LOW DENSITY POLYETHYLENE GRADE TRANSITION CONTROL USING NEURAL WIENER MODEL PREDICTIVE CONTROL WITH SOFT SENSOR

This result shows that having a nonlinear block in the NW model structure has
increased its estimation capability.

(a)

(b)
Figure 4.31 Model validation results from 1900 to 2000 minutes: (a) LDPE

conversion (b) MFI
The summary of the model identification results is presented in Table 4.6. From
the table, the error analysis using the NRMSE agrees with the R2 results but with more
precise values. This because the NRMSE is based on the goodness of fit between the
test and reference data, while R2 is a measure of the proportionate amount of variation

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in the response variable explained by the independent variables in the linear regression
model. Thus, NRMSE can provide a more in-depth insight into the model performance
compared to the R2 calculation.

Table 4.6 Summary of model identification results for SS and NW model

Model Linear Number of R2 NRMSE
Model Hidden Y1 Y2 Y1 Y2
Order Neurons

State space 6 - 0.9509 0.6693 0.7806 0.5764
(SS) 6 9 0.9889 0.9860 0.8949 0.8828

Neural
Wiener
(NW)

4.4 Soft sensor modeling results
The modeling results for the soft sensor development are presented below. The

modeling results include the soft sensor input selection and model identification for
the Multi Input Single Output (MISO) Time delay Neural Network (TDNN) model.

4.4.1 Input selection results

Figure 4.32 shows the preprocessing of the input-output data using a box plot.
From the figure, feed temperature, peak temperature zone 1, and peak temperature
zone 2 have the lowest variability than the other parameters based on their maximum
and minimum values. Since the mentioned parameter values are almost constant (i.e.
uniform), they are discarded from the Pearson correlation coefficient (PCC) analysis.

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Figure 4.32 The input and output data plotted using Box plot; (a) feed temperature
(b) peak temperature zone 1 (c) peak temperature zone 2 (d) peak temperature zone 3

(e) peak temperature zone 4 peak (f) temperature zone 5 (g) temperature valley (h)
temperature exit temperature (i) initiator 1 flow rate (j) initiator 2 flow rate (k) CTA

flow rate (l) polymer exit density (m) LDPE conversion (n) MFI

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Based on the PCC results in Table 4.7, peak temperature zone 5, reactor exit
temperature, initiator 2 flow rate, and polymer density present the highest correlation
(> 80%) for the LDPE conversion. However, for the MFI, the only notable correlations
obtained are from the CTA flow rate at 63%. As the PCC is relatively based on the
linear correlation of the input-output, which dose not account for the nonlinearity
behavior, another option is required to determine the relevant input parameters
(Jayaweera and Aziz, 2018). Thus, the final selection is typically made based on the
aid of expert knowledge (Curreri et al., 2020). The source of expert knowledge is
obtained from the available literature and parametric analysis in section 4.2.1.

Table 4.7 PCC results for parameter outputs

Parameters PCC MFI
LDPE Conversion 0.10
Peak Temperature Zone 3 0.08
Peak Temperature Zone 4 0.16 0.13
Peak Temperature Zone 5 0.17 0.14
Valley Temperature 0.90 0.12
Exit Temperature 0.19 0.02
Initiator 1 flow rate 0.99 0.12
Initiator 2 flow rate 0.16 0.63
CTA flow rate 0.86 0.19
Density 0.03
0.90

Based on the literature, reactor peak temperatures are identified to be
associated with polymer properties such as conversion (Kiparissides and Mavridis,
1986; Vallerio et al., 2013). This can also be verified from this work's parametric

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analysis results. Cao et al. (2007) have reported that rector temperature distribution
along the reactor could represent polymer quality properties such as average molecular
weight (MW) to a certain extent. Moreover, it is known that the polymer average MW
has a particular relationship with the MFI (Shenoy and Saini, 1986). In addition,
polymer density is a reliable parameter for monitoring the polymerization progress
inside the reactor (Liu and Kiran, 2008).

The final selected inputs for the soft sensor model are tabulated in Table 4.8. It
should be noted that polymer density is removed from the conversion model since it is
more related to polymer MFI than conversion (Seavey et al., 2003). Since the polymer
MFI model is more complex than the LDPE conversion model, it is reasonable to have
more inputs.

4.4.2 Model identification results

Based on the model delay (or historical values) estimation in section 3.7.1(b),
the selected number of historical values for the TDNN model conversion is 7, and the
TDNN model MFI is 22. The modeling results for the TDNN models are presented in
Figure 4.33 and Figure 4.34. Figure 4.33 shows the determination of the number of
hidden neurons for the TDNN conversion model and TDNN MFI model. Each number
of hidden neurons is trained several times, and the best are selected to represent the
model’s hidden neurons. The model validation error is calculated using the NRMSE
analysis. From the figure, hidden neurons 9 for model conversion (with NRMSE =
0.9574) and hidden neurons 7 for model MFI (with NRMSE = 0.9579) have scored
the highest NRMSE values, respectively.

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Table 4.8 Finalized soft sensor input parameters

LDPE Conversion model MFI model

Parameters Source Parameters Source
Peak Temperature PCC PCC
PCC CTA flow rate LR
Zone 5 PCC LR
Exit Temperature Polymer density LR
LR
Initiator 2 flow rate Peak Temperature LR
Zone 3

Peak Temperature
Zone 4

Peak Temperature
Zone 5

Valley Temperature

Exit Temperature LR
Note: PCC (Pearson correlation coefficient); LR (Literature).

Figure 4.34 displays the regression plot for both the corresponding models.
Based on the figure, both models have achieved an excellent correlation with the target
data with minimal disparity. The R2 value for the model conversion is 0.9991, and
0.99891 for the model MFI. Thus, from these validation results, both models are
appropriate to be used as soft sensor models.

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(a) (b)
Figure 4.33 Number of hidden neurons selection for (a) TDNN conversion model

and (b) TDNN MFI model

(a) (b)
Figure 4.34 Regression plot for (a) TDNN model conversion and (b) TDNN

model MFI
4.5 NWMPC control results

The results for the Neural Wiener MPC (NWMPC) performance in controlling
the LDPE tubular reactor are presented in this section. In order to compare the
NWMPC controller performance, the state space MPC (SSMPC) and PID controller
are also developed. This section presents the controller schemes, tuning results, linear
controller (i.e., PID and SSMPC) comparison, and nonlinear controller (i.e., NWMPC)

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performance. Finally, the effect of process time delay on the NWMPC controller is
examined.
4.5.1 Control Schemes

The control schemes developed inside the Matlab Simulink environment are
shown in Figure 4.35 to Figure 4.37. Figure 4.35 shows the PID control scheme
controlling the LDPE tubular reactor, utilizing the dual SISO PID controller. Thus, the
[MV - CV] pairing would be [Initiator 2 - LDPE conversion] and [CTA flow rate -
MFI]. To compare the PID performance, a similar 2-by-2 scheme using the state space
MPC (SSMPC) is developed. The LDPE tubular reactor model is simulated using
Aspen Dynamic, which runs simultaneously with Matlab Simulink during the
simulation.

Figure 4.35 PID control scheme inside Matlab Simulink
Figure 4.36 shows the Neural Wiener MPC (NWMPC) control scheme for
controlling the LDPE tubular reactor. In this scheme, three MVs (i.e., Initiator 1,
Initiator 2, and CTA flow rate) are used to control two CVs (i.e., LDPE conversion
and MFI), which can be considered as a Multi input multi output (MIMO) system.

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Moreover, the NW model block function as the MPC process model to generate model
mismatch, which is used to update the MPC controller at each sampling time. The
SSMPC is also developed as a performance comparison using a similar control
scheme. Here, the SSMPC control scheme can be obtained by changing the NW model
with the SS model.

Figure 4.36 NWMPC control scheme inside Matlab Simulink
Figure 4.37 shows the NWMPC control scheme with a soft sensor to
compensate for the delay effect (from delay block) in a practical LDPE tubular reactor
situation. The existence of the delay in the control loop can create a problem for the
NWMPC controller to control the process since it cannot obtain the current
measurement. Thus, the soft sensor is used to estimate the delayed CV signals based
on MVs and process parameters.

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Figure 4.37 NWMPC control scheme with a soft sensor inside Matlab Simulink

4.5.2 Tuning results

The tuning results for the PID, SSMPC, and NWMPC are presented in Table
4.9. The MPC controllers' initial tuning parameters are obtained from the calculation
(Seborg et al., 2004) and offline simulation using Matlab MPC Tool. These tuning
parameters are then fine-tuned during the online simulation (Jacob and Dhib, 2012;
Wibowo et al., 2009). It should be noted that during the online simulation, only output
weighting is changed to achieve the desired set point profile (Wojsznis et al., 2003).
Since the LDPE tubular reactor is a 3-by-2 multi input multi output (MIMO) system,
two single input single output (SISO) PID controllers are needed. The PID controller's
initial tuning is obtained using the PID Autotuning tool during offline simulation. This
procedure is further explained in Appendix E. During the online simulation, the PID
tuning parameters are further fine-tuned to obtain the desired performance by
manipulating its integral (I) parameters.

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Table 4.9 MPC and PID tuning parameters
MPC Tuning PID Tuning

Parameters SSMPC NWMPC Parameters PID 1 PID 2
0.75
Prediction 45 45 Proportional 0.04 0.13
Horizon (P) (P) 0.22

Control 5 5 Integral 0.35
Horizon (M) (I)

Output 0.11, 1.1, Derivative 0.00
weighting 0.09 2.0 (D)

Input rate 1.5, 1.2, 1.5, 1.2,
weighting 1.2 1.2

4.5.3 Linear controller performance results

From the control perspective, the PID and SSMPC can be considered linear
controllers since both rely on linear equations or models to control the process. The
performance of these linear controllers in controlling the LDPE grade transition is
shown in Figure 4.38 and Figure 4.39. Based on Figure 4.38(a), the SSMPC has
performed well in tracking the polymer grade MFI 5 and MFI 1.5 using less time than
the PID controller. In the meantime, the PID controller has difficulties in controlling
the MFI 5 grade with a small overshoot behavior. This is due to its sluggish MV
controller action that drives the CTA flow rate slower and exceeds the required
amount, as seen in Figure 4.38(b). A similar situation has occurred during the grade
transition from MFI 5 to MFI 2.2 (steady state condition). For the close grade transition
from MFI 2.2 to MFI 1.5 and vice versa, both controllers have shown comparable
results. Based on error analysis, the SSMPC has produced a lower error with ISE value
of 110 than the PID controller with ISE value of 231.

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Figure 4.38 Grade transition profile for PID and SSMPC (a) CV profile (b) MV
profile

Figure 4.39 shows the LDPE conversion profile, which is set at steady state
condition. From the figure, both controllers have managed to control the current
setpoint with ISE value of 0.0007 for the PID controller and ISE value of 0.0156 for
the SSMPC. In this case, the PID controller performance is better than SSMPC due to
its SISO control scheme, which is not affected by multivariable control trade-offs
during grade transition. As for the SSMPC, its CV performance is bound to be affected
when grade transition occurs in the other loop since it has a MIMO control scheme.
However, the SSMPC incursion is still small and can be tolerated.

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Figure 4.39 LDPE conversion profile for PID and SSMPC (a) CV profile (b) MV
profile

Based on these results, a conventional controller such as PID has certain
limitations in handling the medium grade polymer grade transition. This is mainly due
to its controller action based on linear equations, which is not suited for handling high
nonlinearity processes (Seki et al., 2001). Although the SSMPC has performed well
during the grade transition control, it is still based on a linear model. Thus, section
4.5.4 will explore the capability of the MPC with a nonlinear model, namely the Neural
Wiener MPC (NWMPC), in controlling the LDPE process.

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4.5.4 Nonlinear controller performance results

4.5.4(a) Grade transition
Figure 4.40 demonstrates the performance of the SSMPC and NWMPC in

controlling a similar grade transition operation, as in section 4.5.3. Based on Figure
4.40(a), the NWMPC has managed to reach grade MFI 5 and MFI 1.5 faster with a
shorter rise time than the SSMPC, despite having the same controller output in the first
50 minutes (refer to Figure 4.40(b) for the MV profile). This performance is
accomplished by the NWMPC lowering its initiators’ flow rate, as seen in Figure
4.41(b) and Figure 4.41(c) since there is a rate limitation on the CTA flow rate
(Ohshima and Tanigaki, 2000). Thus, by lowering the initiator flow rates, the polymer
MFI can be increased, as discussed in section 4.2.1(a) and section 4.2.1(b). Moreover,
the decrease in the initiator flow rates has produced a minimal effect on the LDPE
conversion. A similar situation can be observed during the grade transition step down
from MFI 2.2 to MFI 1.5. However, this time the initiators' flow rates are increased to
balance the CTA flow rate decreased to achieve lower grade MFI.

Based on the error analysis, the NWMPC has produced an ISE value of 43.288
and 0.009, while SSMPC ISE is 88.080 and 0.013 for the MFI and LDPE conversion
profiles. Thus, it can be noted that the NWMPC has accomplished the LDPE grade
transition control using the optimized controller outputs with a faster grade transition
and reduced resources (CTA and initiators) consumption.

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Figure 4.40 Comparison of grade transition control using NWMPC and SSMPC:
(a) MFI profile (b) CTA flow rate profile

Figure 4.41 Comparison of grade transition control using NWMPC and SSMPC:
(a) Conversion profile (b) Initiator 2 flow rate profile (c) Initiator 1 flow rate profile

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4.5.4(b) High Grade transition

In this test, the controllers are evaluated to control the LDPE high-grade
transitions, which are MFI 22 and MFI 55. The results are presented in Figure 4.42
and Figure 4.43. Based on Figure 4.42(a), both controllers have reached the targeted
high-grade MFI at a similar time. This can be justified by the identical CTA flow rate
profiles in Figure 4.42(b), primarily due to both controllers using the maximum MV
rate as described in section 3.8.1. Since high grade MFI requires more CTA in the
polymer mixture, maximizing the CTA flow rate is the best option for both the
controllers.

Figure 4.43(a) shows that the SSMPC controller exhibits wavering responses
to maintain the LDPE conversion at a steady state. This can be observed by the
oscillatory SSMPC controller output in the initiator 2 flow rate profile, as seen in
Figure 4.43(b). This oscillatory response is due to the increasing model mismatch in
the SSMPC control loop due to its limited linear model capability when dealing with
high grade MFI set points. This can be verified by the SS model performance in Figure
4.30(b). Compared to the SSMPC, the ability of the NWMPC to control LDPE
conversion is better with no oscillations and achieving the target. Moreover, the
NWMPC has quickly reduced the initiator 1 flow rate compared to the SSMPC, which
is an excellent move to achieve a high-grade MFI.

In terms of the MFI’s profile results, the NWMPC has shown a better
performance with an ISE value of 1979 than the SSMPC with an ISE value of 2077.
In addition, the NWMPC is also better at maintaining the conversion set point during
the grade changes with an ISE value of 0.501 compared to the SSMPC with an ISE

136

value of 0.588. Therefore, the NWMPC has the advantage over SSMPC when dealing
with grade transition of high-grade MFI due to its nonlinear model capability.

Figure 4.42 Comparison of high-grade transition control using NWMPC and
SSMPC: (a) MFI profile (b) CTA flow rate profile

Figure 4.43 Comparison of high-grade transition control using NWMPC and
SSMPC: (a) Conversion profile (b) initiator 2 profile (c) initiator 1 profile
137

4.5.4(c) Conversion change

The conversion change test is performed at time 60 minutes after the LDPE
grade is changed to MFI 5, as shown in Figure 4.44(a) and Figure 4.45(a). The
controllers have managed to maintain the current MFI grade during the conversion
change, with the NWMPC producing a smaller deviation compared to SSMPC, as
shown in Figure 4.44(a). From Figure 4.45(a), both controllers have presented a
comparable performance in tracking the conversion change. However, the NWMPC
has reached the setpoint slightly earlier than the SSMPC, for example, at 95 minutes.
This can be verified based on error analysis, which shows that the NWMPC has
obtained an ISE value of 0.095 compared to the SSMPC ISE value of 0.122 for the
LDPE conversion change. Meanwhile, for the MFI, the NWMPC has produced an ISE
value of 72.975 compared to 76.048 using SSMPC.

The MV profiles in Figure 4.45(b) and Figure 4.45(c) show mixed responses.
During the step up, the NWMPC has utilized lower initiator 1 and initiator 2 amounts
than the SSMPC. Then, after step down starting at time 115, the NWMPC has
consumed more imitator amounts than the SSMPC. A similar observation can be seen
in Figure 4.44(b), where the NWMPC used more CTA amounts than the SSMPC
during the conversion step down. Thus, the NWMPC has the advantage of controlling
the LDPE conversion during the step-up process by consuming fewer resources.
However, during the step-down process, the NWMPC has utilized more resources (i.e.
using more CTA and initiators flow rate) than the SSMPC. This indicates that the
nonlinear model of the NWMPC has certain issues in estimating the conversion step-
down profiles. In addition, the MPC multivariable control scheme has made the
excursion responses in the MFI profile due to the control tradeoff effect among the
CVs.

138

Figure 4.44 Comparison of conversion change control using NWMPC and
SSMPC: (a) MFI profile (b) CTA flow rate profile

139

Figure 4.45 Comparison of conversion change control using NWMPC and
SSMPC: (a) Conversion profile (b) initiator 2 profile (c) initiator 1 profile

4.5.4(d) Disturbance rejection 1: Feed stream pressure loss
The disturbance rejection of pressure loss in the feed stream is shown in Figure

4.47 and Figure 4.46. Based on Figure 4.47(a), the NWMPC can reject such
disturbances in the MFI profile faster than the SSMPC by using a lesser amount of
CTA (refer to Figure 4.47(b)). This shows that the NWMPC has used a more optimized
control move than the SSMPC, which is significant since the effect of pressure loss is
more evident in the MFI profile than the LDPE conversion profile. However, the fast
response from the NWMPC in Figure 4.46(a) has exerted it to use more initiator 1 flow
rate than the SSMPC (refer to Figure 4.46(c)).

140

Figure 4.46 Comparison of disturbance rejection results for pressure loss in the
feed stream using NWMPC and SSMPC (a) MFI profile (b) CTA profile

Figure 4.47 Comparison of disturbance rejection results for pressure loss in the
feed stream using NWMPC and SSMPC (a) LDPE conversion (b) initiator 2 flow

rate (c) initiator 1 flow rate
141

Based on this test, the controllers have managed to estimate the disturbance
from the process measurement and take the necessary control action to maintain the
desired condition since the disturbance is not measured. The faster action from the
NWMPC has demonstrated the advantage of the nonlinear controller in estimating the
unmeasured disturbance and driving the controller output to ensure zero offsets on the
CVs (Jacob and Dhib, 2012). In terms of error analysis in the MFI profile, the NWMPC
has generated an ISE equal to 4.359 compared to the SSMPC with an ISE value of
6.349. From the LDPE conversion profile, the ISE produced from the NWMPC and
SSMPC are 0.003 and 0.006, respectively. Therefore, based on these results, the
NWMPC is expected to be able to compensate for the pressure loss disturbance in the
feed stream.

4.5.4(e) Disturbance rejection 2: Reduced feed stream flow rate
The controllers’ capability in managing the disturbance in the feed stream flow

rate is studied in Figure 4.48 and Figure 4.49. From Figure 4.48(a), the NWMPC has
succeeded in rejecting the disturbance faster with minimal oscillation compared to the
SSMPC. This can be demonstrated by its aggressive controller output in driving the
CTA flow rate, as seen in Figure 4.48(b). Moreover, the SSMPC response in the LDPE
conversion profile has undergone a larger oscillation than the NWMPC, as shown in
Figure 4.49. Nevertheless, despite its superior performance, the NWMPC has only
consumed a smaller amount of resources than the SSMPC, as observed in Figure
4.49(b) and Figure 4.49(c).

142

Figure 4.48 Comparison of disturbance rejection results for reduced flow rate in
the feed stream using NWMPC and SSMPC (a) MFI (b) CTA flow rate

Figure 4.49 Comparison of disturbance rejection results for reduced flow rate in
the feed stream using NWMPC and SSMPC (b) initiator 2 flow rate (c) initiator 1

flow rate
143

Based on the observation in Figure 4.48(b), the CTA profile using SSMPC has
dropped first and then stepped up again. The reason for this behavior is due to the
SSMPC prediction error during the disturbance rejection test. This error originates
from its linear model limitation, which at the beginning is not able to produce an
accurate process response, resulting in an incorrect control trajectory. However, after
a few steps ahead, the SSMPC is able to re-correct itself based on the new inputs from
the process. A similar behavior can be observed in Jacob and Dhib (2012) when they
compared the NMPC and the LMPC control performances.

Based on the error analysis, the NWMPC has performed better compared to
the SSMPC with an ISE value of 2.141 against an ISE value of 5.358 for the MFI
profile. For the conversion profile, the ISE generated for the NWMPC is 0.004
compared to ISE 0.021 for the SSMPC. Thus, the overall process output responses
indicate that the NWMPC controller could reject the disturbance without noticeably
shifting the product grade and reducing resource consumption.

4.5.4(f) Disturbance rejection 3: Reduced ethylene gas feed purity

Among the disturbances, the accumulation of the impurity in the feed stream
contributes to the highest effect on the MFI grade, as explained in section 3.8.3(c). The
close-loop results demonstrated in Figure 4.50(a) and Figure 4.51(a) show that both
the controllers have performed well in maintaining the CVs at their set point despite
the disturbance. Based on Figure 4.50(a), the NWMPC has only taken 20 minutes to
reject the disturbance compared to the SSMPC, which consumed much more extensive
time and sustained an offset. This offset originated from the CTA flowrate that has
reached the minimum level (refer to Figure 4.50(b)), and yet, the process output is still
slowly returned to the set point.

144

Figure 4.50 Comparison of disturbance rejection results for reduced ethylene
impurity in the feed stream using NWMPC and SSMPC (a) MFI (b) CTA flow rate

Figure 4.51 Comparison of disturbance rejection results for reduced ethylene
impurity in the feed stream using NWMPC and SSMPC: (a) LDPE conversion (b)

initiator 2 flow rate (c) initiator 1 flow rate
145

This situation can be referred to as the saturation effect when a particular part of a
feedback control system reaches a physical limit (Haidekker, 2013).

The NWMPC has also faced a similar situation. Alternatively, the NWMPC
has exploited the initiator’s flow rates, as observed in Figure 4.51(b) and Figure
4.51(c), in its effort to reduce the MFI grade further. As a result, the NWMPC has
managed to reinstate the MFI grade to its nominal value faster than the SSMPC but
has ended up with certain oscillations in its profile due to its tuning parameters. It
should be noted that the current NWMPC tuning parameter is developed based on
grade transition control. Thus, when the controller encounters a large disturbance, it is
expected to experience certain instability in its closed-loop control response. Thus, in
practice, it is typical to have a different tuning parameter for steady state operation and
grade transition control (Skålén et al., 2016).

Based on the error analysis, the NWMPC has only yielded an ISE value of
11.116 for the MFI profile and 0.002 for the conversion profile, while the SSMPC has
produced an ISE value of 26.449 for the MFI profile and 0.005 for the conversion
profile. This proves that the nonlinear model in the NWMPC has assisted it in making
a better and faster decision in handling the impurity disturbance in product quality
(Bindlish, 2015).

4.5.4(g) Robustness Test 1: Fouling

The calculated heat transfer coefficient (HTC) of the fouled tubular reactor is
tabulated in Table 4.10. Based on the table, Zone 3 has experienced the most
considerable fouling effect, continued by Zone 4 and Zone 5. The decreasing effect of
fouling corresponds to the zone location with the reactor feed inlet.

146

Table 4.10 Heat transfer coefficient (HTC) for clean and fouled tubular reactor
based on zones (in BTU unit)

Zone HTC clean HTC fouled Δ HTC%
3 147.5 113.9 22.8
4 110.6 90.6 18.1
5 34.7 32.4 6.5

Figure 4.52 and Figure 4.53 present the effect of fouling in the reactor outputs
and its MV profile. Based on Figure 4.52(a), both controllers are able to adapt to the
fouling situation, with the SSMPC showing a slight deviation in the MFI profile. From
the error point of view, the NWMPC has generated an ISE value of 0.232 compared
with the SSMPC with an ISE value of 1.183 in the MFI profile. In Figure 4.53(a), both
the controllers exhibit comparable performances in maintaining the polymer
conversion, despite the NWMPC using more initiator 1 amount than the SSMPC (refer
to Figure 4.53(c)). Based on the error analysis in the conversion profile, both the
controllers yield a similar ISE with the NWMPC at 0.017 and the SSMPC at 0.018.
Similar results can be observed in Zavala and Biegler (2009) on the NMPC
performance in the presence of fouling inside a LDPE tubular reactor. Hence, the
controllers are proven to be able to accommodate a certain degree of fouling inside the
reactor.

147

Figure 4.52 Performance comparison of fouling effect in LDPE tubular reactor
using NWMPC and SSMPC (a) MFI (b) CTA flow rate

Figure 4.53 Performance comparison of fouling effect in LDPE tubular reactor
using NWMPC and SSMPC (a) LDPE conversion (b) initiator 2 flow rate (c)
initiator 1 flow rate
148

4.5.4(h) Robustness Test 2: Heat of polymerization

The effect of the heat of polymerization (HOP) increment is presented in Figure
4.54 and Figure 4.55. Based on the observation, the value of the initial process output
(i.e., CV) has changed from its original steady state value. This is due to the limitation
of the Aspen Plus model when changing the uncertainty parameters such as heat
transfer coefficient (HTC), heat of polymerization, and initiator efficiency. These
parameters need to be changed at the initial stage before running the simulation. Thus,
when changing these parameters, the system’s initial condition (i.e., steady state) is
inevitably shifted to a new steady state. This explains the new initial condition for the
MFI and the LDPE conversion, as seen in Figure 4.54, Figure 4.55, Figure 4.56, and
Figure 4.57. After running the closed-loop simulation, the controllers would take the
necessary action to bring the CVs to the desired setpoint.

From Figure 4.54(a) and Figure 4.55(a), the increase of the HOP has made the
polymerization process to converge to a new steady state for both process outputs,
which are MFI 3.9 (previously MFI 2.2) and LDPE conversion of 0.27 kg/kg
(previously conversion = 0.3). However, both the controllers have succeeded in
reaching the targeted set points, with the NWMPC reacting faster than the SSMPC in
both cases. This situation can be verified by the faster and larger controller action
employed by the NWMPC in Figure 4.54(b), Figure 4.55(b), and Figure 4.55(c)
compared to the SSMPC. The results correspond with the error analysis in which the
NWMPC produced an ISE value of 3.003 for MFI and an ISE value of 0.046 for
conversion, while the SSMPC yielded an ISE value of 5.213 for MFI and an ISE value
of 0.051 for LDPE conversion. Based on this, the controller’s ability in adapting to the
changes of the HOP in the LDPE polymerization process is proven.

149

Figure 4.54 Performance comparison of the heat of polymerization effect in LDPE
tubular reactor using NWMPC and SSMPC (a) MFI (b) CTA flow rate

Figure 4.55 Performance comparison of heat of polymerization effect in LDPE
tubular reactor using NWMPC and SSMPC (a) LDPE conversion (b) initiator 2 flow

rate (c) initiator 1 flow rate
150

4.5.4(i) Robustness Test 3: Initiator efficiency
Figure 4.56 and Figure 4.57 reveal the closed-loop performance of the reduced

initiator efficiency in the LDPE polymerization process. Like the previous test in
section 4.5.4(h), a change in the reactor design parameter would affect the reactor’s
steady state condition. Based on Figure 4.56(a) and Figure 4.57(a), the new nominal
MFI is increased from 2.2 g/10min to 4 g/10min, and the new nominal conversion is
dropped from 0.3 kg/kg to 0.295 kg/kg. From the figures, both controllers have
managed to bring back the process outputs towards the desired set points, with the
NWMPC outperforming the SSMPC in terms of faster setting time and less overshoot.
In Figure 4.56(a), both the controllers have responded promptly by lowering the CTA
flow rate (refer to Figure 4.56(b)) to reduce the MFI. Likewise, both the controllers
also increased the initiator 2 flow rate (refer to Figure 4.57(b)) to increase the LDPE
conversion to meet the target, as shown in Figure 4.57(a).

However, compared to the SSMPC, the NWMPC has rapidly increased
initiator 1 flow rate (refer to Figure 4.57(c)), which helps the controller to achieve an
improved MFI and LDPE conversion profile performance. This can be backed by the
error analysis, which shows the NWMPC has performed better with an ISE value of
14.073 for the MFI and an ISE value of 0.008 for conversion compared to the SSMPC
with an ISE value of 20.054 for the MFI and an ISE value of 0.010 for conversion.
Similar NMPC robustness results can be observed in Shafiee et al. (2008).

151

Figure 4.56 Performance comparison of initiator efficiency effect in LDPE tubular
reactor using NWMPC and SSMPC (a) MFI (b) CTA flow rate

Figure 4.57 Performance comparison of initiator efficiency effect in LDPE tubular
reactor using NWMPC and SSMPC (a) LDPE conversion (b) initiator 2 flow rate (c)

initiator 1 flow rate
152

4.5.4(j) Performance remarks

The compilation of integral square error (ISE) results for both the controllers
is presented in Table 4.11. Based on the table, the NWMPC has outperformed the
SSMPC in grade transition, conversion change, disturbance rejection, and robustness
tests.

Table 4.11 Performance test results using NWMPC and SSMPC based on ISE

Tests CV NWMPC SSMPC
Grade transition CONV 0.009 0.013
High grade transition 43.2 88.1
Conversion change MFI 0.50 0.59
Disturbance rejection 1 CONV 1979 2078
Disturbance rejection 2 0.095 0.122
Disturbance rejection 3 MFI 72.98 76.05
Robustness test 1 CONV 0.003 0.006
Robustness test 2 4.36 6.35
Robustness test 3 MFI 0.004 0.021
CONV 2.14 5.36
0.002 0.005
MFI 11.12 26.45
CONV 0.017 0.018
0.23 1.18
MFI 0.046 0.051
CONV 3.00 5.21
0.008 0.010
MFI 14.07 20.05
CONV

MFI
CONV

MFI
CONV

MFI

153

The performance shown by the NWMPC is a fast and stable response during
tracking set points and rejecting disturbances while robust towards process
uncertainties. This verifies the advantage of a nonlinear MPC over a linear MPC in
terms of process modeling accuracy (Bindlish, 2015; Jacob and Dhib, 2012; Skålén et
al., 2016). Typically, a nonlinear model should be able to simulate any process with a
much higher accuracy than a linear model. Since the polymerization reactor commonly
exhibits nonlinear behaviors (Ray and Villa, 2000), the decision to apply nonlinear
modeling is well justified. During the tests, there are times that the NWMPC has made
control decisions that can help the controller achieve the target faster, especially when
dealing with a saturation effect. This kind of control decision makes the NWMPC more
compelling than the SSMPC for controlling high nonlinear processes.

Based on several control tests in section 4.5.4, both controllers can achieve
comparable performances. This situation can be explained by the same optimization
method employed by both the controllers, i.e., sequential quadratic programming
(SQP), which is commonly used with the nonlinear process. For the linear process,
quadratic programming (QP) is sufficient to solve the optimization problem (Seki et
al., 2001). However, in this work, SQP optimization is used with the SSMPC instead
of QP since it has been found that the latter method is unable to solve the LDPE
polymerization model by not fulfilling the Karush-Kuhn-Tucker (KKT) conditions.
The KKT conditions are necessary conditions that a solution to a general nonlinear
programming problem must satisfy, provided that the problem constraints satisfy a
regularity condition called constraint qualification. Thus, in this case, the SSMPC and
NWMPC use a similar optimization technique in the MPC controller. This can explain
the comparable performance of the SSMPC with the NWMPC at certain instances
during the tests.

154

4.5.5 Controller performances with delay
4.5.5(a) Bias update

The previous and corrected bias update scheme's performance is presented in
Figure 4.58 and Figure 4.59, respectively. In Figure 4.58, the previous bias update
scheme (Sharmin et al., 2006) is tested using the SSMPC in controlling a grade
transition operation from MFI 2.2 to MFI 5 with delayed measurement. The amount
of delay implemented in this work is ten minutes, as reported by Rallo et al. (2002).
Based on the figure, signal is the initial MFI output and +
signal is the MFI output after using a soft sensor. From the figure, it can be observed
that the existence of a delay in the closed-loop scheme has made the controller
response oscillatory and sluggish when the soft sensor is used. It is found that the
reason behind this poor performance originates from the bias update scheme. The
current bias update scheme only works for cases with continuous signal measurement
without delay. A delay in the update scheme can lead to a progressive error variance
in the output signal measurement (Quelhas and Pinto, 2009).

Figure 4.58 Close-loop grade transition test using delay measurement
155

Nonetheless, this matter can be solved by adding a correction factor (or weight
parameter) to update the bias scheme, as presented in Section 3.7.2. Figure 4.59 shows
the performance of the same grade transition operation using the corrected update
scheme. Based on the figure, the grade transition process has managed to be controlled
within the predetermined time with a smooth process response. Thus, it can be
concluded that the addition of the correction factor ( ) towards the previous update
scheme has managed to resolve the delayed signal issues (Quelhas and Pinto, 2009).
In addition, several values of are also evaluated to study its performances. According
to the test performance results in Figure 4.59, value of 0.2 is selected due to its fastest
response with the lowest deviation.

Figure 4.59 Comparison of the different correction factor for close-loop grade
transition test

156

4.5.5(b) Control performance evaluation
In this section, the performance of the NWMPC with a soft sensor (NWMPC-

SS) in handling delayed information is investigated. Figure 4.60 and Figure 4.61 show
the performance of the NWMPC and the NWMPC-SS in controlling a grade transition
operation with delayed outputs signal. The existence of a delay in the control loop can
cause instability to the current NWMPC, as it was previously tuned during normal
conditions. Thus, to adapt to the delay signal, the NWMPC is retuned using a heuristic
approach. The new tuning for NWMPC is P = {0.011; 0.02} and Q = {37.5; 30; 30}.

Based on Figure 4.60(a), the NWMPC-SS is able to track the MFI grade
transitions with a faster response and shorter settling time than the NWMPC. This can
be verified by the NWMPC-SS handling its MVs as observed in Figure 4.60(b), Figure
4.61(b), and Figure 4.61(c). By manipulating the CTA and initiator flow rates, the
NWMPC-SS can accomplish the grade transitions operation in a shorter time. The new
tuning has made the NWMPC response more sluggish with a considerable settling
time. In this case, the soft sensor model is able to provide a reliable estimation of the
polymer MFI in the absence of such information. This action helps the NWMPC-SS
controller to compute the correct controller action without the presence of a delay.
Based on error analysis, the ISE value using NWMPC-SS is 56.7, while the ISE value
using NWMPC is 484.7. In addition, the NWMPC and NWMPC-SS are able to
maintain the LDPE conversion at the desired target, as shown in Figure 4.61(a).

157

Figure 4.60 The NWMPC and NWMPC-SS comparison in controlling grade
transitions with delayed information: (a) MFI profile (b) CTA profile

Figure 4.61 The NWMPC and NWMPC-SS comparison in controlling grade
transitions with delayed information: (a) LDPE Conversion (b) initiator 2 flow rate

(c) initiator 1 flow rate
158

The conversion change results are shown in Figure 4.62 and Figure 4.63. The
LDPE conversion change test is performed at time 200 minutes after the LDPE
polymer has completely reached grade MFI 5. In this test, the LDPE conversion is
stepped up from the steady state condition at 0.3 to 0.33 and returned to 0.3. Based on
Figure 4.62(a) and Figure 4.63(a), the NWMPC-SS has demonstrated a good tracking
ability for the LDPE conversion change while maintaining the current polymer grade.
This is displayed by the swift and accurate NWMPC-SS controller action in controlling
both outputs, as shown in Figure 4.62(b), Figure 4.62(c), and Figure 4.63(b).
Meanwhile, the NWMPC only able to track the step-up profile and suffers an
oscillatory response during the step down in the conversion change test. Moreover, the
NWMPC has a slow capability in controlling the MFI profile during the conversion
change, as seen in Figure 4.63(a).

Based on the error analysis, the NWMPC-SS has produced the ISE value of
0.18 for conversion change and 89.5 for MFI control, while the NWMPC has produced
the ISE value of 2.46 and 542.8 for a similar test. In this test, the sudden changes in
the LDPE conversion value have generated a large excursion in the MFI profile. This
situation can be prevented by using a smaller magnitude of changes each time
conversion change is conducted.

159

Figure 4.62 The NWMPC and NWMPC-SS comparison in controlling conversion
changes with delayed information: (a) LDPE Conversion (b) initiator 2 flow rate (c)

initiator 1 flow rate

Figure 4.63 The NWMPC and NWMPC-SS comparison in controlling conversion
change with delayed information: (a) MFI profile (b) CTA profile
160

4.5.5(c) Performance with delay remarks
In industrial practice, process delay is a common problem (Wu et al., 2015),

which can create drawbacks for controller the performance. Based on the tests in the
previous section, it can be noted that the soft sensor model has played a significant role
in assisting the NWMPC controller in performing its tasks. This can be proven from
the performance difference between the NWMPC-SS and NWMPC in both the grade
transition and conversion change tests. The ability of the soft sensor model to provide
appropriate estimations of the process has provided the NWMPC-SS with accurate,
current information to make the proper control decision. The retuning of the NWMPC
has made the controller more robust but sluggish in handling the delayed measurement
in the control loop. Without retuning, the NWMPC control response would become
oscillatory and unstable when dealing with the delayed measurement in the control
loop.

Moreover, the update bias scheme’s application is able to update the current
signal with the updated information when available. Such practice can be observed in
the industry by using laboratory tests or analytical instrument results to update the
current process measurement. The selection of the correction factor (or weight
parameter) serves as an adaptive procedure to allow the soft sensor model to update its
estimation results using real measurement. However, the selection of the correction
factor needs to consider several performance test scenarios to produce a robust soft
sensor model.

161

CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions
The Neural Wiener MPC (NWMPC) development and performance evaluation

in controlling a high-pressure LDPE tubular reactor has been performed successfully.
Additionally, a soft sensor model has been developed and combined with the NWMPC
control scheme (NWMPC-SS) to handle delayed measurement issues in the plant. A
modification has been made to the soft sensor model’s bias update scheme, which has
enabled it to deal with lagged data updates properly. Thus, the application of the
NWMPC-SS in controlling the LDPE grade transitions and conversion changes with
delayed measurement in the control loop can be considered the main contribution of
this work. This new control scheme is significant since it would provide the necessary
stability in the control loop in the event of delayed measurement, without the need to
retune the controller.

In this study, the steady state and dynamics of the LDPE simulation model have
been developed successfully using Aspen Plus and Aspen Dynamic software. The
LDPE tubular reactor properties, polymerization mechanisms, and kinetic parameters
are adopted from the literature. The reactor temperature profile validation shows R2
value of 0.981, while the properties validation error for the LDPE conversion is 1.7%,
and the number average molecular weight is 0.8%. Thus, the overall model validation
results show that the simulation model performance is comparable to an industrial
LDPE tubular reactor. In addition, the dynamic LDPE model is embedded with a melt
flow index (MFI) equation, which can be used to estimate the polymer grade online.

Moreover, the nonlinear model identification process for the Neural Wiener
(NW) model has been achieved. The block-oriented NW model consists of dynamic

162

linear and static nonlinear blocks. The dynamic linear block is identified using state
space (SS) model identification, while the static nonlinear block is developed using
the neural network modeling technique. The SS model’s order is determined based on
Hankel singular values, and the NN number of hidden neurons is selected from the
iterative validation method. The developed NW model provides satisfactory regression
results with R2 values of 0.9889 and 0.9860 for the LDPE conversion and MFI profile,
respectively.

In order to overcome the delayed measurement issues in the control loop, a soft
sensor is developed, which can provide an estimation of the current process based on
the available process measurements. The selection for the soft sensor model input is
conducted in several steps, which includes data preprocessing, Pearson correlation
coefficient, and expert knowledge. The soft sensor is developed using Time Delay
Neural Network (TDNN) model based on multi-input single-output (MISO) scheme
to improve its accuracy. The soft sensor model validation results show the R2 value of
0.998 for estimating the MFI and R2 value of 0.999 for estimating LDPE conversion.
The high R2 values demonstrate the excellent accuracy of the developed soft sensor
model. A bias update mechanism is used to update the information from the delayed
measurements into the current signal online. A modification is made to the previous
bias update scheme (Sharmin et al., 2006) to include a correction factor to handle the
soft sensor’s instability during the signal update with delayed measurements.

A summary of the NWMPC and SSMPC integral squared error (ISE) analysis
is presented in Table 4.11. From the table, the NWMPC achieves better control
performance compared to the SSMPC in grade transition, conversion change,
disturbance rejection, and robustness tests. Hence, the nonlinear model application
improves the controller decision-making capability by providing a more

163

comprehensive insight into the current process. The NWMPC is evaluated with a delay
measurement signal to simulate an industrial setting. The delay is due to the location
of the MFI and LDPE conversion measurements, which are situated outside the
reactor. From the tests, the combination of the NWMPC with soft sensor (NWMPC-
SS) has effectively managed the delay measurement issue in the control loop.

Overall, the NWMPC has demonstrated a fast, stable, and robust response in
handling various control scenarios in the LDPE tubular reactor. The application of a
soft sensor model with the NWMPC has provided the controller the capability to
control the process despite the existence of measurement delays in the control loop.
The soft sensor model is added separately to the NWMPC control scheme, and it can
independently be operated if needed. The NWMPC-SS is demonstrated to be a reliable
control solution for the nonlinear process in the polymer industry with measurement
delay issues.

5.2 Recommendations for future research
The following recommendations are suggested for future research:

i. The selection of the correction factor for the bias update scheme should
consider all the available soft sensor model outputs. Thus, the selection needs
to be on an individual basis to provide a fair trade-off for the output variable
performance, especially for a multi-input multi-output (MIMO) system.

ii. The correlation equation used to estimate the LDPE melt flow index (MFI) was
based on the simulated polymer molecular weight and branching information
from the literature. However, in practice, the LDPE MFI information is
difficult to estimate directly since many factors influence it. Moreover, the
LDPE molecular weight information cannot be measured online and is

164

typically obtained using a detailed simulation model. Thus, to make the MFI
estimation more practical, such information needs to be acquired from
laboratory test results or analytical measurements.
iii. An industry's primary goal is to operate as close as possible to the point where
profit is maximum. Thus, using an economy MPC with an inherent profit-based
objective function gives better control of the LDPE process from an economic
point of view. The application of multiple objective functions can also help the
controller select the best control action with multiple considerations on process
safety, production rate, and energy saving.

165

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