A pulp mill benchmark problem for control: application of plantwide control design

A pulp mill benchmark problem for control: application ofplantwide control design

J.J. Castroa,1, F.J. Doyle IIIb,*aChemical Engineering Department, University of Delaware, Newark, DE 19711, USA

bChemical Engineering Department, University of California, Santa Barbara, CA 93106, USA

Abstract

A heuristic for design of plantwide control strategies is introduced and applied to the millwide control of a previously presentedpulp mill benchmark. Two control strategies (decentralized control and unit-based model predictive control) are compared

according to their capacity to reduce the total error and maximize the operating profits. The control strategies are studied throughclosed-loop simulations of the process including several disturbances and setpoint changes in the digester, oxygen reactor, bleachplant, recausticizing plant and lime kiln.

# 2003 Published by Elsevier Ltd.

Keywords: Plantwide control; Decentralized control; Model predictive control; Pulp mill

1. Introduction

The problem of plantwide control has attractedresearch attention for over 40 years. There have beenmany published contributions on plant-wide controldesign based on heuristics, mathematics, and processunderstanding. Buckley et al. [4] was a pioneer inplantwide control and proposed to divide the controlstructure synthesis into two stages: (i) material balancecontrol and inventory design (low frequency loops), and(ii) product quality control (high frequency loops).Umeda et al. [28] proposed a unit-based approach byfirst designing the best control structure for each indivi-dual unit and then combining all the structures togenerate the complete plantwide design. Morari et al.[18–20] presented a unified formulation for the problemof synthesizing control structures for chemical processesbased on a hierarchical partition of the process systemand feasibility analysis of the control structures. Priceand Georgakis [23] employed a tiered framework toclassify the control loops according to their importanceto reach a consistent structure. Skogestad and Post-lethwaite [27, pp. 397–448] provide an excellent discussionon the issues involved on the design of plantwide controlsystems. Luyben et al. [13] published a heuristic method,consisting of nine steps to hierarchically determine the

control structure. Recently, Zheng et al. [29] presented ahierarchical procedure for synthesizing optimal plant-wide control structures where alternative plantwidecontrol systems were synthesized and compared, basedon economics.Several authors have demonstrated applications of

plantwide control of chemical processes includingdecentralized control as well as centralized model-basedstrategies like Model Predictive Control (MPC). Luybenet al. [12,14] have studied plantwide control of severalindustrial processes using decentralized control. TheEastman challenge problem has been studied in detailby several authors including: McAvoy and Ye [16],Lyman and Georgakis [15], Kanadibhotla and Riggs [7],Banerjee and Arkun [3], and McAvoy et al. [17]. Ricker[25] applied nonlinear MPC with state estimation to theEastman problem and compared its performance withthe decentralized structure presented by McAvoy andYe [16]. In their work, MPC was shown to be superiorto decentralized SISO multi-loop strategies. Later,however, Ricker [24] presented a decentralized PI basedstrategy for the Eastman problem and concluded that awell designed decentralized control strategy gave similarperformance to the nonlinear centralized modelpredictive controller with state estimation.In the first part of this article, an industrial bench-

mark problem of a pulping process was described. Thebenchmark problem is based on a nonlinear dynamicmathematical model of an actual pulp mill process

0959-1524/03/$ - see front matter # 2003 Published by Elsevier Ltd.

doi:10.1016/S0959-1524(03)00012-X

Journal of Process Control 14 (2004) 329–347

www.elsevier.com/locate/jprocont

* Corresponding author.1 Present address: Weyerhaeuser Co. Valliant, OK 74764, USA.

http://www.elsevier.com/locate/jprocont/a4.3d

(including the fiberline and chemical recovery areas).The benchmark is applicable to several process systemsengineering objectives, including modeling, control,estimation and fault diagnosis. In this article, an appli-cation of plantwide control is presented. A heuristic fordesign of plantwide control strategies is introduced. Aplantwide control study of the process is presented witha comparison of decentralized control and unit-basedmodel predictive control (MPC). Both control strategiesare compared according to their capacity to reduce thetotal error and maximize the operating profits. Thecontrol strategies are analyzed through closed-loopsimulations of the process including several dis-turbances and setpoint changes in the digester, oxygenreactor, bleach plant, recausticizing plant and lime kiln.

2. Control structure design methodology

Plantwide control is commonly seen as composed ofthree main steps: (i) determination of control variables,manipulated variables and process measurements, (ii)control configuration, and (iii) controller selection anddesign [13]. The control configuration refers to deter-mining the interconnections between the process mea-surements/control variables and the manipulatedvariables. The controller selection and design involvesthe determination of control algorithm (SISO PID, cas-cade, multi variable model-based) as well as the con-troller parameters for closed-loop operation. Thesesteps could be addressed sequentially; however, all thesteps are closely related to each other as each step hasan effect on the others. In practical applications, it maybe necessary to go through several iterations beforedesigning the most effective plantwide control structureconfiguration.Many research contributions in plantwide control

have concentrated on the first two steps. A typicalsource of disagreement seems to lie in the last step(controller selection and design). Some researchersbelieve that decentralized SISO control loops are thebest strategy for an industrial plantwide process. Otherscontend that multivariable techniques like Model Pre-dictive Control have solved the issue of control con-figuration and controller selection/design altogether.The views on this subject are quite strong and severalpapers have been written claiming that MPC is superiorto decentralized control and vice versa. The problemwith pre-conceived ideas about controller selection anddesign is that it influences the first two steps of the con-trol structure design procedure. Some authors havedesigned plantwide control methodologies with theimplicit assumption that decentralized P/PI/PID con-trollers are used in the process. Others simply imple-ment centralized MPC controllers for control of alloutputs with all manipulated variables.

This section presents a plantwide control methodol-ogy where steps 2 and 3 are combined to simultaneouslydetermine the control configuration and the controllerselection based on closed-loop performance anddynamic economic performance. In the methodology,all the controlled variables are divided into three cate-gories: primary variables, secondary variables and eco-nomic variables. Secondary variables are controlled usingSISO control loops. Control of primary variables andeconomic variables may be accomplished by decentralizedcontrol, model-based control, or a combination of both.The methodology compares candidate designs on the

basis of closed-loop performance (measured by theabsolute error) and economic performance (maximizesthe profit or minimizes the cost). The methodology usesprocess knowledge and mathematical tools like RGA asa guide in control configuration design/controllerdesign. Plantwide control is an open-ended problem,therefore the control structure designs developed willrepresent possible solutions to the problem and not the‘‘optimal’’ solution.The following methodology was used to determine

several control strategies for plantwide control of thepulp mill process. The same strategy may be applied toa complete manufacturing process, a process area, or aunit operation. The procedure was divided in three parts(problem definition, control structure selection andcontroller design, closed-loop analysis). The followingsubsections detail each of the steps and the next sectiondescribes an application to the millwide control of thepulp mill model.

2.1. Problem definition

The purpose of this part is to obtain as much infor-mation as possible of the process to define the controlobjectives and determine the control variables, manipu-lated variables and any auxiliary measurements thatmay be used for state estimation or partial control. Thiswas divided into six separate steps.Step 1: Obtain information about the process objectives

and constraints. Before initiating work on the controlstructure design, is it necessary to obtain all informationrelevant to process control. The people involved in thecontrol structure design should have an intimateknowledge of the process, otherwise important variablesmight be omitted from the controller design. It isimportant to detail all the process constraints (safety,environmental and operational). Finally, the objectivesof the process (product quality, production rate, pro-duct grades, reactor yields) are specified. The processobjectives and constraints will determine the lower/upper bounds on the control variables as well as set-points on quality variables.Step 2: Determine the control variables and divide them

in two categories; primary variables (supervisory control)

330 J.J. Castro, F.J. Doyle III / Journal of Process Control 14 (2004) 329–347

and secondary variables (regulatory control). It isrecommended to use steps 3–8 from the plantwide con-trol design procedure by Luyben et al. [14] to determinethe control variables in the process. However, at thisstage, no attempt is made to pair control variables withmanipulated variables. This differs from the Luybenstrategy that was developed under the assumption thatSISO decentralized control would be used. Therefore, inthat strategy, as the control variables are identified theyare also paired with manipulated variables. This woulddefeat the purpose of the present analysis since it isdesired to determine multiple control configurationsinvolving SISO control as well as MIMO control.Separating control variables into primary and sec-

ondary is a subjective decision. Primary control vari-ables are usually related to product quality andproduction rate but may also include variables relatedto safety, environmental and operating constraints aswell as variables with rich dynamics and multivariableinteractions. Secondary control variables are usuallyrelated to level, pressure, and temperature control in theprocess and can be easily controlled with SISO PIDcontrollers.Primary variables are typically measured at slow

sampling rates (minutes to a few hours) and secondaryvariables at faster sampling rates (seconds to minutes).Primary variables may be sampled at fast rates (sec-onds) due to their impact on other variables. An exam-ple of this is product purity in distillation columns,where the column temperatures (measured at fastsampling rates) are typically used for product qualitycontrol.Table 1 lists some rules of thumb that may be used to

divide the variables into primary and secondary. Whenin doubt, it is always possible to classify a variable asprimary since it can later be considered secondary.This process can still be carried out in cases where

regulatory control and supervisory control are present.It is possible to discover variables that are not currentlycontrolled but should be and classify them as primary/secondary variables. Furthermore, some of the super-visory control loops can be opened to determine if it ispossible to improve the current control configuration.

Step 3: Postulate new control variables to improveeconomics. If the number of manipulated variablesavailable is greater than the number of primary vari-ables, it is possible to improve the economics of theprocess with the additional degrees of freedom (MV). Inthis case, new control variables are postulated toimprove process economics by specifying setpoints formake-up chemicals, utilities and if possible reactoryields. The extra degrees of freedom can be used to keepthese new control variables at their setpoints. However,at this point the only requirement is to postulate thenew economic control variables and their setpoints,without making input–output pairings. This will bedone later in the controller design.Step 4: Obtain information on available measurements

and determine the need for using auxiliary variables forstate estimation. This includes sampling rates andmeasurement delays. It is not uncommon to discoverthat measurements of primary variables have slow sam-pling rates. Under such circumstances, it is worthwhileto examine the possibility of using state estimation toobtain estimates of the primary variables at faster sam-pling rates. This is important to improve the performanceof any controller.Step 5: Determine the number and location of all the

manipulated variables. All the relevant manipulatedvariables must be counted, identified and located in theprocess. In most situations, existing processes willalready have regulatory and supervisory control loops.In this case the setpoints to the regulatory loops willbecome manipulated variables for plantwide controldesign. If some of the existing supervisory control loopsare opened, the corresponding manipulated variablesbecome available for control.Step 6: Obtain the best possible mathematical model of

the process. A mathematical model can be used todetermine input–output pairings for decentralized con-trol, to provide a model for modelbased controllers, andto test the different control strategies through open/closed loop simulations. The model can range from gaininformation (steady-state) to step response (empiricallinear dynamics) to a fundamental dynamic description.

2.2. Control structure selection and controller design

Step 1: Find the input–output pairings for decentralizedcontrol of the secondary variables and implement thoseloops in the process/process model. The input–outputpairings can be chosen on the basis of process knowl-edge, input–output gains, and RGA analysis. Whileextensions of the RGA exist for integrating andunstable processes [2,6], we advocate stabilizing suchloops prior to application of the standard RGA in thepresent strategy.After stabilizing the process, the input–output pair-

ings for the remaining secondary control variables are

Table 1

Rules for categorizing control variables

Secondary variables
Primary variables
Fast sampling
Slow sampling
Vessel level
Compositions
Pressure
Production rate
Temperature
Quality variables
Conductivity
Complex dynamics
Density

Flowrate

Open-loop unstable

Simple dynamics

J.J. Castro, F.J. Doyle III / Journal of Process Control 14 (2004) 329–347 331

obtained. Finally, the controller parameters are deter-mined and the secondary loops implemented in theprocess.The level in most storage vessels and some reactors

should be controlled with proportional (P) only control[14]. For reactors in which the residence time is critical,proportional integral control (PI) should be used.However, in such cases, it is important to use a largevalue for the integral time to avoid introducing highfrequency oscillations. It is important to recognize thatvessel level can either be controlled using an upstreamor a downstream flow by simply changing the sign of theproportional constant. While such a selection does notaffect the response for the level controllers, it has aneffect on the resulting control configuration. In parti-cular, the MV for production rate control is directlyrelated to the various MVs used to control the levels.Hence, for every combination of level control configur-ations, a different strategy is possible for productionrate control.For the other secondary variables, PI control is

recommended, or PID if the signal to noise ratio islarge. To determine the tuning parameters of such con-trollers, auto-relay control [1] can be used to find theultimate gain and period. Another possibility is to usethe IMC tuning rules [26] for first order plus time delaymodels to find the tuning parameters. However, thisrequires identifying first order plus time delay modelsfor all the input–output pairs.Step 2: Determine multiple strategies for the control of

the primary variables and economic variables. These mayinclude: decentralized control, MIMO for different unitoperations in combination with decentralized control,or MIMO controllers for all the primary and secondaryvariables.The purpose of this step is to enumerate different

candidate solutions to the plantwide control problem.This step includes both the determination of input–out-put pairings for control of the process and the controllerdesign.Initially, decentralized control should be considered

for all the control variables. This includes configur-ations like cascade control, ratio control, feedforwardcontrol, and model-based control provided the con-trollers are SISO controllers. The input–output pairingscan be determined using RGA analysis (steady-state/dynamic) as in Castro and Doyle [5]. This controlstrategy will then be used as the base case to considerthe application of advanced model based strategies forcontrol of the process.For the other candidate strategies, MIMO controllers

can be used to control all the primary variables andeconomic variables or a combination of MIMO con-trollers and decentralized SISO controllers can be used.An example of such control strategies would be to con-trol the process with several block based MPC

controllers and use decentralized control for the pri-mary/economic variables with minimal interactions. Anextreme alternative is to use centralized MPC for theentire process.

2.3. Closed-loop analysis

Step 1: Use closed-loop simulations to determine per-formance of the control configurations. The control stra-tegies are tested in closed-loop simulations using anonlinear model (if available) with pre-determined dis-turbance sets as well as setpoint changes. Performance isdetermined from graphical analysis of the primary vari-ables as a function of time and using two different per-formance measures; error improvement percent (EIP)and profit improvement percent (PIP). These are definedas follows:

IAE ¼X

k

r kð Þ � y kð Þ��

EIP ¼ 100IAEbase � IAEnew

IAEbaseTOP ¼

X

k

X

i

ciF i kð Þ ð1Þ

PIP ¼ 100TOPbase � TOPnew��

TOPbaseð2Þ

where ‘‘base’’ refers to the base case design and ‘‘new’’denotes an alternative design.IAE is the integral absolute error and it can be com-

puted for each of the outputs. The process setpoint isrepresented by r and the output by y. The performanceimprovement percent can be obtained for each of theoutputs. If the new control strategy is better than thebase control strategy (according to these measures), theEIP should be positive.TOP represents the total operating profit of the pro-

cess. It does not consider capital costs, costs from sal-aried personnel, and controller implementation/commissioning as well as other costs that are notdependent on production rates. Such costs are assumedto be constant for all the control strategies. Therefore,TOP represents the sum of all the costs of raw materials,utilities, and the profits made from sales of products.The coefficients ci, represent the cost/sales price per unitof measure (mass, volume, power, etc.) of utilities, raw-materials, penalties from environmental regulations orproduct quality violations, and products. F

-represents

the amounts of such materials, utilities and productsused or sold during process operation.Finally, PIP represents the profit improvement per-

cent that compares the increased profits between thebase control strategy and the new control strategy.Therefore, from an economical point of view, a positive


PIP means that the new control strategy increases theoperating profits.For purposes of this analysis, the base case should be

the existing plantwide control strategy implemented inthe process, otherwise, it should be the decentralizedstrategy. There are many possible control configurationalternatives for each control strategy (decentralized,unit-based MPC, centralized MPC). These are deter-mined by the implementation of the secondary variablescontrol as well as the decisions made for the primaryvariables. If multiple control configurations aredetermined for each of the three strategies, they shouldall be tested according to the performance measuresdescribed.Step 2: Make recommendations about which control

configuration should be implemented. A subjective deci-sion must be made about which control strategy shouldbe implemented. The scores in the EIP, and PIP may beused as a guide to determine which control strategy isthe best suited for control of the process. A good con-trol strategy should be able to reduce the error andimprove the process economics simultaneously.

3. Plantwide control of the pulp mill process

This section presents the application of the controldesign methodology described earlier for the control ofthe pulp mill benchmark presented in the first part ofthis article.

3.1. Problem definition

Step 1: The process constraints, quality requirements,production rates and product grades are described inTables 1–4 (first part of the article). There is only onegoal in every company and that is to make money.Therefore, the goal for the process is to produce pulp atthe desired brightness (according to the pulp grade) andproduction rates at a minimum cost.Step 2: As described above (Section 2), it was recom-

mended to use steps 3–8 of the Luyben et al. [13] plant-wide control design procedure to determine the controlvariables. The reader should bear in mind that such aprocedure is meant to design a complete control con-figuration of a plantwide process and not just to determinecontrol variables.From open-loop simulations, it was determined that

the temperature of the oxygen reactor washer filtratemust be controlled to maintain stability in the process.

Table 2

Secondary control-loops for the fiberline area

Loop
Output MV KC tI
1
12 5 1.132 2.5
2
13 7 1.132 2.5
3
14 8 1.132 2.5
4
15 4 0.755 2.5
5
17 10 0.020 2.2
6
18 11 0.090 2.2
7
20 14–15 0.050 1.0
8
21 17 0.450 120.0
9
23 22 1.500 3.0
10
25 25 1.500 3.0
11
27 9 1.000 13.0
12
28 31 �0.050 13.0
13
29 33 �0.050 13.0
14
30 72 0.13 13.0
15
31 19 0.050 13.0
16
32 30 0.040 13.0
17
33 28 0.12 13.0
18
34 18 �1.670-
19
35 36 �3.436 20.0
20
36 29 �0.069 1.0
21
37 37 1.000 30.0
22
38 38 �5.0
Table 3

Secondary control-loops for the chemical recovery area

Loop
Output MV KC tI
23
53 62 5.0 –
24
57 46 3.0
25
59 47 �0.15 44
26
60 50 �5.0 30
27
72 56 �1.0 44
28
73 60 �2.92 –
29
74 63 �2.92 –
30
76 71 0.1 5.0
31
78 70 0.16 2.2
32
82 55 �0.8 30
33
88 41 1.0 530
34
90 64 1.0 14.0
35
91 51 0.2 22
36
92 67 0.2 20
37
93 68 0.21 20
38
96 65 �0.0057 22
39
100 66 0.0812 22
40
101 49 0.2 2.2
Table 4

Control loops for the pulp mill primary variables

Loop
Output MV KC �I
41
3 1 0.01 44
42
5 Loop 3 setpoint �0.5 40
43
39 2 0.06 90
44
30 3 0.35 55
45
46
47
24 Loop 59 setpoint 0.09 70
48
49
44 42, 43 0.37 42.5
50
51
79 Loop 31 setpoint 0.16 2.2
52
81 Loop 30 setpoint 0.1 5.0
53

The oxidation of NaSH to Na2S2O3 in the oxygenreactor is exothermic and this heat of reaction must beremoved from the process. The hot filtrate from thepost-oxygen washer is used as wash liquor in the brownstock washing sections and the digester. This tempera-ture is open-loop unstable and must be controlled. Thisis achieved with a cooler using water to remove the heatof reaction and transferring it to utilities. Another tem-perature that must be controlled is the temperature ofliquor into the emcc cook zone of the Kamyr digester.The pulping reactions in the digester are exothermic andcreate an oscillating disturbance in the liquor tempera-ture which propagates through the process. Control ofthese two temperatures is essential for the stable oper-ation of the process. The other temperatures are con-trolled to remove thermal disturbances from the process.These temperatures do not affect the process stability butare important for the effective controllability of theprocess.The production rate of the process is the downstream

flowrate of pulp from the D2 bleaching tower. At thispoint, no manipulated variable is assigned for control ofthe production rate.From the point of view of quality control, Kappa no.

is a very important variable. Kappa no. is controlled atthe digester, the oxygen reactor, and the E bleachingtower. The most important quality variable is thebrightness of the product, which is measured at the dis-charge of the D2 bleaching tower. In the chemicalrecovery loop, the main quality variables are the limeresidual carbonate and the EA of the first causticizer.From an operational point of view, it is necessary tocontrol the [OH�] before the E washer to avoid pre-cipitation of the lignin. Additionally, it is necessary tocontrol the upstream consistency at the post-oxygenreactor washer. The oxygen reactor operates at highconsistency. In order to pump the pulp to the washer, itmust be diluted to the specified consistency. From anenvironmental point of view, it is necessary to controlthe kiln exhaust gas oxygen fraction so it does notviolate the lower limit.The process has several vessels that require level

(volume) control. Therefore, the level of every vessel iscontrolled. The process model used for dynamic simu-lations assumes perfect level control in the digester/impregnation vessel, the oxygen reactor, and the D1 andE bleaching towers. For all the other vessels, level con-trol is necessary. It is also assumed that the digester isunder perfect pressure control. The pressure in the oxy-gen reactor should be controlled to maintain the level ofdissolved oxygen for the delignification reactions. Thepulp mill process has several recycle streams. In order toprevent ‘‘snowball effects’’, some recycle streams werecontrolled.The concentrations of NaOH and NaSH must be

controlled to satisfy component balances in the process.

NaOH of the white liquor is controlled at the exit of thewhite liquor clarifier tank and NaSH is controlled at theexit of the smelt dissolving tank. The Ca(OH)2 of thelime mud before the kiln is controlled to balance thecalcium cycle and prevent over-liming.Finally, there are several variables that should be

controlled for the optimal operation of several unitoperations. The dilution factor is controlled in all thepulp washers of the fiberline process and the washliquor ratios are controlled in the dregs filter and thetwo lime mud filters. The residual EA in the upper andlower extract flows in the digester is controlled toimprove the strength properties of the pulp. When thoseconcentrations decrease, it is necessary to increase thecooking temperatures to achieve the required Kappa no.This affects the strength of the pulp fibers produced atthe digester blow line. The dissolved solids mass frac-tion in the black liquor leaving the evaporators mustalso be under control. Low solids content in the blackliquor decreases the efficiency in the recovery boiler, andhigh solids content causes fouling in the evaporatorswhich decreases the heat transfer coefficients. Finally,the density in the lower zone of the liquor clarifiers mustbe controlled to improve the efficiency of the settlingoperation and minimize soda looses. Tables 2–4 showall the control variables (primary and secondary) usedin the control studies, the input–output pairings (forSISO control), as well as, tuning of the controllers.Step 3: The simplest way to improve economics in the

fiber line is through heat integration. The exothermicheats of reaction in the digester and the oxygen reactorcan be used to minimize the steam usage in the digesterand/or the oxygen reactor. The steam used in the oxy-gen reactor is chosen as the variable to be minimized.Another variable to optimize is the makeup flowrate ofcaustic to the oxygen reactor.The oxygen fraction in the kiln stack gases can be

maintained near the lower limit. This reduces fuel usagein the kiln. The flowrate of fresh lime should be mini-mized by decreasing the residual carbonate in the limeand increasing the flowrate of lime mud fed to the kiln.Table 5 shows the list of variables that will be mini-mized by the plantwide strategies as well as the input–output pairings used for control.Step 4: Table 2 in the first part of this article shows

the different measurements available in the process withinformation on sampling times and measurement

Table 5

Control loops for the pulp mill economic variables

Loop
Economic variable MV Kc �I
64
MV12 12
65
MV14, MV15 Loop 19 setpoint �6.0 13
66
MV53 Loop 39 setpoint 0.7 160
67
MV71 Loop 51 setpoint – –

delays. For purposes of the control studies developed, itwill be assumed that on-line analyzers for Kappa no.,[OH�] in the E washer, and black liquor solids fractionare available. The concentrations of NaOH andNa2CO3 were estimated using on-line density and con-ductivity measurements in combination with off-linemeasurements (every 2 h).Step 5: The fiberline process has 38 manipulated

variables and the chemical recovery process has 44manipulated variables for a total of 82 manipulatedvariables that are available for control of the process.Tables 5–10 (first part of the article) show the list of allthe variables in the process. Figs. 2–9 (first part of thearticle) may be used to determine the location of all themanipulated variables. Most of the variables representvolumetric/mass flowrates of chemicals, steam andcooling water. Others represent revolutions per minute(rpm) for screw-type feeders.Step 6: A nonlinear model of the process (imple-

mented in MATLAB with SIMULINK) is used to gen-

erate dynamic linear models and test the differentcontrol strategies under closed-loop simulations.

3.2. Control structure selection and controller design

Step 1: The input–output pairings for the secondaryvariables can be determined from steady-state RGAanalysis. It is recommended that one stabilize the pro-cess to reach steady-state operation. This requiresdetermining a priori the input–output pairings for theunstable/integrating modes. These modes includeinventory control, temperature control for exothermicreactions and component balances in the process.Most of the vessels in the process require level con-

trol. This can be accomplished using upstream ordownstream flows to control level. Whenever possible,level should be controlled using P-only control. In thefiberline, the level in the storage tank and the D2 towerare controlled with the downstream flowrates of pulpfrom these vessels. The other vessels are assumed to beon perfect control. In the recausticizing/lime kiln areas,the levels of all the storage tanks were controlled usingthe incoming flowrates of liquor to the tanks. The flow-rates from the slakers/causticizers and clarifiers is byoverflow, therefore, perfect control is assumed for thesevessels. Proportional control was used in all the levelcontrol loops.

Table 6

MPC controller for digester and oxygen reactor (Ts=10, p=80, m=3)

�Y
Output
1.5
Production rate
1.5
Digester Kappa no.
0.75
Digester upper EA
0.75
Digester lower EA
1.0
O Kappa no.
0.0
O steam flow
0.0
Upper conductivity
0.0
Lower conductivity
�U
MV
30.0
Wood chips flowrate
20.0
WL flow (cook zone)
20.0
WL flow (wash zone)
20.0
Loop 1 setpoint
10.0
Loop 2 setpoint
10.0
Loop 3 setpoint
10.0
Loop 58 setpoint
10.0
O caustic flow
10.0
Loop 19 setpoint
10.0
Loop 18 setpoint
10.0
Loop 22 setpoint
Table 7

MPC controller for bleach plant (Ts=10, p=50, m=3)

Gy
Output
1.0
E Kappa no.
1.0
E washer [0H1
1.0
D2 brightness
Gu
MV
10.0
Loop 59 setpoint
10.0
Loop 60 setpoint
10.0
Loop 61 setpoint
Table 8

MPC controller for evaporators and slaker temperature (Ts=5,

p=100, m=3)

Gy
Output
1.0
Black liquor solids%
1.0
Slaker temperature
0.0
GL cooler coolant flow
Gu
MV
5.0
Effects 1–2 steam flow)
5.0
Loop 26 setpoint
Table 9

MPC controller for lime kiln (Ts=5, p=100, m=3)

Gy
Output
1.0
Kiln O2 excess%
1.0
Kiln CaCO3 residual%
0.0
Fresh lime screw speed
0.0
Kiln fuel flow
0.0
Kiln air flow
Gu
MV
2.0
Loop 30 setpoint
2.0
Loop 31 setpoint
2.0
Loop 40 setpoint

The control strategy used for inventory control willhave direct implications for control of production ratein the process. Given the strategy used to control levelsin the fiberline, the only MV left for production ratecontrol is the flowrate of wood chips into the digester.An alternative strategy would be to control the levels ofthe storage tanks and the D2 tower using the incomingflowrates of pulp. The production rate would be con-trolled using the downstream flowrate of pulp from theD2 tower. Hence, the control of primary variables isaffected by the selections made to control the secondaryvariables. This implies that for different control con-figurations of the secondary variables, it is possible todesign different control strategies for the primary vari-ables, regardless of whether decentralized control, MPCor any other model-based controllers are used.The pressure in the oxygen reactor is also an unstable

mode. The pressure is controlled using the flowrate ofoxygen into the reactor with a PI control loop.The temperature of the post-oxygen washer filtrate is

an unstable mode and must be controlled. There is afiltrate cooler installed in the process. Therefore, theflowrate of coolant to the cooler is used to control thefiltrate temperature. The exothermic heat of reactionduring delignification in the Kamyr digester createsoscillations in the emcc liquor temperature. This is notan unstable mode; however, it produces sustained oscil-lations that complicate any type of dynamic/steady-state analysis of the process. There are several steamheaters installed in the digester and one of these is usedto heat-up the liquor before entering the emcc zone.Therefore, the flowrate of steam into the heater is used

to control the emcc temperature. Open-loop simulationsof the heater and the cooler were used to determinetuning parameters for those temperature PI controlloops.Next, the component balances for NaOH, NaSH and

Ca(OH)2 are controlled. The EA of white liquor afterthe clarifier is controlled using the make-up flow ofNaOH. The concentration of NaSH after the smelt dis-solving tank is controlled using the addition of salt-cake(Na2SO4) in the evaporator plant. Finally, Ca(OH)2 iscontrolled by manipulating the stoichiometric ratio ofNa2CO3 to Ca(OH)2 necessary for the causticizingreaction. This is done taking into consideration themass of CaO and Ca(OH)2 present in the reburned limeand calculating the amount of fresh lime necessary tomaintain the stoichiometric ratio.After all the unstable modes have been stabilized, it is

possible to calculate the steady-state input–output gainsof the process and the RGA. From these, the input–output pairings for the rest of the secondary controlvariables can be determined. The control parameters forall the PI control loops are determined using an auto-relay controller or IMC tuning rules with first order plustime delay models for each loop. Tables 2 and 3 showsthe input–output pairings and the tuning parameters forall secondary control loops in the fiberline and chemicalrecovery areas.Step 2: Two different control configurations are cho-

sen for control of all the primary variables and the eco-nomic variables. These configurations include:decentralized control and unit-based MPC. The detailsof each strategy are provided in the following sections.Fig. 1 shows the RGA matrix when the outputs arechosen as the primary and economic variables, and theinputs are chosen as the manipulated variables that areconsidered relevant for control based on physical con-siderations. The inputs and outputs have been rear-ranged to make the matrix as close as possible to adiagonal matrix. A close examination of the RGAshows that there are three sub-blocks where MIMOinteractions are important. For the other variables, theRGA matrix is essentially diagonal. These sub-blockscorrespond to variables associated with the Kamyrdigester, the evaporators and the lime kiln/recausticiz-ing areas. In Castro and Doyle [5], it was shown that thefiberline process was mostly diagonal with a block ofinteractions in the Kamyr digester. The integration ofthe chemical recovery loop shows the emergence of thelime kiln/causticizing loop and the evaporators asimportant blocks of interactions.

3.2.1. Decentralized control strategyFrom Fig. 1 and open-loop simulations, it can be seen

that interactions between the fiberline and the chemicalrecovery process are weak for the control configurationchosen for secondary variables. Changes in the fiberline

Table 10

Disturbance and setpoint sequence for closed-loop simulations

Time (min)
Event Value
0
Minimize O caustic flow �1.0
0
Kiln O2% �1.0
0
Kiln CaCO3% �1.0
0
Minimize O tower steam �1.0a
0
Minimize fresh lime �1.0a
500
Chips moisture �1.0
1500
Lignin density 1.0
1500
Cellulose density �1.0
2500
ClO2 composition �0.5
3400
Kiln O2% �1.125
3500
ClO2 composition 0.0
4500
Ambient T �1.0
4600
Slaker T 0.25
5000
Filters DR �1.0
5500
Production 1.0
6000
E Kappa no. �0.83
6100
E tower T 1.5
6090
D2 tower T 1.5
6090
D2 brightness 5.0
a For the decentralized strategy, unreachable setpoints were used to

minimize those variables. For the MPC strategy, weights were added

directly to the objective function.


may have an effect in the chemical recovery loop butchanges in the chemical recovery loop will not affect thedynamics of the fiberline significantly. This holds true aslong as the secondary control loops for NaSH andNaOH and dilution factor control for the post-oxygenwasher do not saturate.Hence, it was assumed that the analysis done in Cas-

tro and Doyle [5] to determine the configuration for

decentralized control of the fiberline holds true for con-trol of the fiberline process in the presence of the che-mical recovery process. Therefore, the control loopsused for decentralized control in the fiberline are thesame as described previously [5] with the followingexceptions.Previously, the production rate was controlled at the

digester blow line using the incoming wood chips

Fig. 1. Steady-state RGA matrix of the fiberline and chemical recovery areas: (a) two-dimensional RGA representation with indications of the

different unit operations, (b) three-dimensional RGA representation.


volumetric flowrate as the manipulated variable. Theproduction rate is now controlled at the exit of the D2

tower. The lower extract EA was previously controlledby a cascade using the mcc and emmc flows of WL tothe digester, now the combined flow of WL to thecounter-current zones of the digester is used as amanipulated variable and the ratio of mcc to emcc WLflows is kept constant. The pressure in the oxygen reac-tor is controlled using the flowrate of oxygen. Themathematical model used in Castro and Doyle [5]assumed perfect level control of the D2 tower. In thisstudy the D2 tower level (volume) is controlled using theD2 tower downstream volumetric flowrate. The setpointto the oxygen washer effluent temperature loop is usedto control steam usage. The O caustic makeup flow isminimized to its lower bound unless the O WL flowratereaches the lower bounds. The rest of the control vari-ables in the fiberline are controlled using the samestructure as that presented in Castro and Doyle [5].For control of the evaporators, there are four possible

manipulated variables that can be used for decentralizedcontrol. These include the steam flowrate to effects 1–3and the first dilution factor controller setpoint. This is acase where the RGA analysis is unable to provide agood recommendation of input–output pairings. TheRGA values between the black liquor solid fractionsand all these manipulated variables are all between 0.15and 0.41. However, from physical considerations, it isobvious that the steam flowrates should be the onlyvariables used for control of the black liquor solidsfraction. This reinforces the fact that mathematical toolsfor control structure selection are to be used only as aguide and process knowledge is essential. The steam flow

to the first and second effects is used as the manipulatedvariable and the same signal is sent to both valves.Hence, these valves behave as one valve from a processcontrol point of view.The temperature in the slaker is controlled with the

GL temperature setpoint (secondary loop) as themanipulated variable. This is the only manipulatedvariable with an RGA value close to unity. The setpointto the fresh lime ratio controller could also be used as amanipulated variable; however, the RGA value is morethan an order of magnitude smaller than unity.The control of EA at the causticizers and Ca(OH)2

concentration at the mud filter are not trivial problems.The most effective variable for control of these quan-tities is the setpoint to the fresh lime ratio controller.The problem arises because it is not possible to perfectlycontrol the stoichiometric ratio of Ca(OH)2 andNa2CO3. If the CaO added to the slaker exceeds thestoichiometric requirements, the concentration ofCa(OH)2 in the mud filter increases considerably but theeffect in the causticizer EA is insignificant. However, ifCaO is below the stoichiometric requirements, Ca(OH)2and EA will decrease simultaneously. From RGA stud-ies, it was seen that when control of Ca(OH)2 andcausticizer EA is done simultaneously, some of theRGA elements increase by an order of magnitude.Therefore, it is clear that both quantities cannot beeasily controlled with decentralized control. It wasdecided to control Ca(OH)2 using the ratio controller offresh lime to green liquor (with an RGA value of 1.15).As long as the Ca(OH)2 concentration is kept undercontrol, the EA is also controlled.From RGA analysis, the excess O2 fraction in the

stack gas at the kiln is controlled by manipulating thesetpoint to the BET controller (RGA value of 0.83).Similarly, the residual CaCO3 fraction in the lime iscontrolled manipulating the setpoint to the hot-limetemperature controller (RGA value of 0.95).The flowrate of fresh lime is controlled with the set-

point to one of the recycle flows in the chemical recov-ery loop (recycle 7 with a RGA value of 0.999).Furthermore, it is possible to decrease the fresh limeusage by decreasing the residual carbonate fraction inthe lime as much as possible. The make-up flow ofcaustic in the recovery loop is minimized with 0.94. Theflowrate of natural gas is not easy to control as it will bedirectly affected by the amount of lime processed in thekiln and the desired residual carbonate content. Aftertaking into consideration the remaining unpairedmanipulated variables, there are no suitable variablesleft to control the flowrate of natural gas withoutaffecting control of other variables. Therefore, the goalto minimize natural gas usage is to decrease the excessoxygen fraction as much as possible. This is usuallyachieved by controlling the oxygen to the lowest envir-onmental limit before NOx begins to form.

Table 11

Special loops in the pulp mill process: cascade, ratio, charge and

kappa factor

Loop
Variable MV Kc �I
54
Temcca Loop 2 setpoint �0.005 135
55
Tmcca Loop 1 setpoint �0.005 196
56
EA to wood ratio 2 – –
57
O Kappa factor 59 – –
58
D1 Kappa factor 20 – –
59
E Kappa factor 23 – –
60
D2 Kappa factor 26 – –
61
Ca to Na ratio 53 – –b
62
WL EA 58 – –c
a The purpose of this cascade arrangement is to control Temcc and

Tmcc to pre-determined values at steady-state, but use them as

manipulated variables for Kappa no. control during process dynamics.b To stabilize the process, the ratio of sodium to calcium is con-

trolled at the slaker. This is done by estimating the concentration of

Na2CO3 in the green liquor and calculating the required amount of

fresh lime.c WL EA is controlled by measuring the concentration of the wlc

EA and calculating the amount of caustic make-up necessary to

achieve the desired setpoint.


Tables 4 and 5 show the input-output pairings deter-mined for control of the primary variables and eco-nomic variables as well as the tuning parameters for therespective PI controllers. Table 11 shows the cascade,ratio, kappa factor, and charge control loops used toimprove dynamic performance of primary controllers.The controllers were tuned using two different meth-

ods. In the first method, process reaction curve proce-dures [21] and the IMC-based tuning rules [26] wereused to find the tuning parameters. In the secondmethod, an auto-relay controller [1] was used to obtainthe ultimate gain (Ku) and ultimate period (Pu) and thetuning rules from Luyben et al. [14] were used to obtainthe controller parameters.

3.2.2. Unit-based MPC with decentralized controlIn this configuration, the digester and oxygen reactor,

the bleach plant, the evaporators, and the lime kiln/recaust areas are controlled with one MPC control foreach of the areas for a total of four separate MPC con-trollers. The rest of the process is controlled usingdecentralized control loops as determined by the pre-vious input-output pairings. The selection of control

variables and manipulated variables as well as the par-tition into sub-blocks was based on the knowledge ofthe steady-state RGA from Fig. 1.Tables 6–9 show the control variables and manipu-

lated variables for each of the MPC controllers, theinput/output weights, and the sample time (T3),prediction horizon (p) and move horizon (m) for eachcontroller.As explained earlier, the residual calcium carbonate is

measured in the kiln every 2 h with a 2 h measurementdelay. Hence, the controller used for the lime kiln is amulti-rate MPC controller [8] that operates with twodifferent gains to update the model output predictionaccording to the measurements that are available atevery sampling instant. The controller has a basic timeunit [8] of 5 min. All the outputs (except for calciumcarbonate) are available at every 5 min. The controllerdetermines when the calcium carbonate sample is avail-able and uses a different gain to take into considerationthe measurement. Otherwise, the model prediction isnot updated with the measurement. The estimator gainhas the same form presented by Moran and Lee [9] forthe case of step disturbances with signal/noise filtering,

Fig. 2. Digester outputs closed-loop response: comparison of MPC and PI control; solid line (decentralized), dash (unit-based MPC).


Fig. 3. Bleach plant outputs closed-loop response: comparison of MPC and PI control; solid line (decentralized), dash (unit-based MPC).

Fig. 4. Chemical recovery miscellaneous outputs closed-loop response: comparison of MPC and PI control; solid line (decentralized), dash (unit-

based MPC).


therefore K1=diag[�1,. . .,�Ny] and K2=0. When the

carbonate measurement is not available �2=0, andwhen it is available, 0.04�241.0.

3.3. Closed-loop analysis

The following simulations employed the completenonlinear fundamental model to illustrate the perfor-mance of the decentralized control strategy and the

unit-based model predictive control strategy in closed-loop simulations with several unmeasured disturbancesand setpoint changes. The disturbance/setpointsequence used in all simulations is described in Table 10.Figs. 2–5 show the closed-loop simulations of key

variables in the process during the disturbances andsetpoint changes described above for both control stra-tegies (decentralized control and unit-based MPC).Under these conditions the PI controllers are able tomaintain all outputs within bounds, except for theexhaust gas O2 mass fraction in the lime kiln and the D2

tower brightness. An oxygen level of 1% is considered tobe the lower limit, therefore, during normal operation a

Fig. 5. Lime kiln outputs closed-loop response: comparison of MPC and PI control; solid line (decentralized), dash (unit-based MPC).

Table 12

Performance comparison for primary variables

Output
IAE EJP
SISO
MPC
Production rate
109.6 24.0 78.1
Digester Kappa no.
259.2 84.8 67.3
Digester upper EA
129.1 39.4 69.5
Digester lower EA
49.3 30.7 37.8
O Kappa no.
192.3 75.5 60.7
E Kappa no.
85.9 114.7 33.6
E washer [OH�]
100.2 60.4 39.7
D2 brightness
757.2 619.7 18.2
93.8 90.6 3.38
Slaker temperature
13.1 9.27 29.38
Kiln O2 excess
122.6 52.1 57.4
Kiln CaCO3 excess%
144.5 96.7 33.1
Lime mud Ca(OH)2 conc.
181.1 166.3 8.2
Table 13

Economic performance for decentralized control strategy of the pulp

mill process during the closed-loop simulations

Unit operation
Profit ($)
Digester
1,953,900
Brown stock
�21,695
Oxygen tower
�40,219
Bleach plant
�1,169,900
Evaporators
�108,380
Recausticizing
�62,160
Lime kiln
�42,9110
Total
528,230

violation of this constraint will trigger an alarm, as suchcondition will increase the amount of CO and NOx

produced. The D2 brightness has a quality requirementof �1% of the nominal value (setpoint). These con-straints are violated during the ClO2 disturbance. TheMPC strategy was able to maintain all the variableswithin the established bounds except for the digesterKappa no., the D2 brightness, lime kiln O2 percent, andthe black liquor solids%. In most cases, MPC was ableto recover and reach setpoint faster than the decen-tralized strategy and with a smaller total error.Simulations show that the MPC strategy was superior

[in reducing the IAE as described in Eq. (1)] than thedecentralized strategy. In most situations MPC was ableto obtain a EIP of 15–60% in total error when

compared to decentralized control. Table 12 shows theIAE and EIP for each of the primary outputs during theclosed-loop simulations.Tables 13 and 14 show the economic performance of

both control strategies during the closed-loop simula-tions. Table 11 (first part of the article) has the costs/prices of chemicals and utilities used in the economicanalysis. It was assumed that if the pulp brightnessexceeded �1% (brightness) of the setpoint, the pulpcould not be sold.From the economic results, it is seen that the MPC

strategy was able to improve profits by 30.9%. This ismostly due to the fact that the MPC strategy was able toperform the production rate and D2 brightness setpointchanges faster than the PI strategy which increased

Table 14

Economic performance for unit-based MPC of the pulp mill process

during the closed-loop simulations

Unit operation
Profit ($) PIP
Digester
1,957,600 18.5
Brown stock
�2060 5.05
Oxygen tower
�27,861 30.7
Bleach plant
�1,008,500 13.8
Evaporators
�116,430 �7.43
Recausticizing
�68,005 �9.4
Lime kiln
�43,267 �0.82
Total
691,410 30.9
Table 15

Comparison of PI tuning changes between decentralized strategies: the

old tuning corresponds to the original strategy and the new tuning

corresponds to the improved strategy

CV
Old tuning New tuning
Kc
�I Kc �I
Production rate
0.01 44 0.05 44
E Kappa no.
0.30 70 0.73 37.5
D2 brightness
0.03 90 0.2 25
Fig. 6. Digester outputs closed-loop response: comparison of MPC and PI control; solid line (improved decentralized), dash (improved unit-based

MPC).


Fig. 7. Bleach plant outputs closed-loop response: comparison of MPC and PI control; solid line (improved decentralized), dash (improved unit-

based MPC).

Fig. 8. Chemical recovery miscellaneous outputs closed-loop response: comparison of MPC and PI control; solid line (improved decentralized),

dash (improved unit-based MPC).


product sales and minimized the brightness penaltyduring grade transition. However, the economics of theprocess showed that the profits at the evaporators/recovery boiler were higher for the decentralized strat-egy than when using MPC. This was due to the fact thatthe digester MPC controller changes the production ratetoo quickly for the evaporator MPC controller to beable to reject the disturbance without violating (for ashort period of time) the lower limit. The decentralizedstrategy is slower in making the production rate changewhich gives time to the black liquor solids controller tokeep the output within its bounds. The production ratechange decreases the black liquor solids% exiting theevaporators which in turn minimizes the amount ofsteam produced at the recovery boiler which increasesthe cost. Therefore, while MPC has a smaller total errorthan the decentralized strategy, it gave a smaller profitcost than decentralized control.The lime kiln also showed better economics for the

decentralized strategy than the MPC strategy. When theoxygen setpoint was decreased, the decentralized strat-egy had a considerable undershoot and a slow responseto setpoint. Hence, a slower closed-loop performanceenabled the decentralized controllers to save costs onfuel (by having a low oxygen level). The MPC strategy isable to reach the setpoint faster than the decentralized

strategy and with minimum undershoot. Therefore, itwas not able to save fuel. This is an interesting case,where better control control resulted in higher costs.

3.3.1. Improved control designBoth control strategies can be improved with state-

estimation, feed-forward control or Smith predictors.For the decentralized strategy it is possible to add feed-forward action that accounts for the effect of woodchips flowrate changes to the black liquor solids%.Additionally, Smith-predictors can be used to controlthe bleach plant and minimize the transition betweenthe two different grades of pulp. It is possible to increasethe aggressiveness of the production rate controller;however, this will increase interactions among the othervariables in the digester and affect the performance ofthe Kappa no. controller. For the unit-based MPCstrategy it is possible to improve performance by usingmeasured disturbances and Kalman estimation. Theflowrate of wood chips can be considered a measureddisturbance for purposes of the evaporator MPC con-troller. Additionally a Kalman estimator can be usedwith the Kamyr digester to improve the controllerperformance for disturbance rejection.The decentralized control strategy was improved as

follows. The proportional gain of the production rate

Fig. 9. Lime Kiln outputs closed-loop response: comparison of MPC and PI control; solid line (improved decentralized), dash (improved unit-based

MPC).


controller was increased to minimize the transition timeduring production rate changes. A Smith-predictor wasadded for the E Kappa controller and the D2 brightnesscontroller to allow higher tuning in the PI controllers.Table 15 shows the changes in tuning for the decentralizedcontrol strategy.Finally, a feed-forward controller was added to com-

pensate for wood chips flowrate changes (measured dis-turbance) in the strong black liquor solids%. This was

done by modeling the response of the black liquor solidsto the wood chips flow as a first order plus time delaymodel and calculating the lead-lag parameters (seeOgunnaike [22, pp. 435–436]) to obtain Kff=�2.5,�=50, �=10, and �D=70.The MPC strategy was modified by adding a Kalman

estimator for the digester MPC controller to improvedisturbance rejection. Integrators were used to modelunmeasured disturbances for the digester and O towerKappa no., the upper/lower extract EA and the pro-duction rate. Two other unmeasured disturbances wereconsidered by including the dynamic models of thewood chips moisture (unmeasured disturbance) and lig-nin disturbances into the Kalman estimator calculationsand using the upper/lower extract conductivities as sec-ondary measurements for state estimation. The blackliquor evaporator MPC controller was modified toinclude the flowrate of wood chips as a measured dis-turbance to improve the MPC response during thechanges in production rate.Figs. 6–9 show the closed-loop simulations of key

variables using the two control strategies with theimprovements described earleir. Tables 16–18 show theresults of the EIP and PIP analysis. It can be seen thatMPC still has an advantage over decentralized controlwhen minimizing the total error for most of the vari-ables. For most variables (specially in the digester andlime kiln) MPC has an EIP between 20 and 60%.However, the economic advantages of MPC overdecentralized control have shrunk down to 3.68% dueto the superior performance of the improved decen-tralized strategy during pulp brightness setpoint changes.From the simulation results obtained, it is concluded

that both control strategies (decentralized control, unit-based MPC) are able to meet the operating objectives.Furthermore, the best control strategy seems to be usingone MPC controller for the digester (with state estima-tion) and one for the lime kiln, and decentralized con-trol (with Smith predictors for the bleach plant andfeed-forward control for the evaporators) for the rest ofthe process.

4. Conclusions

A heuristic was presented for the design of plantwidecontrol strategies. The heuristic was used to develop twodifferent control strategies for a previously presentedmillwide benchmark as an application in plantwidecontrol. These strategies included an application ofdecentralized control for the entire millwide process andmodel predictive control of several sub-blocks/unitoperations of the process. Both strategies included sev-eral regulatory loops as well as ratio control and Kappafactor control. For the MPC strategy, four controllerswere used to control the digester and the oxygen reactor,

Table 16

Performance comparison for primary variables for improved control

strategies

Output
IAE EIP
SISO
MPC
Production rate
75.5 33.3 56.6
Digester Kappa no.
302.6 128.6 57.5
Digester upper EA
131.7 56.5 57.2
Digester lower EA
53.1 50.5 5.0
O Kappa no.
145.5 85.9 40.9
E Kappa no.
71.9 83.8 �16.7
E washer [OH�]
82.3 43.1 47.6
D2 brightness
568.0 534.9 5.82
88.0 67.6 23.1
Slaker temperature
13.8 15.3 �10.3
Kiln O2 excess%
128.5 50.7 60.6
Kiln CaCO3 excess%
155.5 116.6 25.0
Lime mud Ca(OH)2 conc.
185.8 148.6 20.02
Table 17

Economic performance for improved decentralized control strategy of

the pulp mill process during the closed-loop simulations

Unit operation
Profit ($)
Digester
�801,530
Brown stock
�2,198
Oxygen tower
�25,749
Bleach plant
1,816,930
Evaporators
�116,100
Recausticizing
�66,998
Lime kiln
�43,243
Total
760,760
Table 18

Economic performance for improved unit-based MPC strategy of the

pulp mill process during the closed-loop simulations

Unit operation
Profit ($) PIP
Digester
�801,990 0.06
Brown stock
�2107 4.12
Oxygen tower
�26,351 �2.34
Bleach plant
1,845,840 7.97
Evaporators
�114,820 1.10
Recausticizing
�68,761 �2.63
Lime kiln
�43,018 0.52
Total
788,790 3.68

the bleach plant, the evaporators and the slaker tem-perature, and the lime kiln. The control strategies werecompared through several closed-loop simulations thatincluded disturbances in the digester, bleach plant, andchemical recovery section, as well as, several setpointchanges across different parts of the process.Simulations showed that pulp mill processes can

indeed be controlled with conventional decentralizedcontrol as well as with a combination of decentralizedcontrol and unit-based MPC. MPC was able to show aconsiderable reduction in the total error (as measuredby the EIP) over the decentralized control strategy formost of the outputs, as well as, increased profits of 30%above the decentralized strategy. However, there wereseveral cases (digester Kappa no. and black liquorsolids%) where MPC had a higher overshoot thandecentralized control (even though MPC had a smallerIAE than decentralized control).To improve the performance of the MPC strategy,

Kalman state estimation was used in the digester/Otower and the wood chips flowrate (MV) was used as ameasured disturbance for the evaporator plant MPCcontroller. The decentralized strategy was improved byincluding a Smith-predictor for control of the bleachplant E Kappa no. and D2 brightness and feedforwardcontrol for wood chips flow disturbance rejection in theevaporator. MPC continued to have an EIP between 20and 60% for most of the outputs; however, the PIP wasreduced from 31% down to 3.7%. It was shown that thebest control strategy for the process was to use MPC inthe digester/O tower and the lime kiln and decentralizedcontrol for the rest of the process. Furthermore, MPCshould be combined with a Kalman estimator (if possi-ble) for better disturbance rejection of the Kappa no. inthe digester.Loeblein and Perkins [10,11] have shown that control

structures that are considered ‘‘sub-optimal’’, whenstudied in isolation, can exhibit superior economic per-formance when integrated with a realtime optimization(RTO) system. Furthermore, the structure of the opti-mizer itself can influence the economic performance ofcontrol structures. The integration of RTO and plant-wide control design is an active area of research and it isnot considered in the plantwide design control heuristicpresented here.

Acknowledgements

The authors gratefully acknowledge the support ofthe National Science Foundation under Grant CTS9729782, the University of Delaware Process Controland Monitoring Consortium, and the University ofDelaware Presidential Fellowship.

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A pulp mill benchmark problem for control: application of plantwide control design

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