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APPENDICES

APPENDIX A MODIFYING HEAT OF FORMATION IN ASPEN PLUS

In Aspen Plus, DHFORM is the heat of formation for general components. For

the polymer segment, the heat of formation (DHFVK) parameter can be used to adjust

the heat of formation to obtain the desired heat of polymerization (HOP). The procedure

for modifying the DHFORM is presented below:

i. Setup a flowsheet that consists of a heater block with a Feed stream and a
Product stream

ii. Set up Prop-Sets for liquid enthalpy of PS and Styrene
iii. Set up a Design Spec case to vary the DHFVK parameter for the Styrene

segment to match the heat of polymerization data.
Below is a systematic procedure by using polymer Polystyrene as an example:

Figure A.1

Figure A.2
Figure A.3

Figure A.4
Figure A.5

APPENDIX B NWMPC S-FUNCTION SCRIPT

%% Neural Wiener MPC
function [sys,x0,str,ts,simStateCompliance] =
mynmpcwn(t,x,u,flag,mpcpar,u0,uF0,Ts,FUN,varargin)
%guna stelah flag: mpcpar,u0,uF0,1/60,FUN,const,net : 1/60 =
Ts; const &
%net = varargrin / paramater tambahan (disini cont dan neural
network)
switch flag,

case 0,

[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes(mpcpar,u0
,uF0,Ts).

case 2,
sys=mdlUpdate(x,u,mpcpar,FUN,varargin);

case 3,
sys=mdlOutputs(x,mpcpar);

case 9,
sys=[];

otherwise
DAStudio.error('Simulink:blocks:unhandledFlag',

num2str(flag));
end

function

[sys,x0,str,ts,simStateCompliance]=mdlInitializeSizes(mpcpar,u0

,uF0,Ts)

nc = mpcpar.nc;

nu = mpcpar.nu;

ny = mpcpar.ny;

nx = mpcpar.nx;

sizes = simsizes;

sizes.NumContStates = 0;

sizes.NumDiscStates = (nc+1)*nu;

sizes.NumOutputs = nc*nu;

sizes.NumInputs = ny+nx;

sizes.DirFeedthrough = 0;

sizes.NumSampleTimes = 1;

sys = simsizes(sizes);

x0 = [u0;uF0];

str = [];

ts = [Ts 0];

simStateCompliance = 'UnknownSimState';

function sys=mdlUpdate(x,u,mpcpar,FUN,varargin)
nu = mpcpar.nu;
ny = mpcpar.ny;
dP = mpcpar.dP;
dF = mpcpar.dF;
icubvector = mpcpar.icub;
iclbvector = mpcpar.iclb;
uubvector = mpcpar.uub;
ulbvector = mpcpar.ulb;
uk = x(1:nu);

uF = x(nu+1:end);
yspk = u(1:ny);
xk = u(ny+1:end);
options = optimset('Display','Off');
A = [dF;-dF];
B = [dP; -dP]*uk+[icubvector; -iclbvector];

% Objective fucntion
uFopt = fmincon(FUN,uF,A,B,[],[],ulbvector,uubvector,...
[],options,yspk,uk,xk,mpcpar,varargin); %fmincon = sqp

xnew = [uFopt(1:nu); uFopt];
sys = xnew;

function sys=mdlOutputs(x,mpcpar)
nu = mpcpar.nu;
nc = mpcpar.nc;
uFk = x(1:nu*nc);
sys = uFk;

APPENDIX C PROPERTIES REGRESSION USING PC-SAFT EOS

The regression results for selected ethylene and LDPE properties using Aspen

Properties with PC-SAFT equation of state (EOS) are displayed here. The experimental

data (Exp) are referred from Bokis et al. (2002) study. These regression results are

simulated using Aspen Properties within Aspen Plus. Based on the figures, the Aspen

Plus model using PC-SAFT EOS has managed to regress the LDPE and ethylene

physical properties within acceptable margins. Thus, this validates the selection of PC-

SAFT EOS for simulating the LDPE polymerization process.

Density (gm/cc) 0.9 Aspen 1 Bar
0.88 Aspen 300 Bar
0.86 Aspen 600 Bar
0.84 Aspen 1000 Bar
0.82 Aspen 1400 Bar
0.8 Aspen 2000 Bar
0.78 Exp 2000 bar
0.76 Exp 1400 bar
0.74 Exp 1000 bar
0.72 Exp 600 bar
0.7 Exp 300 bar
Exp 1 bar
400 410 420 430 440 450 460 470 480 490 500
Temperature (K)

Figure C.1 LDPE density with PC-SAFT

23 Exp
22 Aspen Model

21

Cp (cal/mol-K) 20

19

18

17

16

15

14 100 200 300 400
0 Temperature (C)

Figure C.2 Heat capacity of amorphous LDPE

60
exp

Aspen Ethylene vp
50

Pressure (Bar) 40

30

20

10

0 150 200 250 300
100 Temperature (K)

Figure C.3 Ethylene vapor pressure with PC-SAFT

0.7

0.6 290 est
330 est
0.5 400 est
450 est
Density (gm/cc) 0.4 500 est
500 est
0.3 600 est
290 exp
0.2 330 exp
400 exp
0.1 450 exp
500 exp
550 exp
600 exp

0 1000 1500 2000 2500 3000
0 500 Pressure (Bar)

Figure C.4 Ethylene supercritical density with PC-SAFT

30
330K

Cp (cal/mol-K) 25 450K
550K

20 600K

Aspen 330K
15

Aspen 450K

10 Aspen 550K
Aspen 600K
5
0 500 1000 1500 2000 2500 3000 3500
Pressure (Bar)

Figure C.5 Heat capacity of supercritical ethylene with PC-SAFT

Pressure (bar) 300 130
250 190
200 0.05 0.1 0.15 Aspen 130C
150 Mass fraction ethylene Aspen 190C
100 0.2
50

0
0

Figure C.6 Vapour liquid equilibrium of LDPE-ethylene binary mixture

APPENDIX D NWMPC PROCESS MODEL RESULTS

 State space model:
dx/dt = A x(t) + B u(t) + K e(t)

y(t) = C x(t) + D u(t) + e(t)

A=

x1 x2 x3

x1 -1.332 -3.502 0.02141

x2 7.718 -3.555 -0.1425

x3 0.0834 0.3448 0.3332

x4 -1.09 7.226 -0.1488

x5 -0.9678 4.713 -0.1262

x6 -0.4277 -0.5984 -2.353

x4 x5 x6
x1 -1.249 -0.8645 0.2167
x2 0.3994 0.08033
x3 0.1001 -2.241
x4 0.7038 0.3416 2.366
x5 0.6626 -0.3623
x6 -0.004703 2.98 -0.4786
0.8134
-0.7814 -6.413

B= u2 u3
u1 0.08477 -0.388

x1 0.03957 0.2616 0.975
x2 -0.02097 0.9823 -10.58
x3 0.711 -0.1705 -0.4504
x4 -0.03958 -0.2756 0.9932
x5 -0.0926 -2.398
x6 -1.73 25.71

C=
x1 x2 x3 x4

y1 -12.85 -3.436 -0.2772 -2.868
y2 0.6461 0.08375 -17.02 0.6203

x5 x6
y1 -8.142 0.09071
y2 0.001163
-7.042

D=
u1 u2 u3

y1 0 0 0
y2 0 0 0

K= y2
y1 -4.232

x1 -4.365 10.39
x2 -0.9498 -115.5
x3 -31.54 -4.708
x4 9.182
x5 4.323 10.99
x6 76.65 276.5

 Neural network model
function [Y,Xf,Af] = neural_function(X,~,~)
% NEURAL_FUNCTION neural network simulation function.
% ===== NEURAL NETWORK CONSTANTS =====
% Input 1
x1_step1.xoffset = [-0.11415007450997;-0.179329146559265];
x1_step1.gain = [2.61979626929981;2.40213239614389];
x1_step1.ymin = -1;

% Layer 1
b1 = [3.0522612246587845775;-0.072051379088355349545;-
2.4894894405044136754;2.7392223532376291928;0.21771303773982134
122;2.6799453284115828389;1.623333502744154444;-
2.0190677688651028632;-4.8741388079446146264];
IW1_1 = [0.3071327677683392543
4.8864780422123805792;0.32785515322385838655 -
0.77497680134704927113;0.68721363841708260622
5.1968463435982226173;-0.69912531654436183004 -
5.8362868652800425906;0.30721761832150201732
0.14750667498223044016;0.89221179309802445268 -
1.0611187923408256228;1.4118634975388804076 -
0.094763674194409258655;-0.81029217769034123098 -
2.5097819812665274064;-2.2342786152736500149
1.8314223995614675733];

% Layer 2
b2 = [-0.53219127385866638047;1.6799798073395559861];
LW2_1 = [-0.05849283353894543791 0.3911608498894988406
0.14444504831900722985 0.12679761407486164759
1.8391519813306420605 1.0012784191924291033
1.034795545638637293 -0.12425691024589115286
1.5041736462866779345;-0.01665307542109036032 -
0.91514198608717944872 1.7353739946308097686
1.5695001026605854832 1.1685813981913668602 -
4.7269433965427669619 0.26601576233763302159
0.19404347778946925973 -2.3073150258734655971];

% Output 1
y1_step1.ymin = -1;
y1_step1.gain = [2.72226058874659;2.23911199786974];
y1_step1.xoffset = [-0.184590222397142;-0.0302615291530434];

% ===== SIMULATION ========

% Format Input Arguments
isCellX = iscell(X);
if ~isCellX

X = {X};
end
% Dimensions
TS = size(X,2); % timesteps
if ~isempty(X)

Q = size(X{1},2); % samples/series
else

Q = 0;
end

% Allocate Outputs
Y = cell(1,TS);

% Time loop
for ts=1:TS

% Input 1
Xp1 = mapminmax_apply(X{1,ts},x1_step1);

% Layer 1
a1 = tansig_apply(repmat(b1,1,Q) + IW1_1*Xp1);

% Layer 2
a2 = repmat(b2,1,Q) + LW2_1*a1;

% Output 1
Y{1,ts} = mapminmax_reverse(a2,y1_step1);
end

% Final Delay States
Xf = cell(1,0);
Af = cell(2,0);

% Format Output Arguments
if ~isCellX

Y = cell2mat(Y);
end
end

% ===== MODULE FUNCTIONS ========
% Map Minimum and Maximum Input Processing Function

function y = mapminmax_apply(x,settings)
y = bsxfun(@minus,x,settings.xoffset);
y = bsxfun(@times,y,settings.gain);
y = bsxfun(@plus,y,settings.ymin);

end
% Sigmoid Symmetric Transfer Function

function a = tansig_apply(n,~)
a = 2 ./ (1 + exp(-2*n)) - 1;

end

% Map Minimum and Maximum Output Reverse-Processing Function
function x = mapminmax_reverse(y,settings)

x = bsxfun(@minus,y,settings.ymin);
x = bsxfun(@rdivide,x,settings.gain);
x = bsxfun(@plus,x,settings.xoffset);
end

APPENDIX E PID Tuning using Matlab PID Autotuning

Automatic PID tuning is the process of tuning controller gains based on a plant

model or plant data. This study uses a Real-time PID Autotuning application, which lets

the user deploy an embedded automatic tuning algorithm as a standalone application for

model-free tuning against a physical plant. The PID Autotuning application injects test

signals into the plant to estimate plant frequency response near the target control

bandwidth. It uses the resulting response to compute PID controller gains to balance

robustness and performance. In general, the application operates as follows:

i. Injects a test signal into the plant at the nominal operating point to collect plant
input-output data and estimate frequency response in real-time. The test signal
is a combination of sine and step perturbation signals added on top of the
nominal plant input measured when the experiment starts. If the plant is part of
a feedback loop, the block opens the loop during the experiment.

ii. At the end of the experiment, tunes PID controller parameters based on
estimated plant frequency responses near the open-loop bandwidth.

iii. Updates the PID Controller block or custom PID controller with the tuned
parameters, allowing the user to validate closed-loop performance in real-time.

In this study, we are following the methodology presented below:
i. Develop a linear model of the LDPE tubular reactor using Matlab System
Identification
ii. Develop the dual SISO PID control scheme with the identified model (i.e., P2D)
inside Matlab Simulink environment, as shown in Figure E.1

Figure E.1 PID control scheme
iii. Click the PID block and choose the Tune option
iv. Start tuning the process into the desired target by observing the real-time control

response (Tuned response). This can be done by modifying the Response time
and Transient behavior option, as shown in Figure E.2. The Tuned PID
controller parameters can be displayed by clicking the Show Parameters option.

Figure E.2 PID Tuner menu
v. After satisfied by the tuned closed loop process response, click the Update Block

option to update the respective PID controller

LIST OF PUBLICATIONS

1. Muhammad, D., and Aziz, N. (2017). Simulation and Sensitivity Study of Industrial
Low Density Polyethylene Tubular Reactor. Chemical Engineering Transactions
56, 757-762.

2. Muhammad, D., and Aziz, N. (2017). Review: Control Schemes for Low Density
Polyethylene Reactor. Chemical Engineering Transactions 56, 769-774.

3. Muhammad, D., Ahmad, Z., and Aziz, N. (2018). Modeling and nonlinearity studies
of Low-Density Polyethylene (LDPE) tubular reactor. Materials Today:
Proceedings 5, 21612-21619.

4. Muhammad, D., Ahmad, Z., and Aziz, N. (2019). Low density polyethylene tubular
reactor control using state space model predictive control. Chemical Engineering
Communications, 1-17. (Q3)

5. Muhammad, D., Ahmad, Z., and Aziz, N. (2020). Temperature control of Low-
Density Polyethylene (LDPE) tubular reactor using Model Predictive Control
(MPC). IOP Conference Series: Materials Science and Engineering 736, 042014-
042014.

6. Muhammad, D., Ahmad, Z., and Aziz, N. (2021). Modeling of Low Density
Polyethylene tubular reactor using nonlinear block-oriented model. Materials
Today: Proceedings, 42, 39-44.

7. Muhammad, D., Ahmad, Z., and Aziz, N. (2021). Low Density Polyethylene
Tubular Reactor Control using Neural Wiener Model Predictive Control, Asia-
Pacific Journal of Chemical Engineering, (Under review).