J OURNAL OF FOREST PRODUCTS & INDUSTRIES, 2014, 3(3), 158-160 ISSN: 2325–4513( PRINT) ISSN 2325 - 453X (ONLINE )
Research Article 158
Multivariable Prediction Based Controller Design for Important
Controlled Variables of Wet End of Paper Machine
1
1
Pradeep Kumar Juneja , 2A. K. Ray*
School of Electronics, Graphic Era University, Dehradun, India
e-mail: pkj33dpt@iitr.ernet.in
2
Department of Paper Technology , IIT Roorkee,
(Received: March 23, 2014; Accepted: May 18, 2014)

Abstract— The implementation of retention control in the wet end
is important because of requirement of higher paper quality with
decreased basis weights. Multivariable control system with these
two controlled variables is considered in present case. As
experimental data on dynamics for this process is not available on
industrial scale, known dynamics is considered for analysis.
Controller for multivariable subsystem with retention and basis
weight in wet end paper machine as controlled variables have
been designed in the present work using Model Predictive Control
strategy. Controller is tested for its setpoint tracking, disturbance
rejection and robustness capabilities. Robustness issues are
investigated for the subsystem by evaluating the performance
after making perturbations in the original system. The response
exhibit excellent set point tracking and acceptable disturbance
rejection. Also there is not much adverse effect on the
performance because of model uncertainty and hence the
controller is robust.
Index Terms — Controller, MPC
multivariable transfer function model
strategy,
prediction,
I. INTRODUCTION
R
etention is a critical parameter used for quality
development for many industries. It is extremely important
for fiber processing industries like paper, textiles, polymer,
rubber, dye, pigment, asbestos etc., many metallurgical
industries in connection with filtration and separation of fillers
and fibers and waste water treatment for color and COD
retention by nanofiltration membranes, for desalination, and
inorganic and organic chemical industries.
In paper industry this parameter is of paramount importance for
paper quality development by better formation of fibrous mat
on wet end wire. It is an important factor in wet end control of a
paper machine.
As per definition, retention of a material is the fraction of that
material fed to the machine through the head box slice that is
retained in the paper sheet. Definitions of retention depend on
the specific types of materials retained on wire such as total
solids, filler, fines, retention aids, chemicals, sizing particles,
interfering substances and fibers. This is further defined based
on either overall retention, first pass retention, first pass total
solids retention or total solids retention, considering paper
located at pope reel at the dry end of the entire machine or paper
*Corresponding author e-mail: akrayfpt@iitr.ernet.in
web leaving the couch roll at the end of wet end formation
stage.
Retention is affected by many variables like retention aids,
stock pH values, stock flow rate, shear forces, pulp quality,
head box slice geometry, raw material contaminants, drainage,
machine speed and structure of white water system etc [1].
As the thick stock consistency, percent retention and white
water consistency are all interlinked; the variability of retention
strongly depends on variations in qualities of the thick stock
and recycled white water consistency [2].
The advanced consistency measurement methods used in
retention applications rely on a combination of optical
measurement principles including depolarization, absorption
and scattering [3].
To reduce variability of the output variables in the paper
machine, the physical properties of thick stock should be
constant. Fluctuations of the consistency, the fines content and
the dissolved solids generally cause variations in the first pass
retention and basis weight [4].
Rooke and Wang applied semi-physical method i.e. combined
neural network and physical model to the retention process in
papermaking. The retention included fines, fillers and fibers on
the papermaking wire [5].
Retention of individual components is close to constant over a
reasonable operating regime. The observed variation in total
retention was due to variations in the fines content and to a
smaller degree, variations in the fines retention [6].
The First Pass Retention monitoring and control is a vital part
of the paper machine control. It gives a practical indication of
the efficiency by which fine materials are retained in a web of
paper as it is being formed. It should have a steady value, and
that value should be high enough to avoid operational problems
or an excessively two-sided sheet. Some operational problems
that can be caused by its low values are increased frequency of
deposit problems, filling of wet-press felts, poor drainage, and
unsteady drainage rates and sheet moisture.
It is very important to control the white water consistency and
thus also the retention levels on paper machines. There are
many economic benefits derived from white water consistency
control including stabilization of paper machine operation.
Besides there are some other potential advantages, which
includes, improved operational stability and runnability of
paper machines, increased production of saleable paper, less
variation in white water, headbox ash consistencies, basis
weight, moisture and thickness, enhanced final product quality,
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J OURNAL OF FOREST PRODUCTS & INDUSTRIES, 2014, 3(3), 158-160 ISSN:2325–4513( PRINT) ISSN 2325 - 453X (ONLINE )
accurate retention aid dosage and better control and
understanding of the wet end dynamics.
In present analysis, MPC based controller is designed and
robustness issues are investigated for this subsystem by
evaluating the performance after making perturbations in the
original system.
II. MULTIVARIALE
FUNCTION
PROCESS
TRANSFER
Due to constant variations of all of the input variables during
paper production and the involvement of fluid dynamics during
the formation phase on the wire section, the system is dynamic,
nonlinear and stochastic. An added complexity is that the
retention is coupled strongly with other chemical systems in the
wet end, such as sizing and wet strength control systems. This
means that an accurate physical model of the retention process
is very difficult to obtain and as a result, model based feedback
control of retention has remained an unsolved problem.
Orccotoma et al [7] investigated the effect of disturbances on
the two output variables of paper machine with twin wire
formers, viz, basis weight and first pass retention by using the
concept of controllability. Time delays and high frequency
disturbances of the thick stock consistency were shown to
affect the process. First-pass retention is considered an
uncontrolled variable and found to be dependent on fines
content of the thick stock. Nonlinear processes such as, basis
weight and first pass retention can well be represented by linear
models. Non-linearity did not pose any significant error.
Figure 1: Plant outputs for Servo Response for Unit Step in fpr
set-point showing peak time and peak amplitude
IV. ROBUSTNESS ANALYSIS
The selected linearized multivariable process transfer function
model of the paper machine forming section is perturbed by
increasing all the values by 20% and the controleer designed
based on MPC strategy is analyzed for its setpoint tracking and
disturbance rejection capability.
III. MPC BASED CONTROLLER DESIGN
The controller for the selected subsystem is designed for
analyzing its set-point tracking, disturbance rejection and
robustness capability based on MPC strategy.
A. Servo response for unit step change in fpr set-point
For simulating this scenario, control interval is selected as 2
minutes. Weight is selected as 0 for both f and bw, 1 for fpr and
Rate weight is selected as 0.4 for fpr.
The set-point response for unit step change is shown in fig. 1.
The fpr response attains the steady state very soon at about 4
seconds. The response exhibits excellent set-point tracking.
B. Effect of unit step change in measured disturbance
A step change in the measured disturbance, Consistency, is
defined with Initial value = 0, Size = 1, Time = 0. All output
set-points set at zero.
From the plant output fig. 2, it can be inferred that the outputs
deviate very little from their set-points. Due to step change in
consistency variable, which is one of the measured disturbance
variable, there is a little deviation in the form of overshoot in
fpr of peak amplitude 0.26 units, which soon settle down in
about nine seconds.
Figure 2: plant outputs for feedforward response
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J OURNAL OF FOREST PRODUCTS & INDUSTRIES, 2014, 3(3), 158-160 ISSN:2325–4513( PRINT) ISSN 2325 - 453X (ONLINE )
A. Comparison of set-point responses for step change in fpr
The comparison of set-point responses for step change in fpr is
made for the original and the perturbed model. As shown in fig.
3, the set-point tracking for fpr slightly degrades for perturbed
system but both responses settles at approximately same time of
12 seconds with the peak time and peak amplitude same for
both the models.
V. CONCLUSION
Multivariable control system analysis of for first pass retention
and basis weight in wet end of paper machine is performed
using MPC strategy based controller design. Robustness issues
are investigated for the subsystems by evaluating the
performance after making perturbations in the original system.
The setpoint response for unit step change in fpr shows that the
fpr response attains the steady state very soon and the response
exhibits excellent setpoint tracking. Due to step change in
consistency variable, which is one of the measured disturbance
variable, there is a little deviation in the form of overshoot in
fpr of peak amplitude, which soon settle down.
The comparison of setpoint responses for step change in fpr is
made for the original and the perturbed model. The setpoint
tracking for fpr slightly degrades for perturbed system but both
responses settles at approximately same time. The comparison
of load responses for step change in consistency disturbance is
made for the original process model and the perturbed model.
From the comparison responses made by giving step change in
one of the measured disturbance, consistency for the original
process model and the perturbed model, the conclusion can be
made that the disturbance rejection improves for the perturbed
model.
Figure 3: Comparison of set-point responses for step change in
fpr for the original and the perturbed model
1.
B. Effect of perturbations on disturbance response
The comparison of disturbance responses for step change in
consistency disturbance is made for the original process model
and the perturbed model as shown in fig. 4.From the
comparison responses made by giving step change in one of the
measured disturbance, consistency for the original process
model and the perturbed model, the conclusion can be made
that the disturbance rejection improved for the perturbed
model.
2.
3.
4.
5.
6.
7.
Figure 4: Comparison of disturbance responses for step change
in consistency for the original and the perturbed model
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Wang, H., Wang A.P. and Duncan, S. R., Advanced
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Scott W.E., Principles of Wet End Chemistry, Tappi
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