅ F [ bs ⋅ (θ − R ) ⋅ Q − cs ] + aw ⋅ G [ bw ⋅ (θ − R ) ⋅ Q − cw ] where yˆ (k + 1) is the vector of one-step-ahead predicted outputs; yˆl , yˆ nl are the vectors of linear and nonlinear estimators; θ is the memory vector of regressors defined by θ = [ y (k ),..., y(k − ny ),

u(k ),..., u(k − nu ), d (k ),..., d (k − nd )] ; u(k), y(k) and d(k) are the vectors of input, output and disturbance variables, respectively; nu , n y and nd are the lags of input, output and disturbance;


6

Page 7 of 45

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


R is the mean value of the regressor vector; P and Q are the matrices of linear and nonlinear subspace parameters; L is the vector of linear term coefficients in the wavelet function; D is the vector of output offsets; as , bs and c s are the scaling coefficients; aw , bw and cw are the wavelet coefficients; F [φ ] and G [φ ] are the scaling and wavelet functions. This latter two are defined as follows:

F [φ ] = e−0.5φ ⋅φ

T

G [φ ] = (nr − φ ⋅ φ T )e −0.5φ ⋅φ

(2)

T

where T is a transpose operator and nr is the number of regressors. In order to simplify presentation, the WNARX model in eq 1 can be rewritten in a compact form as follows:

yˆ (k + 1) = fˆ  y ( k ) ; u ( k ) ; d ( k )  yˆ (k + 1) = fˆ [ y(k ),..., y(k − ny ), u (k ),..., u(k − nu ), d (k ),..., d (k − nd )]

(3)

where fˆ is the nonlinear function. The vectors y(k), u(k) and d(k) denote the output, input, and disturbance regressor, respectively.

2.2 Nonlinear Optimization Strategy Input-output (I/O) linearization is a nonlinear control technique that algebraically transforms nonlinear system dynamics into linear ones.

It has been widely applied to many control

problems due to the use of few tuning parameters and a guarantee of closed-loop stability. A control strategy that uses MPC together with I/O linearization was also reported by Soroush and colleagues21–23, but there are several differences in the controller formulation compared with this proposed method. The control method of Soroush and colleagues 21–23 integrates an analytical controller such an I/O linearization in the MPC formulation, for which a physical model is


7


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

Page 8 of 45

applied in the control formulation and for which the objective is to minimize the squared error of the requesting output responses and their set points. In contrast, the control method proposed in this work is formulated as an optimization of energy consumption with the closed-loop I/O linearizing response treated as the constraint. For application to high-purity distillation, the process gains for some input-output pairs are relatively very small compared with other pairs due to the ill-conditioning of the system. With the ill-conditioning of the distillation model, the control formulations in21–23 become non-convex optimization problems. The obtained control actions may be not possible to achieve the desired requesting responses. The proposed method does not have such a difficulty because the solution should satisfy the tracking constraint. To further develop the proposed controller, let requesting closed-loop linear responses of the outputs with their relative orders equal to 1 in discrete-time form be as follows:

 y (k + 1) − y (k )   + y (k ) = v( k ) ∆t  

β

(4)

where y (k ) is the vector of current outputs, y (k + 1) is the vector of one-step-ahead future outputs, v is the vector of reference output set points, ∆t is a time interval and β is the vector of tuning parameters to set the speed of the output responses. For estimating the values of the future outputs, the WNARX model for one-step-ahead output prediction in eq 3 is applied. Thus, the I/O linearizing responses in eq 4 can be rewritten as  fˆ  y ( k ) ; u ( k ) ; d ( k )  − y ( k )   + y (k ) = v(k )   ∆t  

β

(5)

The proposed control method is derived as a nonlinear optimization problem for minimizing the energy consumption of the distillation column with the requesting linear responses in eq 5 posed as constraints. The following constrained optimization problem is solved at each time interval:


8

Page 9 of 45

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


min w% ⋅ u(k )

(6)

u (k )

Subject to

 f  y ( k ) ; u ( k ) ; d ( k )  − y (k )   + y ( k ) = v( k ) β  ˆ

 

∆t

 

yˆlb ≤ yˆ (k + 1) ≤ yûb ulb ≤ u (k ) ≤ uub where w% , {ulb , uub } and { yˆlb , yˆ ub } denote the vectors of the energy conversion factor, the lower bound of the manipulated inputs and upper bound of the predicted outputs, respectively. A WNARX-based compensator (see eq 7) is introduced into the control system to compensate the output offset from unmeasured disturbances and model mismatch:

 ∆t  η (k + 1) = fˆ  y ( k ) ; u ( k ) ; d ( k )  − 1 −  ( n(k ) − y (k ) ) β  y% (k ) = η (k ) ν = ysp − y (k ) + y% (k )

(7)

where y% , η are the vectors of the estimate outputs, ysp is the vector of the output set points, and

ν is the vector of compensated set points. A schematic diagram of the proposed control system, consisting of the WNARX-based optimal control with I/O linearizing constraint and the WNARX-based compensator, is illustrated in Figure 2.


9


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

Page 10 of 45

Figure 2. Schematic diagram of the proposed control system.

3. PROCESS DESCRIPTION OF THE ETHYLENE DICHLORIDE PURIFICATION COLUMN Ethylene dichloride (EDC) is a raw material used in the production of vinyl chloride monomer (VCM) and polyvinyl chloride (PVC) plastic.

A simple block flow diagram of a VCM

production is illustrated in Figure 3.

Figure 3. A block flow diagram of a VCM process.


10

Page 11 of 45

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


To produce VCM, high-purity EDC (>98% by weight) is fed into a cracking furnace at a temperature in the range of 400-500˚C and a pressure in the range of 6-35 atm. VCM formation can be expressed as the following endothermic reaction, with conversion yield of 50-60%:

C2 H 4Cl2 → C2 H 3Cl + HCl After formation, the cracked gas is subsequently fed to the quencher to reduce the temperature before separating VCM and HCl products. The recycled EDC, off-spec EDC and the EDC streams from oxychlorination and direct chlorination have to pass an EDC purification unit to separate the light ends and 1,1,2-trichloroethylene (TCE) from the purified EDC product. TCE is a byproduct of the direct chlorination that impacts the EDC conversion yield. Figure 4 shows a simple schematic of the EDC distillation. The coolant rate ( u1 = Fc ), reflux rate ( u2 = R ) and reboiler duty ( u3 = QB ) are the inputs, while the top column pressure (

y1 = P1 ), the EDC mole fraction of the top and bottom products ( y2 = xD , y3 = xB ) are the outputs. The EDC column parameters and nominal operating conditions are given in Table 1. Changes in the feed flow ( d1 = FF ) and feed composition ( d 2 = xF ) are the upsets which commonly found in the EDC distillation column. In this work, step disturbances in the feed flow and feed composition are employed since these disturbances frequently occur during the changes in the recycled rate of off-spec EDC and the production rates of oxychlorination and direct chlorination units.

The disturbances can also affect the internal mass dynamics and the

composition profile through the column resulting in the variation in product composition.


11


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

Page 12 of 45

Figure 4. A simple schematic of the EDC distillation column.


12

Page 13 of 45

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


Table 1. EDC Column Parameters and Nominal Operating Conditions

Parameter

Value

Column specifications Tray type

Sieve

Column diameter

2.3

m

Tray spacing

0.6

m

Weir height

0.03

m

Number of trays

37

stages

Feed tray

19

stages

Top column pressure

1.02

bar

Condenser temperature

87.84

o

Coolant outlet temperature

78.20

o

Coolant rate

58,000

kg/hr

Reboiler temperature

111.34

o

Reboiler heat duty

4. 0

GJ/hr

Distillate rate

18,420

kg/hr

EDC mole fraction of the top product

0.998

mole/mole

Bottom rate

9,300

kg/hr

EDC mole fraction of the bottom product

0.500

mole/mole

Reflux rate

20,517

kg/hr

Reflux ratio

1.11

Feed pressure

1.35

bar

Feed temperature

100.3

o

Feed rate

27,720

kg/hr

EDC mole fraction of the feed

0.84

mole/mole

Nominal operating conditions

C C

C

C


13


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

Page 14 of 45

4. MODELLING OF THE EDC DISTILLATION COLUMN Using ASPEN Plus®, a steady-state model of the EDC distillation column is developed based on the process description in Table 1. The column is modeled by RADFRAC Block with Redlich-Kwong chosen as the property method, and the column model is then exported to ASPEN Plus Dynamics® for a flow-driven simulation in which input/disturbance step changes are performed. The collected data as shown in Figures 5–7 (N=160,000 data points) were then used for developing the desired MIMO WNARX model using the MATLAB® System Identification Toolbox. To determine the model structure, the number of output lags (ny) is varied by trial-and-error approach, while both the numbers of input (nu) and disturbance (nd) lags are kept constant to a value of two. The value of two is the maximum time delay between input and output pairs (see Table S1) divided by time interval. Akaike Final Prediction Error (FPE) criterion is used to justify the optimal number of lags in the prediction outputs. The smaller FPE number, the more accurate is the model. The FPE equation can be described as follows:

 1 + Nd  N FPE = L f   1 − Nd   N

(8)

where L f is a weighted sum of squared error, N d is the number of estimated parameters in the model, and N is the total number of the data points.


14

Page 15 of 45

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


Figure 5. Training data sets of (a) top column pressure ( y1 ), (b) EDC mole fraction of the distillate product ( y2 ) and (c) EDC mole fraction of the bottom product ( y3 ).


15


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

Page 16 of 45

Figure 6. Training data sets of (a) coolant rate ( u1 ), (b) reflux rate ( u2 ) and (c) reboiler duty ( u3 ).


16

Page 17 of 45

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


Figure 7. Training data sets of (a) feed rate ( d1 ) and (b) EDC mole fraction of feed ( d2 ).


17


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

Page 18 of 45

Table 2 summarizes the FPE results of the ten cases of the trained (33) MIMO WNARX model. It is found that model Case 7 showing the smallest FPE value, is the most appropriate model for representing the EDC column dynamics in this study. Details of the model structure, its compact form and the model parameters can be found in Appendix A, Table S2 and the supporting data file of the Supporting Information, respectively.

For model validation, model

Case 7 is compared with the ASPEN dynamic model under the step inputs with a constant feed rate ( d1 =27720 kg/hr) and EDC feed fraction ( d2 =0.84), as shown in Figures 8 and 9. It is found that the prediction error is 5.17E-20, which corresponds to the FPE value of the selected model (cf. Table 2). The model Case 7 is used in the formulation of the control system studying in the next sections.

Table 2. Summary of the Akaike Final Prediction Error (FPE) for Ten Different Cases of the Trained WNARX Model

Case 1 2 3 4 5 6 7 8 9 10

yˆ1 (k + 1)

yˆ 2 ( k + 1)

yˆ3 (k + 1)

[n1,y1,n1,y2,n1,y3] [2, 0, 0] [2, 2, 2] [2, 0, 2] [2, 0, 2] [2, 0, 2] [2, 0, 4] [2, 0, 4] [4, 0, 4] [4, 0, 4] [4, 0, 4]

[n2,y1,n2,y2,n2,y3] [0, 2, 0] [2, 2, 2] [0, 2, 2] [0, 2, 0] [0, 2, 0] [0, 2, 0] [0, 2, 0] [0, 2, 0] [0, 4, 0] [0, 4, 0]

[n3,y1,n3,y2,n3,y3] [0, 0, 2] [2, 2, 2] [2, 2, 2] [2, 2, 2] [4, 2, 2] [4, 2, 2] [4, 1, 2] [4, 1, 4] [4, 1, 4] [4, 4, 4]

Nd 669 771 1061 995 813 839 1332 947 951 981

FPE 6.05E-20 5.71E-20 5.69E-20 5.86E-20 5.28E-20 5.23E-20 4.98E-20 5.27E-20 5.23E-20 5.23E-20


18

Page 19 of 45

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


Figure 8. Validation of the WNARX model: (a) top column pressure ( y1 ), (b) EDC mole fraction of the distillate product ( y2 ) and (c) EDC mole fraction of the bottom product ( y3 ).


19


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

Page 20 of 45

Figure 9. Inputs for model validation: (a) coolant rate ( u1 ), (b) reflux rate ( u2 ) and (c) reboiler heat duty ( u3 ).


20

Page 21 of 45

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


The high-purity EDC distillation column is a multivariate system with ill-conditioning. In Figures 8 and 9, the coolant flow and reboiler duty both affect the top column pressure, but in a different direction. The column pressure ( y1 ) is increased approximately 0.10 bar either by 3250 kg/hr decreasing in the coolant flow ( u1 ) or by 1.08 GJ/hr increasing in reboiler duty ( u3 ). The gain matrix of the system is nearly singular, resulting in a difficulty to design the controller for handling such effect.

5. IMPLEMENTATION OF THE HIGH-PURITY DISTILLATION CONTROL SYSTEM 5.1 Formulation of the WNARX-Based Nonlinear Optimization Function In the study, the high-purity EDC distillation column, the top column pressure, the distillate EDC fraction and bottom EDC fraction are regulated by adjusting the reboiler heat duty, coolant rate, and reflux rate, respectively. A formulated optimization problem to minimize the energy consumption of the high-purity EDC distillation column under the requesting output responses and input/output constraints is attained by applying the process model of eq 3 with the parameter configuration of Case 7 to the proposed method.

The following constrained optimization

problem is solved at each time interval: min

u1 ( k ),K,u3 ( k )

w%1 ⋅ u1 (k ) + w% 2 ⋅ u2 (k ) + w% 3 ⋅ u3 (k )

subject to

( ) β ( fˆ  y ( k ) ,K , y ( k − n ) , u ( k ) , u ( k − 1) , d ( k ) , d ( k − 1)  − y (k ) ) / ∆t + y (k ) = v (k ) β ( fˆ  y ( k ) ,K , y ( k − n ) , u ( k ) , u ( k − 1) , d ( k ) , d ( k − 1)  − y (k ) ) / ∆t + y (k ) = v (k ) β1 fˆ1  yi ( k ) ,K , yi ( k − n1, y ) , ui ( k ) , ui ( k − 1) , di ( k ) , di ( k − 1)  − y1 ( k ) / ∆t + y1 (k ) = v1 (k ) i

2

2

i

i

2, yi

i

i

i

i

2

2

3

3

i

i

3, yi

i

i

i

i

3

3

2

3

yî ,lb ≤ yî (k + 1) ≤ yî ,ub ui ,lb ≤ ui (k ) ≤ ui ,ub

i = 1, 2,3 (9)


21


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

Page 22 of 45

A compensator, described by eq 10, is applied to eliminate the offset from the process–model mismatch and process disturbances:  ∆t  ηi (k + 1) = fî  y ( k ) ; u ( k ) ; d ( k ) −  1 −  ( ni (k ) − yi ( k ) )  βi  y%i (k ) = ηi (k )

ν i = yi , sp − yi (k ) + y%i ( k )

(10) i = 1, 2,3

The parameters w%1 , w% 2 and w% 3 are the specified constant for converting the units of inputs to energy unit (GJ/hr). The values of conversion factors and tuning parameters of the proposed method are listed in Supporting Information (Table S3). 5.2 Simulation Environment One of the difficulties in controller design for complex chemical processes is the lack of an efficient tool for evaluating closed-loop performance. In this work, a co-simulation environment of Aspen Plus Dynamics and MATLAB/Simulink is introduced as a computing technique. Aspen Plus Dynamics is a comprehensive flowsheet simulating software that has a large chemical database, thermodynamic properties of relevant substances, and multiple built-in rigorous equipment models for studying dynamics and predicting the performance of complex processes. MATLAB/Simulink is a numerical computation program that has many functions allowing for complex calculation. Using the co-simulating environment that works via the AM Simulation block in Simulink, a system engineer can efficiently design and evaluate an advanced controller for complex chemical processes with process interaction and non-ideal system behaviors.


22

Page 23 of 45

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


Figure 10 and Figure S1 show diagrams of the co-simulation environment and its implementation in SIMULINK. The ASPEN dynamic model of the EDC distillation column, considered as a process, communicates with SIMULINK via the AM Simulation block. The algorithm of the proposed control system is implemented in the interpreted MATLAB function block, and a fmincon function is applied to solve the optimal control problem. Then, the obtained control action is fed back to the EDC distillation column dynamic model for a change in input.

Figure 10. Schematic diagram of the software environment for closed-loop simulation.

6. SIMULATION RESULTS Performances of the proposed method in closed-loop responses, set point tracking, and disturbance rejection tests are compared with those of MPC and PI controllers. MATLAB MPC toolbox is used for implementation of the MPC controller for which the dynamic model and optimization problem are defined as follows


23


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

x(k + 1) = Ax(k ) + Bu (k )

Page 24 of 45

(11)

y (k ) = Cx(k ) + Dd (k )

2   3 y   w i  ∑   y k + j + k − y k + j + ( 1 ) ( 1) ( )  i   j=0 s yj i      2  3  1 w∆u   2 i   min + ∆ u ( k + j k ) + ρ ε ∑  ∑ u i ε ∆u (k k),L, ∆u ((k +1 k),ε   i =1  j =0 s j      2    1 wiu    + ∑ s u ( ui (k + j k ) − ui (k + j k ) )     j =0 j   subject to

(12)

ulb ≤ u ≤ uub ylb ≤ y ≤ yub where A, B, C, and D are constant matrices; wu , w ∆ u , w y are the input, input rate, and output weights; ∆ u is the input rate; s y and su are the input and output scaling factors; and (k + j k ) denotes the predicted value for a time k+j when the time is k. The coefficient matrices of the linearized model (A, B, C, D) are obtained by using the Control Design Interface (CDI) in Aspen Custom ModelerTM. The tuning parameters of the proposed controller and the PI controller are selected according to the IMC tuning method, while the MPC tuning parameters are chosen by the Tuning Advisor available in the MPC Toolbox. Tuning parameters of the PI and MPC controllers are given in the Supporting Information (Tables S4 and S5). 6.1 Closed-loop Responses In the simulation, the process begins at the steady state: y1,0 = 1.06 bar, y2,0 = 0.998, y3,0 = 0.5. The set point of the distillate EDC fraction is changed to y2,sp = 0.99 at 5 hrs, while the set points of the top column pressure and bottom EDC fraction are kept at their initial conditions (y1,sp =


24

Page 25 of 45

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


1.06 bar and y3,sp = 0.5). The closed-loop responses of the outputs and the manipulated input profiles under the controllers are shown in Figures 11–14. The controller needs to reduce the reflux flow, coolant and reboiler duty to maintain the internal mass dynamics of the distillation column, causing the swing in the pressure at the beginning. The results indicate that the proposed method successfully forces the top column pressure (y1) to the new set point and stabilizes the remaining outputs at the desired set points with a faster response (within 7 hrs) and less oscillation compared to the MPC controller.

For the PI

controller, the outputs are not stable at their set points (as the stabilization attained is only local), and the controller itself must be tuned with the slow output responses to avoid the effect of highgain direction. Meanwhile, the proposed and MPC controllers are both in a class of optimal control. The MPC is an error-based optimization with open-loop prediction, which means that aggressive movement of the MPC control action may occur while seeking the optimal solution for an ill-conditioned system, resulting in significant high-gain directional errors. In contrast, the proposed method, formulated as the minimization of energy consumption, can relax the impact of any high-gain directional effect. Since the PI controller shows a poor performance under the closed-loop test where the set points were stepped from the initial steady state to the new desired set point, only the MPC controller is used as a benchmark for the set point tracking and regulatory tests.


25


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

Page 26 of 45

Figure 11. Output responses of the closed-loop system with the proposed controller.


26

Page 27 of 45

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


Figure 12. Input profiles corresponding to the closed-loop system in Figure 11.


27


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

Page 28 of 45

Figure 13. Output responses of the closed-loop system with the PI and MPC controllers.


28

Page 29 of 45

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


Figure 14. Input profiles corresponding to the closed-loop system in Figure 13.


29


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

Page 30 of 45

6.2 Set Point Tracking Performance The outputs are designed to track a sequence of step set points where y1sp is changed from 1.02 to 1.06 bar at 5 hrs, y2sp is changed from 0.998 to 0.99 at 20 hrs, and y3sp is changed from 0.5 to 0.49 at 30 hrs in sequence. The set point of the top column pressure was selected such that the top column pressure should not be changed by more than 10% of the nominal design pressure24. The control performance of the proposed method is compared with that of the MPC. To this end, the responses of the set point tracking test are shown in Figures 15 and 16. To increase the column pressure, the proposed controller forces the output y1 to the target and stabilizes the bottom and distillate EDC compositions by decreasing the coolant rate and increasing the reboiler duty simultaneously. For a step change in the set point of y2 which decreases the distillate EDC composition, the top column pressure swings slightly in the time immediately following the change due to a decrease in the reflux rate caused by the control action. The proposed controller compensates for this effect by reducing reboiler duty and coolant rate to maintain internal mass dynamics, taking less than 5 hrs to stabilize the system.

It also

successfully tracks the new set point of y3 and stabilizes other outputs by increasing the reboiler duty and coolant rate by slightly adjusting in reflux flow. Although the MPC controller has the same success for tracking the sequences of set points as the proposed controller, it undertakes the excessive control actions resulting in undesirable spikes in the outputs. Table 3 shows and compares the performances of both the proposed method and MPC for various indexes. The results support the claim that the proposed method exhibits overall better performance compared with the MPC controller, as it gives less fluctuation in the inputs. The proposed method also provides a shorter settling time with noticeably lower ISE values of all outputs.


30

Page 31 of 45

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


Figure 15. Closed-loop responses of (a) the top column pressure ( y1 ), (b) EDC mole fraction of the distillate product ( y2 ) and (c) EDC mole fraction of the bottom product ( y3 ) under the set point tracking.


31


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

Page 32 of 45

Figure 16. Profiles of (a) coolant rate ( u1 ), (b) reflux rate ( u2 ) and (c) reboiler heat duty ( u3 ) corresponding to the closed-loop responses of Figure 15.


32

Page 33 of 45

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


Table 3. Summary of Performance Results under Set Point Tracking Performance Index Rise time (hr) Settling time (hr) Overshoot (%) Period of oscillation (hr) Total ISE of y1 Total ISE of y2 Total ISE of y3

Step change in y1 MPC Proposed 2.26 1.60 5.42 2.52 0.22 0.77 5.50

4.12

3.78E-02

5.44E-04

Step change in y2 MPC Proposed 0.09 2.90 7.67 2.90 821.08 0 0.26

0

4.10E-04

1.99E-05

Step change in y3 MPC Proposed 0.09 1.65 5.41 1.65 14.10 0 0.19

0

8.31E-04

6.51E-05

6.3 Regulatory Performance As mentioned previously about the effects of disturbances in EDC feed to the EDC distillation column, regulatory tests are performed by applying -10% step disturbances in the EDC feed composition after 5 hrs and in the feed rate after 20 hrs, sequentially. Figures 17–19 illustrate the output, input and disturbance profiles under the proposed and MPC controllers. When a step disturbance is applied to the EDC feed composition, the proposed controller successfully rejects the disturbance within 5 hrs by reducing coolant and increasing the reflux and reboiler duty. After the second disturbance is applied, the controller also successfully rejects it within 6 hrs by increasing the coolant rate, reflux rate, and reboiler duty to stabilize the distillation column at the set points. Although the MPC controller can also reject the applied disturbances in both cases, it takes a longer time to reach the set point compared with the proposed method. Table 4 shows performance indexes of the output responses under the both cases of the step disturbances. The results demonstrate that, in terms of all indexes relative to the MPC controller, the proposed controller performs noticeably better. The proposed method provides a shorter setting time and lower Integral Square Error (ISE) values (with the exception of that obtained for the output y3) to reject a disturbance in the EDC feed composition.


33


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

Page 34 of 45

Figure 17. Closed-loop responses of (a) the column pressure ( y1 ), (b) EDC mole fraction of the distillate product ( y2 ) and (c) EDC mole fraction of the bottom product ( y3 ) under step disturbances in the EDC feed composition and feed rate.


34

Page 35 of 45

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


Figure 18. Profiles of (a) coolant rate ( u1 ), (b) reflux rate ( u2 ) and (c) reboiler heat duty ( u3 ) corresponding to the closed-loop response of Figure 17.


35


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

Page 36 of 45

Figure 19. Disturbance profiles of the regulatory test: (a) column feed rate ( d1 ), (b) EDC feed composition ( d2 ).


36

Page 37 of 45

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


Table 4. Summary of Performance Results under Regulatory Tests

Performance Index Settling time (hr) Maximum absolute overshoot ISE Performance Index Settling time (hr) Maximum absolute overshoot ISE

Under -10% Step Disturbance in the EDC Feed Composition y1 y2 y3 MPC Proposed MPC Proposed MPC Proposed 4.62 2.53 3.30 1.39 9.44 5.93 0.10 bar 0.13 bar 0.00041 0.00035 6.09E-03 6.07E-03 3.14E-07 1.28E-07 Under -10% Step Disturbance in the Feed Rate y1 y2 MPC Proposed MPC Proposed 3.77 2.28 6.72 2.23

0.0083 1.63E-04

0.11 bar 1.18E-02

0.0203 7.58E-04

0.03 bar 5.08E-04

0.00028 2.42E-07

0.00025 3.05E-08

0.0222 9.74E-04

y3 MPC Proposed 7.59 4.18 0.0052 4.25E-05

7. CONCLUSION A new WNARX-based optimization strategy was proposed for the multivariable control problem which exists in a high-purity EDC distillation column with the presence of illconditioning.

The controller is formulated to minimize the energy consumption of the

distillation column with the requesting I/O linearizing output responses posed as hard constraints. These I/O linearizing constraints force the outputs to reach the desired set points, while the formulated energy consumption function is used as the optimal relaxed objective function for the high-gain directional system. The co-simulation environment of ASPEN Plus Dynamics® and MATLAB/Simulink is introduced as an efficient tool for evaluating the closedloop performance of the complex chemical processes. In such an environment, the proposed method provides better performance with a noticeable improvement for both set point tracking and robustness with less aggressiveness in the control action, compared to a PI controller and MPC.

The proposed method provides several key advantages including (i) ease of


37


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

Page 38 of 45

implementation for processes with complex dynamics (Actual collected plant data and data generated from a reconciled model of ASPEN Plus Dynamics can be utilized for WNARX modeling.), (ii) less complexity in the controller formulation compared with the controllers16-18, and (iii) improvement of control performance for the ill-conditioning system. The proposed method successfully forces the outputs to desired set point with the optimum in energy cost. It has fewer tuning parameters and less computational time compared with the general MPC controller, resulting in simplicity in the selection of the tuning parameters. Futuremore, a control performance evaluation through the co-simulation environment allows a system engineer to test the proposed control strategy under the rigorous dynamics of complex chemical processes effectively. Supporting Information Description of the WNARX structure in model Case 7; time delay between inputs and outputs of the EDC distillation column; a compact form of WNARX model configuration in model Case7; tuning parameters of the proposed controller; tuning parameters of the PI controller; tuning parameters of the MPC controller; SIMULINK diagram of the closed-loop simulation; excel file of WNARX model parameters in model Case 7. The Supporting Information is available free of charge on the ACS Publications website (http://pubs.acs.org).

ACKNOWLEDGMENTS This research was financially supported by the Institutional Research Fund Grant (Thailand Research Fund) (IRG5980004), the Faculty of Engineering, Kasetsart University, Center for


38

Page 39 of 45

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


Advanced Studies in Industrial Technology, and the Center of Excellence on Petrochemical and Materials Technology. Support from these sources is gratefully acknowledged.

NOMENCLATURE

ai

=

output values from neuron i

asi

=

scaling coefficient of component i

awi

=

wavelet coefficient of component i

B

=

molar bottoms flow rate

bi

=

bias in neural network

bsi

=

scaling dilation coefficient of component i

bwi

=

wavelet dilation coefficient of component i

cg

=

average heat capacity of the mixed gas (J/kg K)

csi

=

scaling translation coefficient of component i

cwi

=

wavelet translation coefficient of component i

d

=

measured disturbance

D

=

molar distillate flow rate

D

=

differential operator

di

=

output offset of component i

e

=

output error

F

=

scaling function

F

=

molar feed flow rate

G

=

wavelet function

h

=

vector nonlinear functions

j

=

vector nonlinear functions

Kc

=

controller gain


39


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

Li

=

linear term coefficient in wavelet function of component i

Lf

=

loss function

N

=

number of estimation data

nu

=

maximum lag time of input variables

ny

=

maximum lag time of output variables

Nd

=

number of estimated parameters

Nr

=

number of regressors

P

=

constraint horizons.

Pi

=

linear subspace parameter of component i

Qi

=

nonlinear subspace parameter of component i

QR

=

reboiler heat duty

r

=

relative order

R

=

molar reflux rate

ri

=

mean value of regressor of component i

u

=

control action

ubias

=

controller bias

wi , Wi

=

weight in neural network

x

=

vector of state variables

xi

=

set of previous times inputs and outputs of component i

XB

=

mole fraction of bottom product

XD

=

mole fraction of distillate product

XF

=

mole fraction of feed

y

=

controlled outputs

ysp

=

desired output set point

yi

=

output variable of component i

Page 40 of 45


40

Page 41 of 45

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


yl , i

=

linear term output variable of component i

ynl ,i

=

nonlinear term output variable of component i

β

=

tuning parameter (s)

ν

=

vector of compensated set points.

=

transpose operator

Greek Letters

Superscripts T


41


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

Page 42 of 45

REFERENCES

(1) Ou, J.; Rhinehart, R.R. Grouped neural network model-predictive control. Control Eng. Pract. 2003, 11, 723–732. (2) Jana, A.K.; Samanta A.N.; Ganguly, S. Observer-based control algorithms for a distillation column. Chem. Eng. Sci. 2006, 61, 4071–4085. (3) Zhang, J.; Lin, M.; Chen, J.; Li, K.; Xu, J. Multiloop robust H∞ control design based on the dynamic PLS approach to chemical processes. Chem. Eng. Res. Des. 2015, 100, 518–529. (4) Mehrpooya, M.; Sima, H. Design and Implementation of Optimized Fuzzy Logic Controller for a Nonlinear Dynamic Industrial Plant Using Hysys and Matlab Simulation Packages. Ind. Eng. Chem. Res. 2015, 54, 11097-11105. (5) Tyagi, B.; others. Application of neural network based control strategies to binary distillation column. Control Eng. Appl. Inf. 2013, 15, 47–57. (6) Mishra, P.; Kumar, V.; Rana, K. P. S. A fractional order fuzzy pid controller for binary distillation column control. Expert Syst. Appl. 2015, 42, 8533–8549. (7) Fuentes, C.; Luyben, W. L. Control of high-purity distillation columns. Ind. Eng. Chem. Proc. Des. Dev. 1983, 22, 361–366. (8) Shaw, A.M.; Doyle III, F. J. Multivariable nonlinear control applications for a high purity distillation column using a recurrent dynamic neuron model. J. Process Control. 1997, 7, 255– 268. (9) Razzaghi, K.; Shahraki, F. Robust control of an ill-conditioned plant using µ-synthesis: A case study for high-purity distillation. Chem. Eng. Sci. 2007, 62, 1543-1547.


42

Page 43 of 45

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


(10) Raghunathan, A. U.; Soledad Diaz, M.; Biegler, L. T. An MPEC formulation for dynamic optimization of distillation operations. Comput. Chem. Eng. 2004, 28, 2037–2052. (11) Jana, A. K.; Samanta, A. N.; Ganguly, S. Globally linearized control system design of a constrained multivariable distillation column. J. Process Control. 2005, 15, 169–181. (12) Lundström, P.; Skogestad, S. Opportunities and difficulties with 5 × 5 distillation control. J. Process Control. 1995, 5, 249–261. (13)

Sotomayor, O. A.; Odloak, D.; Moro, L. F. Closed-loop model re-identification of

processes under MPC with zone control. Control Eng. Pract. 2009, 17, 551–563 (14) Martin, P. A.; Odloak, D.; Kassab, F. Robust model predictive control of a pilot plant distillation column. Control Eng. Pract. 2013, 21, 231–241. (15) Waller, J. B.; Böling, J. M. Multi-variable nonlinear MPC of an ill-conditioned distillation column. J. Process Control. 2005, 15, 23–29. (16) Sriniwas, G.R.; Arkun, Y.; Chien, I.-L.; Ogunnaike, B.A. Nonlinear identification and control of a high-purity distillation column: a case study. J. Process Control. 1995, 5, 149–162. (17) Nazaruddin, Y. Y.; Cahyadi, F. Adaptive predictive control strategy using wavenet based plant modeling. Proceedings of the 17th World Congress the International Federation of Automatic Control, Seoul, Korea, July 6-11, 2008; pp 10898-10903. (18) Udugama, I. A.; Munir, T. M.; Kirkpatrick, R.; Young, B. R.; Yu, W. Advanced dual composition control for high-purity multi-component distillation column. Proceedings of the ADCONIP Conference, Hiroshima, Japan, May 28–30, 2014; pp 345–350.


43


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

Page 44 of 45

(19) Udugama, I. A.; Wolfenstetter, F.; Kirkpatrick, R.; Yu, W.; Young, B. R. A comparison of a novel robust decentralised control strategy and mpc for industrial high purity, high recovery, multicomponent distillation. ISA Trans. 2017, 69, 222–233. (20) Botelho, V.; Trierweiler, J. O.; Farenzena, M. MPC Model Assessment of Highly Coupled Systems. Ind. Eng. Chem. Res. 2016, 55 (50), 12880. (21) Soroush, M.; Kravaris, C. MPC formulation of GLC. AIChE journal 1996, 42, 2377-81. (22) Soroush, M.; Muske, K.R. Analytical model predictive control; Nonlinear model predictive control: Birkhäuser Basel. 2000, 163-179. (23) Soroush, M.; Kravaris, C. A continuous-time formulation of nonlinear model predictive control. Int. J. Control. 1996, 63,121-46. (24) Kister, H. Distillation Operation; McGraw-Hill: New York, 1990.


44

Page 45 of 45

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


For Table of Contents Only


45

Optimization-Based Control Strategy with Wavelet ... - ACS Publications

Recommend Documents