model predictive control (mpc) and its current issues in chemical engineering
TRANSCRIPT
This article was downloaded by: [University of Waikato]On: 14 July 2014, At: 00:41Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Chemical Engineering CommunicationsPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/gcec20
MODEL PREDICTIVE CONTROL (MPC)AND ITS CURRENT ISSUES IN CHEMICALENGINEERINGA. Senthil Kumar a & Zainal Ahmad aa School of Chemical Engineering, Universiti Sains Malaysia , PulauPinang , MalaysiaPublished online: 17 Feb 2012.
To cite this article: A. Senthil Kumar & Zainal Ahmad (2012) MODEL PREDICTIVE CONTROL (MPC)AND ITS CURRENT ISSUES IN CHEMICAL ENGINEERING, Chemical Engineering Communications, 199:4,472-511, DOI: 10.1080/00986445.2011.592446
To link to this article: http://dx.doi.org/10.1080/00986445.2011.592446
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
Model Predictive Control (MPC) and Its CurrentIssues in Chemical Engineering
A. SENTHIL KUMAR AND ZAINAL AHMAD
School of Chemical Engineering, Universiti Sains Malaysia,Pulau Pinang, Malaysia
Model predictive control (MPC) is one of the main process control techniquesexplored in the recent past; it is the amalgamation of different technologies usedto predict future control action and future control trajectories knowing the currentinput and output variables and the future control signals. It can be said that theMPC scheme is based on the explicit use of a process model and process measure-ments to generate values for process input as a solution of an on-line (real-time)optimization problem to predict future process behavior. There have been a numberof contributions in the field of nonlinear model–based predictive control dealing withissues like stability, efficient computation, optimization, constraints, and others.New developments in nonlinear MPC (NMPC) approaches come from resolvingvarious issues, from faster optimization methods to different process models. Thisarticle specifically deals with chemical engineering systems ranging from reactorsto distillation columns where MPC plays a role in the enhancement of the systems’performance.
Keywords Chemical processes; Model predictive control; Optimization
Introduction
Model predictive control (MPC), an important nonlinear control methodology, hascome a long way since its innovation almost five decades ago. Hussain (1999) carriedout an extensive review on model predictive control, and almost a decade later Qinand Badgwell carried out a survey on industrial MPC technology (Qin and Badgwell,2003). Even though several improvements and innovations have been made in thisarea, several issues still remain that have not been touched upon or addressed com-pletely. This article is not a review of the extensive literature that has been publishedduring the past decade on model predictive control, nor is it a general review ofmodel predictive control. This article deals with chemical engineering systemsranging from reactors to distillation columns where MPC plays a role in theenhancement of the systems’ performance. It begins with a brief introduction toMPC, followed by a discussion of the systems to which MPC has been applied byresearchers, which includes the work in brief, the hurdles they encountered, andhow they overcame them. Then follows the unanswered questions that remain in this
Address correspondence to Zainal Ahmad, School of Chemical Engineering, UniversitiSains Malaysia, Engineering Campus, Seri Ampangan, 14300 Nibong Tebal, Seberang PeraiSelatan, Pulau Pinang, Malaysia. E-mail: [email protected]
Chem. Eng. Comm., 199:472–511, 2012Copyright # Taylor & Francis Group, LLCISSN: 0098-6445 print=1563-5201 onlineDOI: 10.1080/00986445.2011.592446
472
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
field and the solutions to them. We close with a conclusion covering how MPC hasbeen so successful and what is awaiting us in the years to come.
Model predictive control is nothing but a combination of all the differenttechnologies to predict future control action and future control trajectories knowingcurrent input and output variables and future control signals. MPC has been popularsince 1963, and the reason for its increasing popularity is the simplicity of the algor-ithm and the use of the impulse and step response model, which, although possessingmany more parameters than the formulations in the state space or input-outputdomain, is usually preferred as being more intuitive and requiring less a priori infor-mation for its identification.
This article focuses on certain specific kinds of MPC that have proven to be use-ful in solving chemical engineering problems and gives detailed examples of applica-tions. As history has seen, in the use of MPC for various chemical engineeringapplications we come across systems ranging from chemical reactors to distillationcolumns to industrial packed bed reactors to fluid catalytic cracking units, and soforth. For the chemical processes, the use of MPC varies from edible oil refining pro-cesses to gas-liquid separation plants to air separation units to ball mill grindingcircuits. Even though there have been several individual reviews published onMPC, namely Froisy (2006) and Qin and Badgwell (2003), not many have actuallyfocused on the various chemical systems that have been used and what are those spe-cial features of MPC that make it a clear winner in the race towards perfect controlof systems.
When the work carried out on these systems is looked at, it is astonishing to seethat MPC has been so special in comparison to other control strategies that havealready been proposed or ones yet to be proposed. Several questions arise, namely,is MPC really a better option? If yes, what is its role and how has it been so success-ful? There are also questions like, what is MPC leading us to? and what does it havefor us in the near future? We also need to know the hurdles faced by researchers whohave opted for this strategy for the past several years and how they have overcomethese hurdles. Intending to answer these questions, a massive review was carried out,arriving at a few conclusions that are presented in this review.
Model predictive control, also referred to as moving horizon control or recedinghorizon control, is the control strategy that depends on empirical (measured or stan-dard) models and also many other models, in particular the mechanistic modelobtained by system identification. System identification refers to a process to obtaina model from a data measurement model used to predict output using input. Hence,model predictive controllers use the models and current plant measurements to pre-dict future control moves in input. The MPC then sends this set of control movesinto the controller.
The MPC structure can be summarised by the following steps:
. At each control interval t, the process output response is predicted p-steps aheadinto the future y (tþl), where l¼ 1, . . . , p. The prediction value y(tþl) depends onthe past actuation and the planned m-step ahead actuation:
½Duðtþ jÞ; j ¼ 1; . . . ; m� 1; m < p�
. The planned moves [Du(tþj), j¼ 1, . . . , m� 1] are calculated from minimizing aquadratic cost function. The cost function index incorporates the errors (the
MPC and Its Current Issues 473
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
difference between the future reference trajectory and the predicted processoutput) and actuation moves. Although the vector of future control moves iscalculated, only u(t) is applied to the process.
. The prediction is corrected at each stage by comparing the current measuredvalues and its predicted values through a filter. The above steps are repeatedat each control interval, and this is referred to as the receding horizon strategy,as shown in Figure 1.
In order to determine the optimal control solution in model predictive control,the model prediction must be propagated a number of steps into the future. The opti-mal control solution is then found by application of an appropriate optimizationroutine. As the size of the nonlinear system in question grows, computational speedbecomes more of an issue, especially for systems with fast sampling time require-ments. The alternative to solving the nonlinear optimization problem is to use anapproximation of the nonlinear model. The goal of approximation is to recast thenonlinear model in a linear form that closely matches the original system, while gain-ing computational savings associated with the simpler linear model. Common meth-ods of approximation include using multiple linear models to span the operatingspace. Nonlinear models lead to nonlinear prediction, but they need nonlinearoptimization; on-line model linearization is a hence a viable alternative.
Model predictive control is a multivariable control algorithm that uses:
. An internal dynamic model of the process,
. A history of past control moves, and
. An optimization cost function J over the receding prediction horizon to calculatethe optimum control moves.
The optimization cost function is given by:
J ¼XN
i¼1
wxiðri � xiÞ2þXN
i¼1
wxiDu2i ð1Þ
without violating constraints (low=high limits), with xi¼ i-th control variable (e.g.,measured temperature), ri¼ i-th reference variable (e.g., required temperature),ui¼ i-th manipulated variable (e.g., control valve), and wxi
¼weighting coefficientreflecting the relative importance of xi, t2E¼weighting coefficient penalizingrelative big changes in ui.
Figure 1. Receding horizon strategy (Mohammed and Abdulrahman, 2009).
474 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
MPC does not refer to a specific control strategy but to a very ample range ofcontrol methods that make explicit use of a model of the process to obtain thecontrol signal by minimizing an objective function. This objective or cost functionconsiders the deviations from a desired trajectory. An advantage of the MPCapproach is that to minimize the cost function, constraints can also be taken intoaccount. Therefore, the basic principle of MPC (Figure 2) (Findeisen and Allgower,2002) is to solve an open-loop optimal control problem at each time step. Feedbackis handled by updating the model at each time step. Normally the disturbance term iscorrected by using the measurements of the output at the current instant.
The ideas common to all predictive control strategies are:
. Explicit use of a model to predict the process output at future time instants(horizon).
. Calculation of a control sequence minimizing an objective function.
. Receding strategy, so that at each instant the horizon is displaced towards thefuture, which involves the application of the first control signal of the sequencecalculated at each step.
The differences between the various MPC algorithms are the models used to rep-resent the process, noise, the cost function to be minimized (Camacho and Bordons,1999). In classical MPC, the control action at each time step is obtained by solving anonline optimization problem. With a linear model, with polyhedral constraints and aquadratic cost, the resulting optimization problem is a quadratic program (QP). Solv-ing the QP using general-purpose methods can be slow, and this has traditionally lim-ited MPC to applications with slow dynamics, with sample times measured in secondsor minutes. One method for implementing fast MPC is to compute the solution of theQP explicitly as a function of the initial state; the control action is then implementedon-line in the form of a lookup table. The major drawback here is that the number ofentries in the table can grow exponentially with the horizon, state, and input dimen-sions, so that ‘‘explicit MPC’’ can be applied reliably only to small problems.
Figure 2. Block diagram of model predictive control system (Findeisen and Allgower, 2002).
MPC and Its Current Issues 475
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Optimization Problem
The term optimization implies a best value for some type of performance criterion.This performance criterion is known as an objective function (Wu, 2001). We firstdiscuss possible objective functions, then possible process models that can be usedfor MPC.
Here, there are several different choices for objectives functions. The first onethat comes to mind is a standard least-squares or ‘‘quadratic’’ objective function.The objective function is a ‘‘sum of squares’’ of the predicted errors (differencesbetween the set points and model-predicted outputs) and the control moves (changesin control action from step to step).
A quadratic objective function, for example, for a prediction horizon of 3 and acontrol horizon of 2, can be written as
U ¼ ðrkþ1 � yykþ1Þ2 þ ðrkþ2 � yykþ2Þ
2 þ ðrkþ3 � yykþ3Þ2 þ wDu2k þ wDu2kþ1 ð2Þ
where yy represents the model predicted output, r is the set point, Du is the change inmanipulated input from one sample to the next, w is a weight for the changes in themanipulated input, and the subscripts indicate the sample time (k is the current sam-ple time). For a prediction horizon of P and a control horizon of M, the least-squaresobjective function is written
U ¼XP
i¼1
ðrkþ1 � yykþiÞ2 þ w
XM�1
i¼0
Du2kþ1 ð3Þ
Another possible objective function is to simply take a sum of the absolute values ofthe predicted errors and control moves.
For a prediction horizon of 3 and a control horizon of 2, the absolute valueobjective function is
U ¼ jðrkþ1 � yykþ1Þj þ jðrkþ2 � yykþ2Þj þ jðrkþ3 � yykþ3Þj þ wjDukj þ wjDukþ1j ð4Þ
which has the following general form for a prediction horizon of P and a controlhorizon of M:
U ¼XP
i¼1
jðrkþi � yykþ1Þj þ wXM�1
i¼0
jDukþij ð5Þ
The optimization problem solved stated as a minimization of the objective function,obtained by adjusting M control moves, subject to modeling equations (equalityconstraints) and constraints on the inputs and outputs
Duk...min
DukþM�1
Uð6Þ
Minimization of objective functions by the least-squares method is by far themost common objective function in MPC. The least-squares method gives analyticalsolutions for unconstrained problems. It also compensates for relatively larger errorsmore than for smaller errors. The absolute value objective function is used in few
476 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
algorithms because linear programming problems result during optimization. Linearprogramming is frequently solved in large-scale allocation and scheduling problems.For an example, an oil company often uses linear programming to decide how to dis-tribute oil to various refineries. Also, linear programming is useful to decide howmuch and what product to produce at each plant. However, the linear programmingapproach is not useful for model predictive control because the manipulated variableoften moves from one extreme constraint to another.
Optimization Tools in MPC
Optimization provides a management tool for achieving the greatest possibleefficiency or profitability in the operation of any given production process. Changesin the operational environment, consisting of current constraints and values for thedisturbance variables, will inevitably alter the optimal position. Hence, the optimiz-ing control must be able to cope with change. The most difficult task in the design ofan optimization control system is the definition of the problem scope and thesubsequent choice of optimization tactics. The need for an on-line optimizing systemcan be ascertained only following an in-depth feasibility study. Process optimizationplays an important role in the efficient use of resources or the minimization ofundesired by-products in chemical engineering. Soft constraints allow for violationof process constraints, penalizing measurement limit violation in an attempt tokeep the process within specifications. Soft constraints significantly affect the con-troller objective function when the process output constraints are violated andavoid the creation of infeasible optimization problems. Adequate performance(minimal constraint violation) can be established by tightening the soft output con-straints to levels much higher than the actual constraint values. If both set-pointtracking and soft constraints are required for a measurement, a new process modelwith the measurement expressed twice can be used, once for enforcing soft con-straints and once for reference tracking. The soft constraints values for a measure-ment are not required to be equal to each other or the reference value. An MPCcontroller can be developed that explicitly accounts for process output controlobjectives. In most situations, specific control objectives are either satisfied ornot satisfied. Discrete (binary) variables can be used to represent the value ofcontrol objectives.
Linearization-Based MPC Solutions
Lack of online measurements and input constraints are two important problems thatare sometimes neglected in academic studies. Most nonlinear control techniques pro-posed are based on feedback linearization or MPC, or, a nonlinear model predictivecontrol based on a piecewise linear Wiener model. Automatic self-tuning within theregulation-optimization loop is not yet a common industrial practice, possiblybecause human supervisors are reluctant to accept automation systems that have ahidden logic. As a result, performance problems in the regulation layer prevent reap-ing most of the benefits of implementing real-time optimization. It is worth notingthat although a linear MPC can handle very efficiently issues such as loop interac-tion, constraints, and unknown delays, these types of controllers cannot deal success-fully with the problem of significant nonlinearities in process dynamics. On the otherhand, nonlinear MPCs (NMPCs) are still too complex and demand significant
MPC and Its Current Issues 477
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
computing power, which makes them impractical for industrial process controlapplications.
As an alternative, model predictive control philosophy can readily integratereduced-order process models that incorporate first principles to face nonlinearities.Yet the resulting controller is simple to analyze and implement in industrial controlsystems even with high sampling rates. The new form of nonlinear predictive control,called parametric predictive control (PPC), avoids the above problems (Assandriet al., 2004).
Advantages of MPC
Conventional controllers just make ad-hoc decisions regarding the current errorsignal, but the predictive controller considers future error signals as well to makea convenient decision. This in turn means that the common proportional-integral-derivative (PID) controller uses whatever error from set point as a reference foraction. MPC has low computational cost for solving the optimization problem inmodel development, while leading to a closed-form controller that is much easierto use than empirically tuning an auto-tuned PID. An attractive attribute of MPCtechnology is its ability to systematically account for process constraints. It has beensuccessfully applied to many various linear, nonlinear systems in process industriesand is becoming more widespread. The MPC’s ability to handle process controlproblems, namely multivariable dynamics, delays, and constraints, in a consistent,systematic manner makes it the one of the most accepted techniques for controllingmultivariable constrained systems. There are some features that individualize MPCin the field of control design, making it attractive. In contrast to other feedback con-trollers that calculate the control action based on present or past information, MPCdetermines the control action based on the prediction of future dynamics of the sys-tem. Due to the future prediction, early control action can be taken accounting forfuture behavior. MPC is able to obtain better control performance in the presence ofconstraints since it is able to determine the current control action for minimizing theerrors caused by constraints that are predicted to become active in the future. Thenumber of computed values in the manipulated variable sequence is finite (finiteinput horizon) and discrete in time, accounting for the fact that the involved optimi-zation problem can be solved with numerical methods.
Salient Features of MPC and Its Applications
A time-continuous approach can lead to extremely demanding numerical problems.Multivariable controllers are often the only solution able to provide desired controlperformance in the presence of interactions, and MPC can successfully handle suchcases. MPC has several interesting characteristics for this application, such as(Camacho and Bordons, 1999):
1. It can be used to control a great variety of processes, from those with relativelysimple dynamics to other more complex ones, including systems with long delays,nonminimum phase, or unstable ones.
2. It intrinsically has compensation for dead times.3. It introduces feed-forward control in a natural way to compensate for measurable
disturbances.
478 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
4. Its extension to the treatment of constraints is conceptually simple and this can beincluded systematically during the design process, etc.
Current Issues and Their Solutions Pertaining to Various ChemicalEngineering Systems
Predictive control, which is a useful advanced industrial control technique, has beenaccepted worldwide in recent years. It took more than 15 years after MPC appearedin industry as an effective means to cope with constraints on the state or control sig-nal control problems that its mathematical background appeared in a steady frame-work. The issues of feasibility of on-line optimization, stability, and performance areacceptably understood for systems described by linear models. Many challenges havebeen dealt with due to these issues for nonlinear systems as well, but there are manyquestions still remaining about practical applications. This review takes up the sys-tems listed below based on the manner in which MPC has been applied to each indi-vidual system and how the systems behave while giving the desired results so as tomake the modeling process easy and also overcoming the drawbacks that are gener-ally faced in other control technologies.
Potential Problems in Chemical Systems Involving MPC
In this section we present the issues faced by researchers in the past, and the corre-sponding solutions proposed by them are discussed in the section following, wherevarious chemical systems are discussed in detail.
An important obstacle in the operation of batch reactors that is blocking thewidespread use of NMPC is the computational complexity of the associated rigorousdynamic models, which comprise large sets of highly nonlinear differential andalgebraic equations (DAEs) that are an issue when larger and more sophisticatedprocess models are considered. Also, the question of closed-loop stability is of greatimportance. In continuous stirred tank reactors (CSTRs), the plants may be suffi-ciently nonlinear to hinder the successful application of linear MPC (LMPC). Theuse of NMPC for plant-wide control is problematic due to complications associatedwith dynamic modeling, state estimation, and on-line optimization. Large-scale non-linear models are extremely difficult to obtain using fundamental modeling andavailable techniques for empirical nonlinear modeling. Another complication is thatunmeasured state variables must be estimated from available on-line measurements.This requires the design of a nonlinear observer, which is a difficult task despiterecent advances. Even if a suitable nonlinear model is available, a nonlinear pro-gramming problem must be solved at each sampling period to generate the controlmoves. For large-scale systems the optimization problem may be computationallyintractable due to the large number of decision variables and the complexity ofthe constraints resulting from the nonlinear model equations. In case of tubular reac-tors the formulation of a meaningful objective function is not always easy in terms ofthe end use properties of produced products. The control system design andimplementation have to solve challenging tasks. The multivariable character of theprocess presenting strong interactions, the nonlinear behavior leading to the needfor nonlinear control, and the demand to operate the unit in the presence of materialand operating constraints are the main ones. Additionally, the control system has tocope with both large and short time constants and to face changing operating
MPC and Its Current Issues 479
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
conditions, in the presence of usually unmeasured disturbances. The conventionalMPC technique is not designed to exploit the periodic nature of repetitive processesand therefore lacks the ability to improve the control performance as runs arerepeated.
Issues and Their Solutions Pertaining to Various Chemical EngineeringSystems
Batch Reactors
Karer et al. (2007) and Causa et al. (2008) proposed formulations for a hybrid fuzzymodel; the former’s model was based on a hierarchical structure and can be writtenin a compact form, whereas the latter used the design of hybrid fuzzy predictive con-trol based on a genetic algorithm (GA) (HFPC-GA) on a batch reactor for which theprediction model is given by a nonlinear function as a T-S fuzzy hybrid model andthe manipulated variable and=or state variable are integer=discrete. Karer et al.(2007) introduced an efficient parameter-estimation method. They proved that ahybrid fuzzy model is suitable for implementation in the MPC of nonlinear hybridsystems with discrete inputs based on a reachability analysis. Their goal was to con-trol the temperature of the ingredients that were stirred in the reactor core so thatthey synthesized into the final product. The results suggest that by suitably determin-ing the cost function, satisfactory control can be attained, even when dealing withcomplex hybrid nonlinear-stiff systems such as batch reactors. Finally, a comparisonbetween MPC employing a hybrid linear model and a hybrid fuzzy model was made.Causa et al. (2008) used the simulation example of a real batch reactor. The resultsshowed that the computation time in the case of the GA remains constant during thewhole simulation.
Xaumier et al. (2002) used the DAE system that is solved over the predictionhorizon at each iterative step of the nonlinear programming (NLP) procedure forthe control of a reactive distillation column and for the control of a laboratory-scalefixed-bed water-gas shift reactor. Their main objective was to show experimentalresults of the application of such a technique on an industrial batch process: aglass-lined 16L reactor. Their results presented the time evolution of the reactor tem-perature, the temperature set point, and the manipulated variable corresponding tothe heat generation rate profiles and showed that each experiment corresponds to adifferent temperature set-point profile with the desired temperature of the reactionstep. They concluded that an estimation of the dynamic evolution of the heatgeneration rate over a past finite horizon will permit the addition of feed-forwardinformation in the predictions.
Bouchenchir et al. (2006) applied the predictive functional control (PFC) tech-nique to the temperature control of a chemical batch jacketed reactor equipped witha mono-fluid heating=cooling system. The issue they dealt was that batch andfed-batch reactors require good temperature control due to the existence of heat-sensitive chemical reactants and=or products and also to the dependency of reactionrate on temperature. They obtained experimental results for the temperature controlof an exothermic acid-base neutralization chemical reaction between hydrochloricacid (HCl) and sodium hydroxide (NaOH) to test the robustness of the controlsystem when the dynamics change over, due to heat release, during the constantset-point stage.
480 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Ruiz Massa and Ruiz Garcıa (2003) performed a feasibility study for theimplementation of an advanced control technique (predictive control for tempera-ture control for chemical reactors [PCR]) for a batch reactor for polyol production.Their main objective was to improve reactor temperature control. They found thatthe control technique they used suited the process equipment (heating and coolingsystem), so too much work was not necessary to adjust the parameters for all therecipes that run at the same reactor.
The solution to the problems faced by the above-mentioned systems is that thedevelopments in large-scale NLP algorithms and dynamic optimization strategieshave enabled NMPC to become an attractive alternative. Tables I–V highlight thebroad, extensive, and continuing increase in the application of model predictivecontrol approaches in many chemical process control applications, indicating theproblems and their corresponding solutions in each of the systems.
Continuous Stirred Tank Reactors (CSTRs)
Zhu (2001) presented a simple controller coordination strategy for plants that can bedecomposed into a single linear subsystem and a single nonlinear subsystem. Thecontrol objective was to regulate the reactor temperature by manipulating the cool-ant temperature, assuming the coolant jacket dynamics are negligible. Their problemwas that due to the strong reactor nonlinearities, the temperature tracking perfor-mance is very poor and the bottom mole fraction deviates significantly from itsset point. Hence they overcame this by applying a new class of plant-wide controlmethods based on integrating LMPC and NMPC.
Cormos et al. (2005) used a mathematical model of racemic pantolactone (or) a,c-dihydroxy-b, b-dimethyl-butyronitrile synthesis in order to have good control oftemperature in the two-stirred-tank reactor used. To achieve this, simulation wascarried out using the MATLAB Simulink software package. They used both PIDcontrollers and MPC controllers for the study of control of reactor temperature,and their comparison showed that with the MPC controller the cooling agent con-sumption was 8% lower than with the PID controllers. Also, they proved that thereactor temperature was better controlled by the MPC controller even when processdisturbances were present.
Wu (2001) used an extended form of a linear matrix inequality (LMI)-basedrobust MPC technique for a general class of uncertain linear systems with time-varying, linear fractional transformation (LFT) perturbations to study the con-strained control problem for an industrial CSTR. They used the general blockdiagonal scaling matrices corresponding to the structured uncertainty in the LMIoptimization to reduce its conservatism. Their simulation results supported theapplicability of this control technique to industrial problems. They also showed thatthe performance of robust MPC is closely related to the uncertain model derivedfrom an original nonlinear plant.
Akesson et al. (2006) used the approach studied by various researchers that isformulated for constrained MPC-type nonlinear optimal control problems withstructural constraints. They represented the control law with a feed-forward neuralnetwork with one hidden layer with hyperbolic tangent activation functions. Theirsimulation used two examples, namely the pH neutralization process and a simulatedmultivariable non-isothermal with continuous stirred tank reactor, applying anexplicit MPC scheme to the process by using a neural network to approximate the
MPC and Its Current Issues 481
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Table
I.Summary
ofmodel
predictivecontrolapproaches
inchem
icalsystem
s
Reference
Chem
icalsystem
MPC
approach
andproblem
Solution
Kareret
al.
(2007)
Batchreactor
Ahybridfuzzymodel.Goalwasto
control
thetemperature
oftheingredients
stirred
inthereactorcore
sothatthey
synthesize
into
thefinalproduct
Bysuitably
determiningthecost
function,
satisfactory
controlcanbeattained,even
when
dealingwithcomplexhybrid
nonlinear-stiffsystem
sXaumieretal.
(2002)
Batchreactor
Dynamic
model.Objectivewasto
show
experim
entalresultsoftheapplicationof
such
atechniqueonanindustrialbatch
process:aglass-lined
16Lreactor
Theirresultspresentedthetimeevolutionof
thereactortemperature,thetemperature
setpoint,andthemanipulatedvariable
correspondingto
theheatgenerationrate
profiles
Bouchenchir
etal.(2006)
Chem
icalbatch
jacketed
reactor
Batchreactors
requiregoodtemperature
controldueto
theexistence
of
heat-sensitivechem
icalreactants
and=or
products
Theevolutionofcontrolerrors
showsthatat
least
anadequate
model
forthebatch
reactorpermitsabettertemperature
control.
Causa
etal.
(2008)
Batchreactor
Hybridfuzzypredictivecontrolbasedona
GA
(HFPC-G
A).Thegoalwasto
control
thetemperature
oftheingredients
stirred
inthereactorcore
Computationtimein
thecase
oftheGA
remainsconstantduringthewhole
simulation
Ruiz
Massa
andRuiz
Garcıa
(2003)
Batchreactor
Toim
provereactortemperature
control
Deterim
ined
thatthecontroltechniqueused
suited
theprocess
equipment
Zhu(2001)
CSTR
Objectivewasto
regulate
thereactor
temperature
bymanipulatingthecoolant
temperature
Applicationofanew
class
ofplant-wide
controlmethodsbasedonintegrating
LMPC
andNMPC.
Corm
osand
Agach
(2005)
CSTR
Usedboth
PID
controllersandtheMPC
controllersforthestudyofcontrolof
reactortemperature
Showed
thatin
MPC
controller
thecooling
agentconsumptionwaslower
by8%
comparisonwiththePID
controllers
482
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Wu(2001)
CSTR
Usedextended
form
oflinearmatrix
inequality
(LMI)-basedrobust
MPC
technique
Sim
ulationresultssupported
the
applicabilityofthiscontroltechniqueto
industrialproblems
Akessonand
Toivonen
(2006)
CSTR
ExplicitMPC
Sim
ulationresultsshowed
thattheneural
network
controller
achieves
near-optimal
controlperform
ance
forvarious
disturbance
types
Silvaet
al.
(1999)
CSTR
MPC
usingthesimultaneo
ussolutionand
optimizationstrategy
Presentedasimplerform
ulationofthe
nonlinearprogrammingapproach
Lusson
Cervantes
etal.(2003)
CSTR
Presentedaparticularrealizationforthe
Wiener
model.Dealtwithproblem
of
uncertainty
characterizationfor
applicationin
analysisanddesignof
robust
system
s
Proved
thatrobust
WMPC
followstheset
pointbetterthantheother
controllers
Arefiet
al.
(2008)
Nonlinear
plug-flow
tabularreactor
Nonlinearmodelpredictivecontrolbasedon
classic
optimizationmethodswith
nonlinearidentificationusingWiener
model
Set-pointtrackingbehavioroftheregulator
(closed-loop)system
withNMPC,along
withthecoolantflow
signalwascompared
withthelinearMPC
andPIcontrollers;
theresultsprovethehigher
perform
ance
of
theNMPC
fordifferentoperating
conditions
Natarajan
andLee
(2000)
SMB
chromato-
graphysystem
State
space
model.to
solvetheproblem
of
significanttransienterrorcausedin
conventionalfeedback
controllers,like
PID
controllers
Repetitivemodel
predictivecontrol
(RMPC),whichisthecombinationof
repetitivecontrol(R
C)andmodel
predictivecontrol(M
PC)
Songet
al.
(2006)
SMB
Lumped
soliddiffusionmodel.
Multiple-inputmultiple-output(M
IMO)
controlproblem.
Objectivewasto
optimizetheprofitand
maintain
highproduct
purities
(Continued
)
483
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Table
I.Continued
Reference
Chem
icalsystem
MPC
approach
andproblem
Solution
Alamir
etal.
(2006)
SMB
Optimalcontrolproblem.Aim
ofthe
simulationwasto
assesstheflexibilityof
theproposedschem
e
Showed
how
thecontroller
takes
into
accountsudden
changes
inthefired
auxiliary
cost
andincreasesappropriately
thecorrespondingvalue
Shen
etal.
(2009)
Wastew
ater
treatm
ent
ThreedifferentkindsofMPC
strategies:
MPC
algorithms,aQDMC,andNLMPC
Allthemodel
predictivecontrollersperform
wellduringthefirstperiodofsteady
influent
Cristea
and
Agachi
(2006)
Wastew
ater
treatm
ent
First-principlesmodel
fordynamic
behavior
description
Objectivewasthemaintenance
ofthe
effluentsoluble
substrate
(pollutant)
concentration.Foundthattheset-point
trackingperform
ance
oftheMPC
control
approach
isalsoverygood
Holendaet
al.
(2008)
Wastew
ater
treatm
ent
Usedprocess
model
tomaintain
the
dissolved
oxygen
concentrationatagiven
level
Resultsshowed
thatlower
prediction
horizonreducedsignificantlytheintegral
ofabsolute
andsquare
error
Corriouand
Pons(2004)
Wastew
ater
treatm
ent
Extensionofdynamic
matrix
control
(QDMC).
Resultsshowed
thatin
theabsence
of
unmeasureddisturbances,
thecontroller
perform
edverywellandthesetpoints
werefollowed
withoutproblem
Mohammed
and
Abdulrah-
man(2009)
Wastew
ater
treatm
ent
Activesetmethod(projectionmethod)for
solvingthisQPproblem
Proved
thatMPC
algorithm
adapts
quickly
tochangingconditionsofthewatersupply
network
system
Ashoori
etal.
(2009)
Fed-batch
ferm
entor
Novelty
lies
intheinverse
ofpenicillin
concentrationasacost
function
Nonlinearmodel
issubstitutedwith
neuro-fuzzypiecewiselinearmodels
484
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Berenguel
etal.(2004)
Airlift
photo
bioreactors
Cost
effectivemodel
predictivecontrol
(MPC)strategy
Showed
theim
provem
ents
obtained
when
implementinganon-off
predictivecontrol
schem
eRamasamy
etal.(2005)
Nonlinear
continuous
ferm
entor
Showed
thatcontrolofabenchmark
system
,preventionofbatchmode,
and
minim
izationofwashoutoccurs
only
ina
narrow
operatingregion
Proved
thatanalysisofclosed-loop
trajectories
clearlyexplained
relation
betweenmanipulatedinputandsystem
behaviorfordifferentconditionsand
established
regionsforoptimum
controller
perform
ance
Kovarova-
Kovaret
al.
(2000)
Industrial
fed-batch
processes
Acombinationofpredictivecontroland
ANN
model
Showed
thatwithriboflavin
process
product
amountandproduct
yield
are
closely
connectedandcannotbeoptimized
separately
Srinivasarao
etal.(2007)
Fermenter
Apriorimodel
thatwastypicallydeveloped
from
firstprinciples
Sim
ulationresultsapplied
toaheater-mixer
setup.Developed
agreyboxmodelforthis
process
asabenchmark
forvalidatingthe
identified
models
Silvaand
Kwong
(1999)
Biochem
ical
process
control
Adaptiveschem
eADMC
(adaptivedynamic
matrix
control).Controller
objectivewas
tomaintain
productivityattheclosest
possible
desired
level
Maintained
ahighlevel
ofclosed-loop
perform
ance
intheservocontrolproblem
AlSeyaband
Cao(2006)
ALSTOM
gasifier
Developed
apartiallynonlinearWiener
type
model
Proved
thattheproposedcontroller
wasable
tocontroltheplantwithoutany
constraints
violation
YuandYu
(2007)
Chem
icalreactor
system
Designed
andim
plementedthree
decentralizedPID
controllersto
dem
onstrate
theim
provem
entin
on-line
controlperform
ance
usingtheNMPC
schem
ewithPLRBF
models
Resultsconfirm
edthatthecontrol
perform
ance
isnotsignificantly
deterioratedbythedisturbance
andthe
system
stabilityisalsowellmaintained
(Continued
)
485
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Table
I.Continued
Reference
Chem
icalsystem
MPC
approach
andproblem
Solution
Qianet
al.
(2007)
Chem
icalreactor
system
BP-A
RX
model
Resultsshowed
thatNMPC
basedon
BP-A
RX
model
provides
betterset-point
trackingthanRGPC
from
thepointof
quickly
respondto
set-pointchangeand
faster
settlingtime
Mahmoodi
etal.(2009)
pH
neutralization
process
MPC
basedWiener-Laguerre
model
Resultsproved
thatcomparedto
the
Laguerre
model
theWiener-Laguerre
model
modeled
thenonlineargain
better
Cristea
etal.
(2003)
UOPtypefluid
catalytic
crackingunit
(FCCU)
Three-lumpmodel
Resultsobtained
bydynamic
simulation
presentedagoodfitwithindustrial
operatingdata,simulatedvariablesbeing
situatedin
arangecorrespondingto
industrialunitbehavior
Jiaet
al.
(2003)
Fluidized
catalytic
crackingunit
(FCCU)
Objectivewasanadequately
reducedmodel
todescribeim
portantvariable
variations
likepressure
effectsanduse
of
oversimplified
kinetics
Controlobjectivewasto
maintain
the
controlled
variablesatpredetermined
set
points
inthepresence
oftypicalprocess
disturbances
Abou-Jeyab
(2001)
Distillation
column
Objectivewasto
maintain
theoptimum
operatingcondition
Linearprogramming(LP)form
ulationusing
asimplified
model
predictivecontrol
algorithm
Bloem
enetal.
(2001)
Moderate-to
high-purity
distillation
column
simulation
model.
Wiener
model–basedidentificationand
controltechnologyfordualcomposition
control
Resultsshowed
thatdifference
betweenthe
measure
outputandpredictedoutputis
hardly
distinguishable,indicatingWiener
model
isable
todescribeaccurately
the
behaviorofthedistillationcolumnin
aclosed-loopsetting
486
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Table
II.Summary
ofmodel
predictivecontrolapproaches
inbatchreactors
Reference
MPC
approach
andproblem
Solution
Mahfoufet
al.
(2002)
Takagi-Sugeno(T-S)fuzzymodel
Withdifferentfuzzypartitionsoftheinputspace
Bem
poradand
Morari(1999)
andBem
porad
etal.(2002a)
Predictivecontrolschem
eforhybridsystem
ssolved
byusingmixed
integer
quadraticprogramming
(MIQ
P).Themain
problem
withMIQ
Pisits
computationalcomplexity,whichincreasesthetime
required
tofindthesolution
Applied
toagas-supply
system
thatconsiders
quantizedmanipulatedvariables
Bem
poradet
al.
(2000)
Predictivecontroldesignforpiece-w
iseaffine(PWA)
system
s,astheseare
modelsfordescribingboth
nonlinearandhybridsystem
s
Reachabilityconditionsare
established.
Bem
poradet
al.
(2002b)
Hybridsystem
withthepredictivecontrolbasedona
quadraticobjectivefunctionandlinearconstraints
thatisasubclass
ofthemixed
logicaldynamical
(MLD)hybridsystem
Resultopensuptheuse
ofrobustnessandstability
toolsdeveloped
forhybridmodel
classes,to
study
theclosed-loopproperties
ofhybridpredictive
control.
Borrelliet
al.
(2003)and
Borrelli(2003)
Afinite-timeoptimalcontrolsolutionforPWA
system
swithaquadraticperform
ance
criterion
Controller
isbasedonadynamic
programming
recursionandamulti-parametricquadratic
programmingsolver.Thus,theoptimization
problem
issolved
foreach
partitionofthePWA
system
Baoticet
al.(2003)
Alinearcriterionfortheproposedalgorithm
Resultsin
reducedcomputationtime
Thomaset
al.
(2004)
Hybridpredictivecontroller
partitioningin
the
state-space
domain.In
everypartitionsome
variableschange,
whiletheothersremain
constant
Reducescomputationtime
(Continued
)
487
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Table
II.Continued
Reference
MPC
approach
andproblem
Solution
Beccutiet
al.(2003)
Hybridpredictiveapproach
basedonatemporal
decompositionschem
e.Duality
properties
are
used
totranslate
theoriginaloptimalcontrolproblem
into
atemporalsequence
ofindependentsub
problemswithasm
aller
dim
ension
Thissolutionapproxim
atestheoptimal,butthe
computationtimeissignificantlyreduced
Potocnik
etal.
(2004)
Hybridpredictivecontrolalgorithm
withdiscrete
inputs
basedonareachabilityanalysis
Computationtimeisreducedbybuildingand
pruninganevolutiontree
Skrjancet
al.
(2005)
Modelingandidentificationusingtheintervalfuzzy
model
(INFUMO)
Usefulfordescribingafamilyofuncertain
nonlinear
functionsorwhen
system
swithuncertain
physical
parametersare
observed
Nunez
etal.(2006)
Hybridpredictivecontrolstrategybasedonafuzzy
model.Thekey
elem
entofthefuzzyidentification
isthedetectionandestimationofsw
itchingregions
bycombiningfuzzyclusteringandaprincipal
componentanalysis
ThenonlinearNP-hard
optimizationproblem
was
solved
efficientlybyusingthegeneticalgorithms,in
term
sofaccuracy
andcomputationtime
Sarimveisand
Bafas(2003)
Toobtain
agoodsolutionin
areasonable
timefor
thefuzzypredictivecontroloptimizationproblem
SpecializedGA
optimizationmethodforfuzzy
predictivecontrolbasedonTakagi-Sugen
omodels
488
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
optimal MPC strategy for the former and both centralized and decentralized neuralnetwork model predictive controllers designed for the latter. Their inference was thatthe training of the decentralized neural network controllers proved to be moredemanding both computationally and with respect to the quality of training datarequired.
Silva et al. (1999) developed a new algorithm for model predictive control usingthe simultaneous solution and optimization strategy. Their objective was to present asimpler formulation of the nonlinear programming approach using a simultaneousstrategy. They simulated three control problems of continuously stirred tank
Table III. Summary of model predictive control approaches in fermenters
References MPC approach and problem Method and solution
Sheng et al. (2002) The state space formulation ofGPC
For nonuniformly sampleddata systems, whichinclude multi-ratesampled data systems as aspecial case
Amirthalingamand Lee (1999)
A method of identifying alinear fast rate modeltogether with a noise modelusing the sub-spaceidentification approach.
The identified model isfurther used to develop amulti-rate Kalman filterand an inferential linearMPC scheme
Li et al. (2001) Sub-space identification basedapproach
For developing adeterministic fast ratemodel from multi-ratesampled data
Wang et al. (2004) Fast rate model For the case where the inputand output sampling ratesare co-prime
Niemiec andKravaris (2002)
A multi-rate version ofnonlinear model algorithmiccontrol for regularlysampled multi-rate systems
Feedback linearization isused to induce linearclosed-loop input-outputbehavior, whichfacilitates the analysis ofclosed-loop stability andperformance in theabsence of plant modelmismatch
Niemiec et al.(2002)
Applicability of the approachon an experimental reactorsystem
Involving free radicalpolymerization
Prasad et al. (2002) Also applied multi-rateNMPC formulations
To control polymerizationprocesses
Gadkar et al.(2003)
Cybernetic model–basednonlinear multi-rate MPC.
Track the maximumachievable productivity ina continuous bioreactorwith cell recycle
MPC and Its Current Issues 489
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
reactors to demonstrate the effectiveness of the new algorithm. An adiabatic CSTRwith an exothermic, first-order irreversible reaction was used as a single-input, sin-gle-output (SISO) nonlinear process, a stirred tank reactor was used as an exampleof a multiple-input, multiple-output (MIMO) nonlinear process where in twoversions of the nonlinear MPC algorithm were considered, and finally a continuousfermenter subject to disturbances in the model parameters was simulated.
Lusson et al. (2003) presented a particular realization for the Wiener model,where the static gain is described by a piece-wise linear function (PWL). They pre-sented a strategy to identify Wiener models with PWL functions representing thenonlinear gain. A combination of dynamic as well as stationary data was then usedin the evaluation of the uncertainty bounds. They took up a CSTR as their casestudy. They studied the data distribution in order to estimate the generalizationproperties of the resulting model. From their results they proved that conservatismwas reduced. From the simulation results they proved that robust Wiener MPC(WMPC) follows the set point better than the other controllers.
Hahn et al. (2002) considered the simulation of two CSTRs that operate in seriesas the test system. They developed an MPC controller for each model, and theperformance of these controllers subjected to a set-point change and an output
Table IV. Summary of model predictive control approaches in pH neutralization
ReferencesMPC approach and
problem Method and solution
Su and McAvoy(1997)
Development of RNNmodels is considerablymore difficult thandevelopment of FNNmodels
Necessary to evolve a scheme for thedevelopment of a black-box modelin which the model structure can beselected relatively easily and theresulting model is valid over a wideoperating range
Dumont et al.(2004)
Model ofWiener-Laguerre typefor developing anadaptive predictivecontrol scheme
For controlling SISO nonlinearsystems
Sentoni et al.(1998)
Used ANNs For constructing a nonlinear stateoutput map.
Saha et al.(2004)
Model completely fails topredict the plantbehavior when thevalidation data set isused
Wiener-Laguerre model is used fornonlinear model predictive control.Wiener-Laguerre structureimproves the quality of modelingtogether with the rate ofconvergence of SQP in a reasonabletime. The performance of thecontroller based on the identifiedWiener-Laguerre model shows thatthis model presents betterprediction capabilities thna theidentified linear Laguerre model
490 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Table
V.Summary
ofmodel
predictivecontrolapproaches
indryingsystem
s
References
MPC
approach
andproblem
Solution
Meadowset
al.
(2003)
Populationbalance
model
foranon-isothermal
styreneem
ulsionpolymerizationsystem
Tem
perature
profileofthebatchaffectedthebreadth
ofthefinalPSD
alongwiththesurfactantfeed
tothesystem
.Designed
anoptimalcontroller
toachieveatarget
multim
odaldistributionby
manipulatingthetemperature
asamanipulated
variable
Flores-Cerrilloand
MacG
regor
(2003)
Combined
batch-to-batchandwithin-batchonline
controlapproaches
basedonapartialleast
squares
(PLS)model
forthecontrolofthewhole
PSD
ina
semi-batchstyreneem
ulsionpolymerizationsystem
Usedmidcoursecorrection(M
CC)strategiesin
aminim
um-variance
controller
framew
ork
with
batch-to-batchadaptationto
improvethe
perform
ance
ofthePLSmodel
thatpredictedthe
bim
odalend-pointdistribution.Testedthestrategy
forregulatingdisturbancesarisingfrom
uncertainties
inthenucleationstageandtracking
set-pointchanges
thatoccurred
duringthebatch
Park
etal.(2004)
MPC
controller
thatutilizesaPLSmodel.
Predictedtheend-pointbim
odalPSD
inan
experim
entalsemibatchem
ulsion
copolymerizationreactor.
(Continued
)
491
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Table
V.Continued
References
MPC
approach
andproblem
Solution
Alhamadet
al.
(2005)
Applied
adynamic
matrix
controller
(DMC)to
an
experim
entalstyrene=MMA
emulsion
copolymerizationsystem
.
Theaverageradius,particle
size
polydispersity
index
(PSPI),averagemolecularweight(M
n),and
monomer
conversionwereregulatedbytheDMC
totheiroptimaltrajectories.Theoptimal
trajectories
fortheoutputsweredetermined
bytw
oscenarios,
tomaxim
izePSPIandto
maxim
izeMn
Shiet
al.(2006)
Designed
model-basedcontrolalgorithmsfora
continuousandabatchcrystallizer,where
reduced-order
modelsbasedonmoments
ofthe
PSD
wereutilized.
Forthecontinuouscrystallizer,ahybridpredictive
controller
manipulatedthefeed
solute
concentrationto
regulate
thefirstfourmoments
of
thePSD
andthesolute
concentrationto
an
open-loopunstable
steadystate.In
theseeded
batchcrystallizer
case,anMPC
controller
was
designed
thatmanipulatedjacket
temperature
tominim
izethethirdmomentofthecrystalsform
edbynucleation
492
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
disturbance provides the basis for comparison. Their results proved that all fourmodels correctly predict the dynamic behavior of the volume. In all cases that wereevaluated both reduced nonlinear models provided a closer approximation to thesystem behavior than the linear model.
The solution to the problems faced by the above-mentioned systems is aplant-wide control strategy based on integrating LMPC and NMPC, which is thebest option to resolve the issue of decomposing the plant according to the degreeof nonlinearity.
Tubular Reactors (Wiener Digesters)
Wisnewski and Doyle (1998) applied MPC over a Kamyr digester, which is atwo-phase tubular reactor used for the kraft process to convert wood chips to pulpthrough reaction with a heated caustizing solution ‘‘white liquor.’’ Their objectivewas to minimize the variations of the kappa number, the measure of the residuallignin, the glue-like substance binding cellulose fiber together, in the presence ofmeasured and unmeasured disturbances. They used a Weyerhaeuser digester prob-lem (WDP), which is a simplified process model to capture the major dynamic char-acteristics of digester behavior. They used a robust selection procedure to select the‘‘best’’ manipulated input as well as the ‘‘best’’ set of secondary measurements forthe inferential control of the kappa number in the WDP. They compared the noisy,closed-loop kappa number using the modified continuous cool zone (mcc) trim flowrate as the manipulated variable and the secondary measurement set. They foundthat the use of either trim flow rate provides quick disturbance rejection andset-point tracking for the series of disturbances as well as maintains the kappa num-ber. They also noted that the danger of using the trim flow rates to control the kappanumber is that large countercurrent flows of the free liquor can cause the chip flowto stop, increasing their residence time and cooking the chips too long.
Arefi et al. (2008) used a nonlinear model predictive control based on classicoptimization methods with nonlinear identification using the Wiener model for ahighly nonlinear plug-flow tabular reactor. They proposed two methodologies fortemperature control of reactor, namely the direct Q model and HYSYS. Their aimwas to control the temperature of the output liquid of the reactor by manipulatingthe coolant flow. Set-point tracking behavior of the regulator (closed-loop) systemwith NMPC, along with the coolant flow signal, was compared with the linearMPC and PI controllers to find that the results prove the higher performance ofNMPC for different operating conditions, especially when it is far from the pointwhere the linear model is identified, thus concluding that the results showed thecapability of the proposed NMPC controller in rejecting unmeasured disturbances.
Simulated Moving Bed (SMB)
Natarajan and Lee (2000) used a state space model of a SMB chromatographysystem, which is a continuous periodic process. To solve the problem of significanttransient error caused in conventional feedback controllers like PID controllers ormodel predictive controllers due to non-minimum-phase dynamics and model errorsrun after run, they adopted repetitive model predictive control (RMPC), which is thecombination of repetitive control (RC) and model predictive control (MPC). Theirchallenge lay in modeling the complex hybrid dynamics of the process and using
MPC and Its Current Issues 493
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
an appropriate controller that makes use of the periodicity information of the pro-cess. Their objective for optimization was to maximize the product yield, which issubject to the constraints that express purity limits. Their results proved that the per-formance of the reduced order model is comparable with that of the original model.
Song et al. (2006) used an SMB process designed to simulate the solid phasemovement of the corresponding true moving bed (TMB) process, in which the fluidand solid phases flow countercurrently to each other. They preferred the ‘‘local equi-librium theory of chromatography.’’ They used the lumped solid diffusion model todescribe a standard SMB unit with four sections. A case study dealing with separationof the enantiomers of 1-1-bi-2-naphthol was considered with the first principles modelas the virtual process to generate input=output data to be used in process identifi-cation and to carry out simulation studies for the evaluation of the performance ofthe designed controller. Their main objective was to optimize profit and maintainhigh product purities. They evaluated the performance of the controller in two typicalcontrol problems of practical interest for the SMB process, namely, rejection of dis-turbances and tracking of set-point changes. They showed how the process can main-tain its productivity while solvent consumption continuously decreases, which bringsabout continuous reduction of extract and raffinate flow rates.
Erdem et al. (2006) proposed an on-line optimization-based SMB control schemethat allows exploiting the full economic potential of the SMB technology on the basisof minimal information. Their work addressed the experimental implementation of thedeveloped control concept on an eight-column four-section laboratory SMB unit thatis used to separate the binary mixture of nucleosides uridine and guanosine. Thereported results were aimed at demonstrating that the controller is able to deliver pro-ducts with specified purities and to optimize process performance despite uncertaintiesin system behavior and disturbances taking place during operation.
Alamir et al. (2006) used MPC to control the simulated moving bed (SMB) pro-cess by using feedback methodology. They had an optimal control problem that wassolved during the system lifetime in the sense that the iterations leading to its sol-ution are distributed in time. The aim of the simulation was to assess the flexibilityof the proposed scheme and its reactivity to sudden changes in the auxiliary costfunction. They showed how the controller takes into account sudden changes inthe fired auxiliary cost and increases appropriately the corresponding value whilekeeping the purities above the required set points. They also showed the high sensi-tivity of such high-separation SMB to model uncertainties and suggest using someon-line identification scheme in conjunction with the proposed control.
One of the aims is to reduce, during the sampling period, on-line calculation timedue to the optimization task resolution involved by the partial differential equation(PDE) model–based MPC strategy. Indeed, from a practical point of view, one of thedrawbacks of MPC is the computational time aspect, especially when the modelbecomes more complex and more accurate. Indeed, the model is intended to predictfuture dynamic behavior of the process output over a finite prediction horizon andhas to be solved during the on-line constrained optimization problem resolution.
Wastewater Treatment
Shen et al. (2009) aimed at considering a wastewater treatment plant in a large multi-variable frame subject to environmental and operational constraints rather than asingle problem such as dissolved oxygen control or nitrate control. They actually
494 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
used three different kinds of MPC strategies, namely the dynamic matrix control(DMC) algorithm without constraints, which represents the first generation ofMPC algorithms, a quadratic dynamic matrix controller (QDMC) version with hardlinear constraints, which is considered to be a representative of the second generationof the MPC algorithms, and an NLMPC version with hard constraints on the inputsand soft constraints on the outputs. The simulation results presented in this articleindicate that all the model predictive controllers perform well during the first periodof steady influent.
Cristea et al. (2006) used model predictive control on the activated sludge pro-cess in which biological treatment is to convert soluble organic contaminants intoinsoluble organic and inorganic constituents or to CO2 and H2O, specifically theway this control algorithm may be used for the control of a suspended growth aero-bic system. They used the first-principles model both for the dynamic behaviordescription of the unit and for building the simulator on which the model-based con-trol strategies were investigated. They found that the set-point tracking performanceof the MPC control approach is also very good.
Holenda et al. (2008) used a model predictive control to maintain the dissolvedoxygen concentration at a certain set point based on a linear state-space model of theaeration process. They chose two internationally accepted models to simulate theprocesses in the wastewater treatment plant. They used the process model to main-tain the dissolved oxygen concentration at a given level. A basic control strategy wasproposed to test the benchmark; the aim is to control the dissolved oxygen level inthe final compartment of the reactor by manipulation of the oxygen transfer coef-ficient. The results showed that a lower prediction horizon significantly reducedthe integral of absolute and square error; however, input weight had insignificanteffect on the error according the prediction horizon.
Corriou, and Pons (2004) used MPC to control a wastewater treatment plant.They proposed a benchmark that consists of the simulation environment defininga plant layout, a simulation model including influent loads, test procedures, andevaluation criteria. Their aim of the layout was C=N removal and was largely usedfor full-scale plants. It is composed of a biological reactor and a clarifier. The Inter-national Water Association (IWA) activated sludge model was chosen to simulatethe biological processes. Also, the double-exponential settling velocity model wasselected to describe the behavior of the clarifier. They used the extension of QDMC,and they obtained the results using benchmark FORTRAN implementation. Theirresults showed that in the absence of unmeasured disturbances, the controller per-formed very well and the set-points were followed without problem.
Mohammed and Abdulrahman (2009) had the objective of controlling a watersupply network system using MPC algorithm. They used the active set method (pro-jection method) for solving this quadratic programming (QP) problem supported inthe MATLAB software package due to its fast convergence. They developed anSISO linear model of a water supply system for the Gaziantep water supply system.Their results showed the closed-loop response of the output flow rate of the systemto a desired steady-state value. It was seen that the controller takes the systemresponse to the new values, but from their results the performance is comparable,finally proving that the MPC algorithm adapts quickly to changing conditions ofthe water supply network system. The MPC structure can be modified to meet poss-ible requirements concerning energy consumption and to handle the constraintsapplied to the system.
MPC and Its Current Issues 495
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Fermenters
Ashoori et al. (2009) used an unstructured model for penicillin production in afed-batch fermenter, applying MPC. Their novelty lies in the inverse of penicillinconcentration as a cost function instead of a common quadratic regulating one inan optimization block. They compared their results from the displayed controllerwith that of an auto-tuned PID controller used in previous works. Also, in orderto avoid high computational cost, the nonlinear model was substituted withneuro-fuzzy piecewise linear models obtained from a method called the locally linearmodel tree (LoLiMoT).
Berenguel et al. (2004) dealt with the implementation of a cost-effective MPCstrategy for closed airlift photo bioreactors used in the production of high-valuealgal products. Their objective was the control of pH of the culture by means of purecarbon dioxide injection for which the small range of flow injection values that pro-duce nonlinear behavior of the system that is not severe in such a way that a linearmodel of the pH evolution in spite of changes in CO2 injection and solar radiationwas obtained and used within an MPC framework to achieve desired regulationproperties, trying to minimize CO2 losses. Their results showed that the MPC controlalgorithm helps to reduce CO2 losses during daytime periods (with light) from 19.8%using on-off classical control to 5.5%, that is, a reduction of 75%.
Ramasamy et al. (2005) applied MPC to a model of a nonlinear continuous fer-menter. They showed that the control of a benchmark system, prevention of batchmode, and minimization of washout occur only in a narrow operating region. Theyfound from the time series response after implementing MPC on the bioreactor fromone initial condition that the system was successfully controlled to the specified setpoint. They inferred that the controlled bioreactor is not directly driven to therequired set point and also the nonlinearities associated with the system result ininefficient control, causing batch or washout conditions along the controlled systemresponse. This is confounded by the fact that most bioreactors, although assumed tobe homogeneous, actually exhibit large inhomogeneities. They finally proved thatanalysis of the closed-loop trajectories clearly explained the relation betweenmanipulated input and the system behavior for different conditions and establishedregions for optimum controller performance.
Kovarova-Kovar et al. (2000) used artificial neural networks (ANNs) for on-lineoptimization of industrial fed-batch processes. They used a combination of predic-tive control and an ANN model that was used to optimize the industrial fed-batchprocess for commercial production of riboflavin (vitamin B2) by a recombinantBacillus subtilis strain. They found that at the beginning of the fed-batch processthe specific riboflavin production rate and=or cell growth were maximized; later theirimpact diminishes in favor of riboflavin production. They showed that with the ribo-flavin process the product amount and the product yield are closely connected andcannot be optimized separately.
Srinivasarao et al. (2007) studied a process where the quality variables are mea-sured on-line, and time delays involved in the measurement assay are significantlylarge when compared to other process measurements (such as flows, level, tempera-tures, pressures, etc.) or the rate at which the manipulated input moves are alsomade. An a priori model that was typically developed from the first-principlesmodel, with the parameters of the noise model used as tuning knobs, could be a sol-ution but using the noise model parameters as tuning knobs can result in suboptimal
496 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
inter-sample estimation and poor quality of inferential control. Their results indi-cated that it is difficult to make a comparison between the performance of single-rateand proposed multi-rate NMPC on common ground. They gave their simulationresults applied to a heater-mixer setup. They developed a grey box model for thisprocess as a benchmark for validating the identified models.
Silva et al. (1999) used an adaptive scheme ADMC (adaptive dynamic matrixcontrol) to the biochemical process control for maintaining operational conditionsinside a specific optimum range for each process type, microorganism, and mediumsince it can identify the process on-line periodically under open- or closed-loop con-ditions. They used SQP (successive quadratic programming) in NMPC; two NMPCalgorithms and ADMC were applied to a continuous fermentation process whereproductivity is the controlled variable and feed substrate concentration is themanipulated variable. These three algorithms were compared with standard DMC.They used an SISO-type control problem for evaluation of the performance ofpredictive controllers. Their controller objective was to maintain productivity atthe closest possible desired level; the superiority of the nonlinear controllers and theirresults showed that controllers NMPC1 and NMPC2 presented different values forthe manipulated variable when compared to ADMC and DMC. They investigatedthe performance of controller NMPC2, a MIMO-type servo control problemwhere the control objective was to move the system from the given initial conditionto the optimum operational point; the results showed that NMPC2 maintained ahigh level of closed-loop performance in the servo control problem.
Bioprocesses have complicated dynamics, therefore their control is a challengingand delicate task; they also are inherently concerned with nonlinearity and arenon-stationary, which makes modeling and parameter estimation particularly diffi-cult. Moreover, the scarcity of on-line measurements of the component concentra-tions makes this task more sophisticated. Obtaining pure product is the main goalof control. MPC is feasible for on-line optimization and has acceptable performanceas well.
Chemical Reactors
Al Seyab and Cao (2006) used a nonlinear model predictive control based on theWiener model of the ALSTOM gasifier. They preferred a Wiener structure consistingof a linear MIMO state-space part followed by a partially nonlinear static part toidentify a black-box model of the gasifier plant. They showed that the plant=modelmismatch was further reduced by developing a partially nonlinear Wiener typemodel instead of a pure linear model. More specifically, a feed-forward neural net-work (FFNN) was developed as a nonlinear static gain for one of four outputchannels, fuel gas pressure (PGAS), to compensate for its strong nonlinear behaviorobserved in the open-loop simulation. Also, they proved that the proposed controllerwas able to control the plant without any constraint violations and satisfied all thebenchmark challenge requirements.
Yu and Yu (2007) used multiple-input single-output neural models with differentsample rates in model predictive control of a multivariable process, in order toreduce the number of optimized variables and consequently reduce the dimensionof optimization and computing load. They first used three multiple-input single-out-put pseudo linear radial basis function (PLRBF) models with each representing oneoutput followed by adopting a multi-rate control in the NMPC scheme to cope with
MPC and Its Current Issues 497
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
significant difference between dynamics for the three variables and a long trans-mission delay of the heating. They used a neural network model based an NMPCscheme to predict future process response over the specified horizon. On-line controlwas conducted to assess the NMPC control scheme for the same three aspects as inthe simulation. On-line tracking performance proved that the system was stable andtracking was achieved. The tracking results confirmed that the control performanceis not significantly deteriorated by the disturbance and system stability is also wellmaintained. It was finally shown that the overall performance of the multi-rateNMPC scheme based on PLRBF models was better than PID control.
Qian et al. (2007) proposed and elaborated a novel nonlinear dynamic model foruse in NMPC. The proposed model combines a second-order auto regressive withexternal input (ARX) model identified on-line by a recursive least-squares algorithm(RLS) and a BP (back-propagation) neural network trained offline, referred to as theBP-ARX model. They preferred using a three-layer BP network to represent the sys-tem static nonlinearity, where a nonlinear mapping between the system steady-stateinputs and outputs can be carried out using the static network without feedback ele-ments to describe the mapping. Their results showed that NMPC based on theBP-ARX model provides better set-point tracking than recursive generalized predic-tive control (RGPC) from the point of quickly responding to set-point change andfaster settling time. The control effects of NMPC and RGPC demonstrated thatNMPC can track the tank level faster and smoother, thus proving that NMPChas less fluctuation in manipulated variables than RGPC.
Solutions to the problems faced by the above-mentioned systems can be foundby using MPC As a consequence, MPC proves to be a good candidate for imple-menting advanced control due to its multivariable structure, direct approach ofconstraints, and optimal character.
pH Neutralization
Mahmoodi et al. (2009) made use of the Wiener-Laguerre model, which consists ofLaguerre filters and simple polynomials that are used respectively as linear and non-linear parts to evaluate identification of a pH neutralization process. Based on thismodel, a nonlinear model predictive controller was designed for a proper operationof the pH process in different set points, and the results were compared with those ofa linear model predictive controller based on a linear Laguerre model. Their resultsshowed that the linear Laguerre model captured the dynamics of the process but itcannot model its nonlinear gain; they concluded that adding a nonlinear mapping asthe nonlinear gain was necessary to improve model accuracy. Their results provedthat compared to the Laguerre model the Wiener-Laguerre model was the bettermodel for nonlinear gain. From the simulation result with the MPC algorithm basedon the linear Laguerre model they observed that the MPC based on the Laguerremodel performed better than that based on the state-space model, when the operat-ing region is far from the nominal operating conditions (pH 7), also proving thatWiener-Laguerre MPC performed slightly better than the MPC based on the linearLaguerre model. They finally concluded that NMPC based on Wiener-Laguerreshowed better performance than the MPC based on the Wiener model but is slightlybetter than MPC based on the Laguerre model.
Akesson et al. (2005) dealt with the computational issues of model predictivecontrol of nonlinear sampled-data systems. They used a neural network to
498 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
approximate the optimal strategy found by offline calculations. This approach wasapplied to a simulated highly nonlinear pH neutralization process. A neural networkapproximator was used for representing the nonlinear control strategy defined by themodel predictive controller. Their results showed the system parameters as functionsof pH. Robustness with respect to controller approximation was calculated for thepH control system using a small-signal linearized description. They also computedfor an idealized situation with a linearized model and no model uncertainty.
Kocijan et al. (2004) described an NMPC principle with a Gaussian processmodel. They obtained a model that describes the dynamic characteristics of a non-linear system and at the same time provides information about the confidence inthese predictions. They took a pH neutralization process as their case study. ThepH was controlled by manipulating the base flow rate. The dynamic model of thepH neutralization system was derived using conservation equations and equilibriumrelations. The control algorithm was tested for the pH process by simulation. Theyshowed that the closed-loop system response avoids regions with large variance atthe cost of steady-state error.
Polymerization Reactors
Ozkan and Kothare (2006) studied the stabilizing multi-model predictive controlstrategy for controlling a nonlinear process at different operating conditions. In thisresearch they extend the already formulated multi-model predictive control strategyto incorporate a stabilizing contractive constraint. They analyzed stability of theresulting closed-loop system using the multiple Lyapunov function approach andalso proposed two different Lyapunov approaches. They concluded that the use ofmultiple Lyapunov functions enabled them to relax the monotonically decreasingcondition of the Lyapunov function when the control algorithm switches from aquasi-infinite horizon to an infinite horizon strategy. They presented the only theirwork that dealt with the development of a stabilizing control strategy and stabilityanalysis of the closed-loop system.
Ozkan et al. (2003) used an MPC algorithm based on multiple piecewise linearmodels to study the control of a solution copolymerization reactor of methyl meth-acrylate (MMA) and vinyl acetate. Their important control objective was to mini-mize grade transition time, and thereby reduce the amount off-specificationproduct produced during transition, as polymer reactors need to operate in multipleoperating regimes to manufacture several different grades of polymers. Theydeveloped a multiple model MPC technique using the theory of linear matrixinequalities (LMIs)=semi-definite programming. They illustrated the application ofthis algorithm on a low-order CSTR model with an exothermic first-order irrevers-ible reaction. They depicted the effect of number of local models on the performanceof a multi-model MPC and found that as the number of linear models used increases,the response of output variables to control action becomes faster.
Shafiee et al. (2008) used a polymerization reactor to apply NMPC based on apiecewise linear Wiener model over it. They used Wiener and Hammerstein models,which are the block-oriented nonlinear models that are obtained by combining lineardynamic models with static or memoryless nonlinear functions. They modeled thestatic nonlinear element of the Wiener model, which is approximated using the piece-wise linear functions and its dynamic linear element using a state-space description.The presented control scheme was applied to a polymerization reactor, and its results
MPC and Its Current Issues 499
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
were compared to those of a linear MPC. They analyzed the possibilities and theadvantages of the use of a specific Wiener approximation to represent the modelof the process. A comparison of NMPC and LMPC behavior for a polymerizationprocess when the first output set points have changed shows that the NMPC control-ler has better performance, with short settling time and without any overshootchanges. All of the simulations showed that the maximum computation time foroptimization at each sampling interval is sufficiently below the chosen sampling timeand the control signals are feasible due to canonical structure of nonlinear gain.
Park and Rhee (2001) used an LMI-based robust model predictive controller ina continuous MMA polymerization reactor with the polytopic uncertain model inorder to control the monomer conversion and the weight-average molecular weightof the polymer product. They clearly demonstrated that the RMPC guaranteesrobust stability by presenting the regulatory performance of the LMI-based RMPCfor monomer conversion. The simulation results showed that the controller per-formed satisfactorily and steadily in the case of the servo problem, although thejacket inlet temperature slightly oscillates while the conversion approaches the setpoint. Finally, they showed that the LMI-based RMPC gives rise to stable perfor-mance for conversion and average molecular weight.
Espinosa and Van Brempt (2006) used an MPC for a classical batch processwhere the MPC controller used was an extended version of the MPC controllerINCA (IPCOS novel control architecture). Since the main controlled variable in abatch process is the reactor temperature, the temperature was determined by twomechanisms: the heating and cooling capacity of the heat exchangers and the heatabsorbed or generated by the reaction. Models of the heat exchanger tend to be sim-ple and very easy to obtain, either by direct physical modeling or simple identifi-cation experiments. On the other hand, the chemical reactions tend to be complexand difficult to observe. Hence, their results showed that the model is kept synchro-nized with the plant by using a nonlinear observer based on the model.
Dokucu et al. (2008) had the challenge of closed-loop regulation of emulsionpolymerization systems; this presents a challenging control problem due to the com-plexity of the process and the lack of reliable high-frequency measurements. Theydeveloped a multi-rate MPC controller as a combination of the extended QDMCcontroller and the linear multi-rate MPC controller. The proposed algorithm wastested against two types of disturbance scenarios. In both cases the controller wasable to reject the disturbances successfully. This shows that solids content can beused to infer the states of the system against these disturbances.
Kashiwagi and Li (2004) explained the progress on Volterra modeling with ahigh degree of accuracy made by using Volterra kernels of up to the third order,which can now be measured easily by perturbing the plant with a pseudo-randomM-sequence signal that provides enough excitation and yet is acceptable in an indus-trial situation. They used a van de Vusse reactor, where they carried out the controlof two density components by adjusting the amount of input flow. Their resultsshowed that while all nonparametric NMPC controllers offer zero offsets, thethird-order one offers superior performance. They also compared the actual outputand the Volterra estimates responding to a sinusoidal input; they found that thethird-order model offers the best estimation and should be sufficient to precludethe need for a further higher-order model. They finally concluded that the nonpara-metric NMPC formulated from the third-order Volterra model offers the bestclosed-loop performance.
500 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Da Silva et al. (2008) used MPC for emulsion polymerization processes modeledby nonlinear partial distributed equations. They considered model predictive controlof the free surfactant concentration in the aqueous phase, using the surfactant flowrate as a constrained manipulated variable. First, a dynamic model was adapted fol-lowed by control of the emulsion polymerization process for the PDE systems toreduce the on-line resolution time. They considered surfactant feed rate as a manipu-lated variable and free surfactant concentration in the aqueous phase as the con-trolled variable. Their results showed that the choice of the reference trajectory ofthe free surfactant concentration directly influences the final particle size distribution(PSD). They also showed that the time between the two nucleations is very critical.
The solution to the problems faced by the above-mentioned systems is that therepetitive model predictive control (RMPC) is a new formulation of MPC in whichthe basic idea of RC is brought into conventional MPC formulation. The result is atechnique that combines the advantages of both RC and MPC.
Fluid Catalytic Cracking (FCC) Reactors
Cristea et al. (2003) developed a mathematical model for a UOP-type fluid catalyticcracking unit (FCCU). They preferred a three-lump model for the global descriptionof the phenomena taking place in the reactor; the reactor had two parts, the risermodel and the stripper model. Their results obtained by dynamic simulation pre-sented a good fit with industrial operating data, simulated variables being situatedin a range corresponding to industrial unit behavior. Results revealed the superiorbehavior for the case of MPC, with respect to both overshoot and response time.Following the performed simulations it was concluded that, as the number of con-trolled variables is high and the interactions between them are strong, a multivari-able control strategy can be successful and MPC proves to be an effective one.From the results they proved that control performance with MPC is not substan-tially affected by the occurring constraint.
Jia et al. (2003) used MPC on an FCCU where the control goals were to max-imize the production of one or more products in different seasons. Their objectivewas an adequately reduced model to describe important variable variations likepressure effects and use oversimplified kinetics, to overcome the largest discrepanciesappearing in the modeling of the dense bed in the regenerator, and to overcome dis-agreement on the necessity of taking into account the spatial character of the bubblephase in the dense bed; FCC models also have strong implications concerning thefrequently related instability issues. They modeled the regenerator as a two-phasefluidized bed model, popularly known as K and L model. Their control objectivewas to maintain the controlled variables at predetermined set points in the presenceof typical process disturbances while maintaining safe plant operation and restrictingthe magnitude per step of the regenerated and spent catalyst slide valves and flue gasbutterfly valve stem movements. The plots of the control results showed that all thecontrolled variables can be brought to their set points in a fast and smooth fashion.It was observed that differential pressure has the best control performance. Thereactor bed level has poorer control performance in terms of longer settling timeand higher overshoot.
Viera et al. (2005) applied neural network-based MPC to an FCCU. They usedthe first-principles model for simulations. Their main objective was to demonstratethat feed-forward neural network structures that are capable of identifying the
MPC and Its Current Issues 501
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
FCCU and that the resulting MIMO model is a reliable one to be used on-line in aNMPC scheme. An ANN that was used was configured as a fully connectedfeed-forward network, with one hidden layer. They showed good agreement betweenthe rigorous numerical simulations and the neural model predictions. They also com-pared the neural network MPC performance to a well-tuned DMC implementationand found that the neural network MPC response was smoother than that obtainedfrom DMC algorithm implementation.
Roman et al. (2009) presented simulation results obtained with a complexdynamic model of an FCCU. They developed a model that simulates the dynamicbehavior of the reactor-regenerator-fractionator system and predicts the compo-sition of the main products (gasoline and diesel). They developed the FCCU modelbased on reference construction and operation data from an industrial unit. With thenewly developed dynamic simulator they studied the effects of different sets of dis-turbances. Results obtained with the dynamic simulator presented a good fit withindustrial operating data, as simulated process variables are situated in a range cor-responding to industrial unit behavior. To guarantee the stability of the closed-loopsystem even under a finite prediction horizon they used quasi-infinite-horizon non-linear model predictive control (QIHNMPC), in which the prediction horizon isquasi-extended to infinity by introducing a terminal penalty term in the objectivefunction. They compared QIHNMPC results with the nominal NMPC consideredwithout the penalty term and the terminal constraints and found that theQIHNMPC achieved better control performance than the nominal NMPC, with,however, increased computational burden. They found that the overall performanceof the moving horizon estimator (MHE)-NMPC was very good as the temperaturesare kept close to the reference values. MPC based on NMPC performed betterFCCU control than MPC based on LMPC, and both showed superior controlperformance over classical PID control.
The advantages of a modern NMPC approach, the so-called quasi-infinite-horizon nonlinear model predictive control (QIHNMPC) and moving horizonestimator nonlinear MPC (MHE-NMPC), are shown to achieve better controlperformance, with, however, increased computational load. Based on a multipleshooting technique, an efficient solution of on-line optimization is obtained evenfor the case of the high dimensional model.
Distillation Columns
Abou-Jeyab et al. (2001) used a piecemeal fashion to solve the constrained optimiza-tion problem involved in control. Their objective was to maintain the optimum oper-ating condition of a distillation column in the petroleum industry, for which theypreferred MPC. Also, to solve the problem without decomposition, they preferredthe use of the linear programming (LP) formulation using a simplified MPC algor-ithm. The LP approach requires a modest computational approach as it involves avery small size optimization problem. The approach led to cycling in the productcomposition that was present using SISO controllers, which resulted in a 2.5%increase in production rate, 0.5% increase in product recovery, and a significantincrease in profit.
Jin et al. (2003) dealt with the constrained multivariable control problem of dis-tillation columns. They used the sulfonation of linear alkyl benzene (LAB) processas their case study, which consists of HF acid stripper, benzene column, paraffin
502 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
column, and LAB column. They used MPC controllers by tuning them first and thenon-line for three months. They then compared the performance before and afterMPC implementation.
Norquay et al. (1999) used a distillation column to overcome problems inhigh-purity columns, which tend to be ill-conditioned, leading to severe input direc-tionality and output coupling. They undertook the case study of a C2-splitter at theOrica Olefins plant, located at Botany in Sydney, Australia. They had the heavydemand of satisfactory performance at a range of operating points, since the processdoes not have a single operating point about which a controller may be designed, butit must be able to perform equally well at a range of different feed rates and thereforeoperating points, the reason for which was that the plant throughput, based on cus-tomer demand, tends to be changed on a regular basis. Their other problem was thatwhile a significant decrease in feed rate is conducive to a significant decrease in bothreboil and reflux rates, the operators were generally uncomfortable with decreasingthese rates. Another significant disturbance to the column was the vapor fraction ofthe feed. To overcome all these problems they proposed a dual composition control-ler be designed and implemented for the C2-splitter. They used a steady-state deter-ministic model and developed the simulation of the C2-splitter using the MATLABSimulink package and used it to test the proposed control strategy in the face ofset-point changes, feed changes, unmeasured disturbances, and model mismatch.The results of the data collected during the commissioning of the new control strat-egy showed much promise.
Bloemen et al. (2001) used Wiener model–based identification and control tech-nology for dual composition control of a moderate- to high-purity distillation col-umn simulation model. They compared the direct closed-loop identification of alinear model with indirect closed-loop identification of a Wiener model. For thecontrol part they compared the performance of the MPC algorithm based on theidentified linear models and two different approaches to handle the Wiener modelwithin a predictive control framework. Their results showed that the differencebetween the measured output and predicted output is hardly distinguishable, whichindicates that the Wiener model is able to describe accurately the behavior of the dis-tillation column in the closed-loop setting. In the optimization problem of the inverseWiener MPC (IWMPC) algorithm the nonlinearity is inverted and removed from thecontrol problem, resulting in a linear MPC algorithm for the remaining linear block.
Alpbaz et al. (2002) studied the steady-state and dynamic behavior of a binarypacked distillation column simulated using a stagewise approach. They describedthe models as a set of ordinary differential equations in which the height of the col-umn is divided into a number of stages. They used a step response model for MPC.They compared their simulation results with the experimental data and concludedthat a reasonable agreement is obtained. They compared their control results withusing integral of the square of the error (ISE) criteria that the top temperaturereaches to set point in a minimum time and less oscillation; it was concluded thatDMC control has better performance than conventional control strategies.
Assandri et al. (2004) used parametric predictive control (PPC), where MPCintegrates reduced-order process models that incorporate first principles to face non-linearities, applied to temperature control of batch reactors. Their main challengewas the bottom temperature in the column, which had significant feed compositionvariations; the column was to be operated over a broad range of operating con-ditions. The other issue was that for a linear MPC the need for continuous
MPC and Its Current Issues 503
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
adaptation of model parameters, and possibly structure, prevents its practical use inan industrial setting. Their results showed the step changes in the bottom tempera-ture set point. The performance of the controller also was seen to be very good for awide range of operating conditions.
Karacan (2003) used nonlinear long-range predictive control based on theNARIMAX model for a pilot-scale packed distillation column; in order to controlthe top temperature of the column experimentally and theoretically, reflux ratiowas selected as a manipulated variable. They developed a dynamic model for thepacked distillation column. Long-range predictive control (LRPC) was preferredover generalized minimum-variance and pole-placement because of its realistic andpractical approach to a wide class of industrial problems. Their aim of the controlwas to maintain the top product temperature in the packed distillation column atthe desired set point against disturbances in the form of varying feed compositionand temperature. Their results showed that the second-order model was a reasonablecompromise, and the estimated model with no filtering of the top temperature resultis not in good agreement with experimental data.
Ravi Chandra and Venkateswarlu (2007) proposed to design a multistep MPCstrategy for the control of a reactive distillation column. The MPC of their workis based on the auto-regressive moving average (ARX) model structure, whose para-meters are updated on-line using the process measurement information. Their objec-tive was to control the desired product purity in the distillate stream despitedisturbances in column operation. Their results showed the MPC and PI controllerbeing applied for tracking a series of step changes in ethyl acetate composition. TheirISE results show the better performance of MPC towards the set point changes aswell as in stabilizing the operation in the presence of input disturbances. Their resultsshowed the delayed responses in both controllers, however, MPC exhibits betterperformance than the PI controller.
Schwarm and Nikolaou (1999) examined a different aspect of constrained MPCrobustness, namely robustness with respect to satisfaction by the actual system ofinequality constraints posed in the on-line optimization problem. A method of incor-porating model uncertainty into the output constraints of the on-line optimization toimprove the robustness of constrained MPC was their goal. They used a high-puritydistillation process as their case study. To develop a process model and uncertaintydescription for the purpose of demonstrating their method, they generated outputdata from the aforementioned state space model using a pseudo random binarysequence (PRBS) input. They then used standard least-squares techniques to identifymultiple-input-single-output finite impulse response (FIR) models for each outputusing the corrupted data.
Drying Systems
Dufour et al. (2003) addressed the boundary control of nonlinear parabolic partialdifferential equation (PDE) systems characterized by complex nonlinearities in thespatial domain and at the boundary as well. Their aim was to provide an MPCframework for such PDE systems to reduce the on-line resolution time at three levelsfor the control of a catalytic reverse-flow reactor. The control problem consideredwas the tracking of a reference trajectory for the process temperature, subject to con-straints on the infrared flow. The model of the painting film sample infrared dryingis composed of two coupled equations: a nonlinear ordinary differential=integral
504 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
equation and a nonlinear parabolic PDE. Hence, from the results one of the proper-ties of the internal model control (IMC) structure (integral action), and the interestof this IMC=MPC strategy, was confirmed by these experimental results: the track-ing was effective in spite of the fact that the model output used in the control algor-ithm does not track quantitatively the temperature reference trajectory.
Didriksen (2002) used a first-principles model based upon conservation of mass,energy, and momentum of a sugar beet pulp dryer to describe the longitudinalmotion of the mass of gas and solid, the heat transfer from gas to solid, the masstransfer from solid to gas, and the intraparticle effects: water diffusion and heat con-duction. He used plant data from a Danish sugar factory as a basis for the simulationstudies. Simulations were made with an augmented Kalman filter (AKF) versus pro-cess plant data to deal with the problem of evaluating the predictive abilities of themodel when the input to the process is not fully known. He simulated with amodel-based predictive controller (MPC) configuration. The controller is a standarddynamic matrix control (DMC) algorithm. The disturbances were estimated by theAKF, and the estimated disturbances were used in the MPC. The performance wasnot quite as good as in the case of measured disturbances, but on the other handclearly better than the traditional feedback approach.
Daraoui et al. (2007) dealt with MPC of the measured surface temperature evol-ution of a freeze-dried product during the primary stage. They used control software(MPC@CB) allowing solving any other constrained optimal control problems forany processes. Their challenge was the temperature of the product, which must care-fully be controlled during the primary drying stage as it cannot exceed the collapselimit of the cake structure or the melting temperature. They preferred theLevenberg-Marquardt algorithm, for which the codes of the MPC@CB softwarewere written with MATLAB. They showed that the measured temperature tracksvery well its prescribed time trajectory, due to the on-line optimal tuning of themanipulated variable by MPC@CB, and under input constraints.
Panditrao et al. (2005) designed a pilot spray dryer unit for installing in an edu-cational institution. For control purposes they implemented a SISO scheme usingconventional instruments. They designed and implemented MPC on the spray dryer,for which they varied process model identification, where model generation was car-ried out based on a step test and model parameters were calculated. The step test isbased on PRBS. Model validation was the next step, where the comparison wasbetween the ARX models with the FIR model; the good match between them indi-cates good accuracy of the model. This was followed by the development of the MPCoperator interface, tuning MPC controller using the simulation facility, and, finally,process control using MPC.
Future Challenges and Directions
Future work will focus on stability analysis, the development of data-driven techni-ques to perform the plant decomposition, and large-scale process applications. Also,a relevant and worthwhile study, especially from an industrial perspective, would bea comparison of the developed control algorithm with nonlinear MPC techniques onan industrial-scale process. Such a study should consist not only of performancecomparisons and disturbance rejection, but also discuss feasibility, stability, andcomputational features as well. The main advantage of the robust MPC techniqueis its capability to deal with model mismatch and constraints as well as its stability
MPC and Its Current Issues 505
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
guarantee. This discussion reveals current limitations of robust MPC and possibledirections for its future. It should be noted that few experimental validations havebeen performed for many reasons, including lack of adequate hard or soft sensors,actuators, and process control systems. However, the need for better instrumen-tation, control, and automation is recognized. There are also possibilities of continu-ation of current studies. First is the development of the control framework based ona new countercurrent pseudo-homogeneous model which is faster to compute.Second, in order to improve the closed-loop performance, the use of the on-line esti-mation of the stochastic inlet gas concentration acting as a strong input disturbanceshould be pursued. Future progress also includes analysis of the distributed controlproblem. Controller performance can be improved by using two different MPCtunings for different areas of the process or by application of a set-point filter.
Conclusions
The MPC technique requires modest computational resources, with easy implemen-tation and good performance, thus resulting in significant increase in profit. Here themodest computational resources refer to its needs for real implementation (like hard-ware issues, etc.). To overcome the computational obstacle of nonlinear models, theprediction model of each MPC is linearized around the current operating point ateach step. The results indicate that a neural-based controller can achieve tighterregulatory control than is possible with decentralized single-loop controllers whileusing multivariable feed-forward=feedback model predictive control. Comparedwith traditional decentralized PID control, MPC presents better control perfor-mance based on its multivariable feature, inherent prediction ability, and capacityto directly handle constraints using an even larger number of manipulated than con-trolled variables. Nonlinear MPC implementation leads to potential improvement bythe use of dynamic sensitivity analysis. The use of a model to predict future behaviorbased on on-off signals helps to anticipate and account for the delay representing acycle time, taking also into account the on-off nature of the control signal.
The MPC system is superior to conventional control in the following aspects: theskill of the most highly experienced operator has been implementation, then oper-ation and compensation are executed at fairly frequent intervals, and several processvariables can be managed in parallel. The advantage of robust MPC techniqueis its capability to deal with model mismatch and constraints as well as itsstability guarantee. The summary of model predictive control approaches in theabove-mentioned chemical systems has also been provided.
Acknowledgment
This work was supported by the USM Postgraduate Research Grant Scheme(USM-RU-PGRS) 8041010 and USM RU Grant 814076.
References
Abou-Jeyab, R. A., Gupta, Y. P., Gervais, J. R., Branchi, P. A., and Woo, S. S. (2001).Constrained multivariable control of a distillation column using a simplified modelpredictive control algorithm, J. Process Control, 11(5), 509–517.
506 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Akesson, Bernt M., Toivonen, Hannu T., Waller, Jonas B., and Nystrom, Rasmus H. (2005).Neural network approximation of a nonlinear model predictive controller applied to a pHneutralization process, Comput. Chem. Eng., 29(2), 323–335.
Akesson, Bernt M., and Toivonen, Hannu T. (2006). A neural network model predictivecontroller, J. Process Control, 16(9), 937–946.
Al Seyab, R. K., and Cao, Y. (2006). Nonlinear model predictive control for the ALSTOMgasifier, J. Process Control, 16(8), 795–808.
Alamir, Mazen, Ibrahim, Fadi, and Corriou, Jean Pierre. (2006). A flexible nonlinear modelpredictive control scheme for quality=performance handling in nonlinear SMB chromato-graphy, J. Process Control, 16(4), 333–344.
Alhamad, B., Romagnoli, J. A., and Gomes, V. G. (2005). On-line multi-variable predictivecontrol of molar mass and particle size distributions in free radical emulsion polymeriza-tion, Chem. Eng. Sci., 60, 6596–6606.
Alpbaz, M., Karacan, S., Cabbar, Y., and Hapoglu, H. (2002). Application of model predic-tive control and dynamic analysis to a pilot distillation column and experimental verifi-cation, Chem. Eng. J., 88(1–3), 163–174.
Amrutalingam, R., and Lee, J. H. (1999). Subspace based inferential control applied to a con-tinuous pulp digester, J. Process Control, 9, 397–406.
Arefi, Mohammad M., Montazeri, A., Poshtan, J., and Jahed-Motlagh, M. R. (2008).Wiener-neural identification and predictive control of a more realistic plug-flow tubularreactor, Chem. Eng. J., 138(1–3), 274–282.
Ashoori, Ahmad, Moshiri, Behzad, Khaki-Sedigh, Ali, and Bakhtiari, Mohammad Reza.(2009). Optimal control of a nonlinear fed-batch fermentation process using modelpredictive approach, J. Process Control, 19(7), 1162–1173.
Assandri, Armando, Rueda, Almudena, Martınez, Ernesto, and de Prada, Cesar. (2004). Inte-gration of a reduced first-principles model in predictive control of a complex distillationcolumn, Comput. Aided Chem. Eng., 18, 559–564.
Banerjee, A., and Arkun, Y. (1998). Model predictive control of plant transitions using a newidentification technique for interpolating nonlinear models, J. Process Control, 8(5–6),441–457.
Baotic, M., Christophersen, F., and Morari, M. (2003). A new algorithm for constrained finitetime optimal control of hybrid systems with a linear performance index, paper presentedat European Control Conference, University of Cambridge. Available at http://www.nt.ntnu.no/users/skoge/prost/proceedings/ecc03/pdfs/559.pdf
Beccuti, A. G., Geyer, T., and Morari, M. (2003). Temporal Lagrangian decomposition ofmodel predictive control for hybrid systems, in: Proceedings of the 43rd IEEE Conferenceon Decision and Control, vol 3., 2509–2514, IEEE, Piscataway, N.J.
Bemporad, A., and Morari, M. (1999). Control of systems integrating logic, dynamics andconstraints, Automatica, 35(3), 407–427.
Bemporad, A., Giovanardi, L., and Torrisi, F. D. (2000). Performance driven reachabilityanalysis for optimal scheduling and control of hybrid systems, in: Proceedings of the39th IEEE Conference on Decision and Control, 969–974, Piscataway, N.J.
Bemporad, A., Borrelli, F., and Morari, M. (2002a). On the optimal control law for linear dis-crete time hybrid systems, in: Hybrid Systems: Computation and Control: 5th InternationalWorkshop, HSCC 2002, 105–119, Springer, New York.
Bemporad, A., Heemels, W., and Schutter, B. D. (2002b). On hybrid systems and closed loopMPC system, IEEE Trans. Automat. Contr., 47(5), 863–869.
Berenguel, M., Rodrıguez, F., Acien, F. G., and Garcıa, J. L. (2004). Model predictive controlof pH in tubular photobioreactors, J. Process Control, 14(4), 377–387.
Bloemen, H. H. J., Chou, C. T., van den Boom, T. J. J., Verdult, V., Verhaegen, M.,and Backx, T. C. (2001). Wiener model identification and predictive controlfor dual composition control of a distillation column, J. Process Control, 11(6),601–620.
MPC and Its Current Issues 507
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Borrelli, F. (2003). Constrained Optimal Control of Linear and Hybrid Systems, 18, Springer,New York.
Borrelli, F., Baotic, M., Bemporad, A., and Morari, M. (2003). An efficient algorithm forcomputing the state feedback solution to optimal control of discrete time hybrid systems,in: Proceedings of the 2003 American Control Conference, 4717–4722, AmericanAutomatic Control Council, New York.
Bouhenchir, H., Cabassud, M., and Le Lann, M. V. (2006). Predictive functional control for thetemperature control of a chemical batch reactor, Comput. Chem. Eng., 30(6–7), 1141–1154.
Camacho, E. F., and Bordons, C. (1999). Model Predictive Control, Springer-Verlag, London.Causa, Javier, Karer, Gorazd, Nunez, Alfredo, Saez, Doris, Skrjanc, Igor, and Zupancic,
Borut. (2008). Hybrid fuzzy predictive control based on genetic algorithms for the tem-perature control of a batch reactor, Comput. Chem. Eng., 32(12), 3254–3263.
Cormos, Calin, and Agach, Serban. (2005). Advanced process control of pantolactone syn-thesis using nonlinear model predictive control (NMPC), Comput. Aided Chem. Eng.,20, 1435–1440.
Corriou, Jean-Pierre, and Pons, Marie-Noelle. (2004). Model predictive control of wastewatertreatment plants: Application to the BSM1 benchmark, Comput. Aided Chem. Eng., 18,625–630.
Cristea, Mircea V., and Agachi, Serban P. (2006). Non linear model predictive control of thewastewater treatment plant, Comput. Aided Chem. Eng., 21, 1365–1370.
Cristea, Mircea V., Agachi, Serban P., and Marinoiu, Vasile. (2003). Simulation and model pre-dictive control of a UOP fluid catalytic cracking unit, Chem. Eng. Process., 42(2), 67–91.
Da Silva, B., Dufour, P., Othman, N., and Othman, S. (2008). Model predictive control of freesurfactant concentration in emulsion polymerization, paper 1693, in: Proceedings of the17th IFAC World Congress 2008, Seoul, South Korea, 8375–8380.
Daraoui, Nawal, Dufour, Pascal, and Hammouri, Hassan. (2007). Model predictive control ofthe primary drying stage of a freeze drying of solutions in vials: An application of theMpc@Cb software, in: Proceedings of the 5th Asia-Pacific Drying Conference, 883–888,World Scientific, Hong Kong.
Didriksen, Helge. (2002). Model based predictive control of a rotary dryer, Chem. Eng. J.,86(1–2), 53–60.
Dokucu, Mustafa T., Park, Myung-June, and Doyle III, Francis J. (2008). Multi-rate modelpredictive control of particle size distribution in a semibatch emulsion copolymerizationreactor, J. Process Control, 18(1), 105–120.
Dufour, P., Toure, Y., Blanc, D., and Laurent, P. (2003). On nonlinear distributed parametermodel predictive control strategy: On-line calculation time reduction and application toan experimental drying process, Comput. Chem. Eng., 27(11), 1533–1542.
Dumont, G. A., Fu, Y., and Lu, G. (1994). Nonlinear adaptive generalized predictive controland applications, in: Advances in Model-Based Predictive Control, ed. D. Clark, 498–515,Oxford University Press, New York.
Erdem, G., Amanullah, M., Morari, M., Mazzotti, M., and Morbidelli, M. (2006). Optimizingcontrol of an experimental simulated moving bed unit, AIChE J., 52(4), 1481–1494.
Espinosa, Jairo, and Van Brempt, Wim. (2006). Predictive control of polymerization batchreactors using hybrid models, Comput. Aided Chem. Eng., 21, 1329–1334.
Findeisen, R., and Allgower, F. (2002). An introduction to nonlinear model predictive control,paper presented at 21st Benelux Meeting on Systems and Control, Veldhoven.
Flores-Cerrillo, J., and MacGregor, J. F. (2003). Within-batch and batch-to-batchinferential-adaptive control of semi-batch reactors: A partial least squares approach,Ind. Eng. Chem. Res., 42, 3334–3345.
Froisy, J. Brian. (2006). Model predictive control—Building a bridge between theory andpractice, Comput. Chem. Eng., 30(10–12), 1426–1435.
Gadkar, K. G., Doyle III, F. J., Crowley, T. J., and Varner, J. D. (2003). Cybernetic model pre-dictive control of a continuous bioreactorwith cell recycles,Biotechnol. Prog., 19, 1487–1497.
508 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Gatzke, Edward P., and Doyle III, Francis J. (2001). Model predictive control of a granu-lation system using soft output constraints and prioritized control objectives, PowderTechnol., 121(2–3), 149–158.
Hahn, J., Kruger, U., and Edgar, T. F. (2002). Application of model reduction for model predic-tive control, in: Proceedings of the 2002 IFAC World Congress, Barcelona, Spain, 684–688.
Holenda, B., Domokos, E., Redey, A., and Fazakas, J. (2008). Dissolved oxygen control of theactivated sludge wastewater treatment process using model predictive control, Comput.Chem. Eng., 32(6), 1270–1278.
Hussain, M. A. (1999). Review of the application of neural networks in chemical processcontrol-simulation and online implementation, Artif. Intell. Eng., 13, 55–68.
Jia, Chunyang, Rohani, Sohrab, and Jutan, Arthur. (2003). FCC unit modeling, identificationand model predictive control, a simulation study, Chem. Eng. Process., 42(4), 311–325.
Jin, Xiaoming, Rong, Gang, and Wang, Shuqing. 2003. On applying model predictive controlfor distillation system of linear alkylbenzene (LAB) complex, Comput. Aided Chem. Eng.,15(2), 864–869.
Kantor, C. E. Garcia, and Carnahan, B. 232–256, American Institute of Chemical Engineers,New York.
Karacan, Suleyman. (2003). Application of a non-linear long range predictive control to apacked distillation column, Chem. Eng. Process., 42(12), 943–953.
Karer, Gorazd, Mu�ssic, Ga�sspar, Skrjanc, Igor, and Zupancic, Borut. (2007). Hybrid fuzzymodel-based predictive control of temperature in a batch reactor, Comput. Chem. Eng.,31(12), 1552–1564.
Kashiwagi, H., and Li, Y. (2004). Non parametric nonlinear model predictive control, KoreanJ. Chem. Eng., 21, 329.
Kocijan, J., Murray-Smith, R., Rasmussen, C. E., and Likar, Bojan. (2003). Predictive controlwith Gaussian process models, in: The IEEE Region 8 EUROCON 2003: Computer as aTool, vol. A, 352–356, Piscataway, N.J.
Kocijan, J., Murray-Smith, R., Rasmussen, C. E., and Girard, A. (2004). Gaussian processmodel based predictive control, in: Proceedings of the 2004 American Control Conference(ACC 2004), Boston, 2214–2219, American Automatic Control Council, New York.
Kovarova-Kovar, K., Gehlen, S., Kunze, A., Keller, T., von Daniken, R., Kolb, M., and vanLoon, A. P. G. M. (2000). Application of model-predictive control based on artificialneural networks to optimize the fed-batch process for riboflavin production, J. Biotech-nol., 79(1), 39–52.
Li, D., Shah, S. L., and Chen, T. (2001). Identification of fast rate models from multirate data,Int. J. Control, 74(7), 680–689.
Lusson Cervantes, A., Agamennoni, O. E., and Figueroa, J. L. (2003). Robust identificationof PWL-Wiener models: Use in model predictive control, Lat. Am. Appl. Res., 33(4),435–442.
Mahfouf, M., Kandiah, S., and Linkens, D. A. (2002). Fuzzy model-based predictive controlusing an ARX structure with feedforward, Fuzzy Sets Syst., 125, 39–59.
Mahmoodi, Sanaz, Poshtan, Javad, Jahed-Motlagh, Mohammad Reza, and Montazeri,Allahyar. (2009). Nonlinear model predictive control of a pH neutralization processbased on Wiener-Laguerre model, Chem. Eng. J., 146(3), 328–337.
Meadows, E. S., Crowley, T. J., Immanuel, C. D., and Doyle III, F. J. (2003). Nonisothermalmodeling and sensitivity studies for batch and semibatch emulsion polymerization ofstyrene, Ind. Eng. Chem. Res., 42, 555–567.
Mohammed, Nagib G. N., and Abdulrahman, Adel. (2009). Water supply networksystem control based on model predictive control, in: Proceedings of the InternationalMultiConference of Engineers and Computer Scientists 2009, IMECS 2009, vol. II,1172–1177, Newswood, Hong Kong.
Natarajan, Seshatre, and Lee, Jay H. (2000). Repetitive model predictive control applied to asimulated moving bed chromatography system, Comput. Chem. Eng., 24(2–7), 1127–1133.
MPC and Its Current Issues 509
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Niemic, M. P., and Kravaris, C. (2002). Nonlinear multirate model-algorithmic control. 1.Theory, Ind. Eng. Chem. Res., 41, 4054–4063.
Niemic, M. P., Kravaris, C., and Zand, R. (2002). Experimental application to a polymeriza-tion reactor, Ind. Eng. Chem. Res., 41, 4064–4074.
Norquay, S. J., Palazoglu, A., and Romagnoli, J. A. (1999). Application of Wiener model pre-dictive control (WMPC) to an industrial C2-splitter, J. Process Control, 9(6), 461–473.
Nunez, A., Saez, D., Oblak, S., and Skrjanc, I. (2006). Hybrid predictive control based onfuzzy model, in: IEEE World Congress on Computational Intelligence, 9079–9085,Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada.
Ozkan, Leyla, and Kothare, Mayuresh V. (2006). Stability analysis of a multi-model predictivecontrol algorithm with application to control of chemical reactors, J. Process Control,16(2), 81–90.
Ozkan, Leyla, Kothare, Mayuresh V., and Georgakis, Christos. (2003). Control of a solutioncopolymerization reactor using multi-model predictive control, Chem. Eng. Sci., 58(7),1207–1221.
Panditrao, S., Agashe, S., and Shegaonkar, P. (2005). Model predictive control of pilot spraydryer unit designed and implemented for an educational institute, in: IEEE Workshop onProcess Control, 7, Vancouver, Canada.
Park, M. J., Dokucu, M. T., and Doyle III, F. J. (2004). Regulation of the emulsion particlesize distribution to an optimal trajectory using partial least squares model-based predic-tive control, Ind. Eng. Chem. Res., 43, 7227–7237.
Park, Myung-June, and Rhee, Hyun-Ku. (2001). LMI-based robust model predictive controlfor a continuous MMA polymerization reactor, Comput. Chem. Eng., 25(11–12),1513–1520.
Potocnik, B., Music, G., and Zupancic, B. (2004). Model predictive control of systems withdiscrete inputs, in: MELECON 2004: Proceedings of the 12th IEEE MediterraneanElectrotechnical Conference, 383–386, IEEE, Piscataway, N.J.
Prasad, V., Schley, M., Russo, L. P., and Bequette, W. (2002). Product property and pro-duction rate control of styrene polymerization, J. Process Control, 12, 353–372.
Qian, Jixin, Yang, Jianfeng, Zhao, Jun, and Niu, Jian. (2007). Neural network model basedpredictive control for multivariable nonlinear systems, in: International Conference onIntelligent Systems and Knowledge Engineering ISKE 2007, Atlantis Press, Amsterdam.(CD-ROM).
Qin, S. J., and Badgwell, T. A. (1997). An overview of industrial model predictive controltechnology, in: Chemical Process Control-V: Assessment and New Directions forResearch: Proceedings of the Fifth International Conference on Chemical Process Control,ed. J. C.
Qin, S. J., and Badgwell, T. A. (2003). A survey of industrial model predictive control tech-nology, Control Eng. Pract., 11, 733–764.
Ramaswamy, S., Cutright, T. J., and Qammar, H. K. (2005). Control of a continuous bioreac-tor using model predictive control, Process Biochem., 40(8), 2763–2770.
Ravi Chandra, P. V. S., and Venkateswarlu, Ch. (2007). Multistep model predictive control ofethyl acetate reactive distillation column, Indian J. Chem. Technol., 14, 333–340.
Roman, Raluca, Nagy, Zoltan K., Cristea, Mircea V., and Agachi, Serban P. (2009). Dynamicmodelling and nonlinear model predictive control of a fluid catalytic cracking unit,Comput. Chem. Eng., 33(3), 605–617.
Ruiz Massa, Diego, and Ruiz Garcıa, Carlos. (2003). Application of predictive control to abatch reactor, paper presented at ERTC Computing 2003, Milan, Italy.
Saha, P., Krishnam, S. H., Rao, V. S. R., and Patwardhan, S. (2004). Modeling and predictivecontrol of MIMO nonlinear systems using Wiener-Laguerre models, Chem. Eng.Commun., 191, 1083–1119.
Sarimveis, H., and Bafas, G. (2003). Fuzzy model predictive control of non-linear processesusing genetic algorithms, Fuzzy Sets Syst., 139, 59–80.
510 A. S. Kumar and Z. Ahmad
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4
Schwarm, A. T., and Nikolaou, M. (1999). Chance-constrained model predictive control,AIChE J., 45(8), 1743–1752.
Sentoni, G. B., Guiver, J. P., Zhao, H., and Biegler, L. T. (1998). State space non-linear pro-cess modeling, AIChE J., 44, 2229–2238.
Shafiee, G., Arefi, M. M., Jahed-Motlagh, M. R., and Jalali, A. A. (2008). Nonlinear predic-tive control of a polymerization reactor based on piecewise linear Wiener model, Chem.Eng. J., 143(1–3), 282–292.
Shen, Wenhao, Chen, Xiaoqua, Pons, M. N., and Corriou, J. P. (2009). Model predictive con-trol for wastewater treatment process with feedforward compensation, Chem. Eng. J.,155(1–2), 161–174.
Sheng, J., Chen, T., and Shah, S. L. (2002). Generalized predictive control for non uniformlysampled systems, J. Process Control, 12, 875–885.
Shi, D., El-Farra, N. H., Li, M., Mhaskar, P., and Christofides, P. D. (2006). Predictive con-trol of particle size distribution in particulate processes, Chem. Eng. Sci., 61, 268–281.
Silva, R. G., and Kwong, W. H. (1999). Nonlinear model predictive control of chemicalprocesses, Braz. J. Chem. Eng., 16(1), 155–161.
Silva, R. G., Anastacio, C. S., and Kwong, W. H. (1999). Model predictive control algorithmsand their application to a continuous fermenter, Braz. J. Chem. Eng., 16(2). Availableat http://dx.doi.org/10.1590/S0104-66321999000200007
Skrjanc, I., Blazic, S., and Agamenonni, O. (2005). Identification of dynamical systems with arobust interval fuzzy model, Automatica, 41, 327–332.
Song, In-Hyoup, Lee, Sang-Beom, Rhee, Hyun-Ku, and Mazzotti, Marco. (2006).Optimization-based predictive control of a simulated moving bed process using an ident-ified model, Chem. Eng. Sci., 61(18), 6165–6179.
Srinivasarao, Meka, Patwardhan, Sachin C., and Gudi, Ravindra D. (2007). Nonlinear predic-tive control of irregularly sampled multirate systems using black box observers, J. ProcessControl, 17(1), 17–35.
Su, H. T., and McAvoy, T. J. (1997). Artificial networks for nonlinear process identificationand control, in: Nonlinear Process Control, ed. M. A. Henson and D. E. Seborg, ch. 7,Prentice-Hall, Upper Saddle River, N.J.
Thomas, J., Dumur, D., and Buisson, J. (2004). Predictive control of hybrid systems under amulti-MLD formalism with state space polyhedral partition, in: Proceedings of the 2004American Control Conference, Boston, MA. American Automatic Control Council, Vol-ume 3, 2516–2521.
Vieira, W. G., Santos, V. M. L., Carvalho, F. R., Pereira, J. A. F. R., and Fileti, J. A. F. R.(2005). Identification and predictive control of a FCC unit using a MIMO neural model,Chem. Eng. Process., 44(8), 855–868.
Wang, J., Cheng, T., and Huang, B. (2004). Multirate sampled data systems: Computing fastrate models, J. Process Control, 14, 79–88.
Wisnewski, Philip A., andDoyle III, Francis J. (1998). Control structure selection andmodel pre-dictive control of the Weyerhaeuser digester problem, J. Process Control, 8(5–6), 487–495.
Wu, Fen. (2001). LMI-based robust model predictive control and its application to an indus-trial CSTR problem, J. Process Control, 11(6), 649–659.
Xaumier, Florence, Le Lann, Marie-Veronique, Cabassud, Michel, and Casamatta, Gilbert.(2002). Experimental application of nonlinear model predictive control: Temperaturecontrol of an industrial semi-batch pilot-plant reactor, J. Process Control, 12(6), 687–693.
Yu, D. W., and Yu, D. L. (2007). Multi-rate model predictive control of a chemical reactorbased on three neural models, Biochem. Eng. J., 37(1), 86–97.
Zhu, Y. (2001). Multivariable System Identification for Process Control, Pergamon, NewYork.Zhu, Guang-Yan, Henson, Michael A., and Ogunnaike, Babatunde A. (2000). A hybrid model
predictive control strategy for nonlinear plant-wide control, J. Process Control, 10(5),449–458.
MPC and Its Current Issues 511
Dow
nloa
ded
by [
Uni
vers
ity o
f W
aika
to]
at 0
0:41
14
July
201
4