MPC

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MODEL PREDICTIVE CONTROL (MPC) AND ITS CURRENT ISSUES IN CHEMICAL ENGINEERING a

A. Senthil Kumar & Zainal Ahmad

a

a

School of Chemical Engineering, Universiti Sains Malaysia , Pulau Pinang , Malaysia Published 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

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Chem. Eng. Comm., 199:472–511, 2012 Copyright # Taylor & Francis Group, LLC ISSN: 0098-6445 print=1563-5201 online DOI: 10.1080/00986445.2011.592446

Model Predictive Control (MPC) and Its Current Issues in Chemical Engineering A. SENTHIL KUMAR AND ZAINAL AHMAD

Downloaded by [University of Waikato] at 00:41 14 July 2014

School of Chemical Engineering, Universiti Sains Malaysia, Pulau Pinang, Malaysia Model predictive control (MPC) is one of the main process control techniques explored in the recent past; it is the amalgamation of different technologies used to predict future control action and future control trajectories knowing the current input and output variables and the future control signals. It can be said that the MPC scheme is based on the explicit use of a process model and process measurements 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 number of contributions in the field of nonlinear model–based predictive control dealing with issues like stability, efficient computation, optimization, constraints, and others. New developments in nonlinear MPC (NMPC) approaches come from resolving various issues, from faster optimization methods to different process models. This article specifically deals with chemical engineering systems ranging from reactors to 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, has come a long way since its innovation almost five decades ago. Hussain (1999) carried out an extensive review on model predictive control, and almost a decade later Qin and Badgwell carried out a survey on industrial MPC technology (Qin and Badgwell, 2003). Even though several improvements and innovations have been made in this area, several issues still remain that have not been touched upon or addressed completely. This article is not a review of the extensive literature that has been published during the past decade on model predictive control, nor is it a general review of model predictive control. This article deals with chemical engineering systems ranging from reactors to distillation columns where MPC plays a role in the enhancement of the systems’ performance. It begins with a brief introduction to MPC, followed by a discussion of the systems to which MPC has been applied by researchers, which includes the work in brief, the hurdles they encountered, and how they overcame them. Then follows the unanswered questions that remain in this Address correspondence to Zainal Ahmad, School of Chemical Engineering, Universiti Sains Malaysia, Engineering Campus, Seri Ampangan, 14300 Nibong Tebal, Seberang Perai Selatan, Pulau Pinang, Malaysia. E-mail: [email protected]

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MPC and Its Current Issues

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field and the solutions to them. We close with a conclusion covering how MPC has been so successful and what is awaiting us in the years to come. Model predictive control is nothing but a combination of all the different technologies to predict future control action and future control trajectories knowing current input and output variables and future control signals. MPC has been popular since 1963, and the reason for its increasing popularity is the simplicity of the algorithm and the use of the impulse and step response model, which, although possessing many more parameters than the formulations in the state space or input-output domain, is usually preferred as being more intuitive and requiring less a priori information for its identification. This article focuses on certain specific kinds of MPC that have proven to be useful in solving chemical engineering problems and gives detailed examples of applications. As history has seen, in the use of MPC for various chemical engineering applications we come across systems ranging from chemical reactors to distillation columns to industrial packed bed reactors to fluid catalytic cracking units, and so forth. For the chemical processes, the use of MPC varies from edible oil refining processes to gas-liquid separation plants to air separation units to ball mill grinding circuits. Even though there have been several individual reviews published on MPC, namely Froisy (2006) and Qin and Badgwell (2003), not many have actually focused on the various chemical systems that have been used and what are those special features of MPC that make it a clear winner in the race towards perfect control of systems. When the work carried out on these systems is looked at, it is astonishing to see that MPC has been so special in comparison to other control strategies that have already 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 successful? There are also questions like, what is MPC leading us to? and what does it have for us in the near future? We also need to know the hurdles faced by researchers who have opted for this strategy for the past several years and how they have overcome these 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 receding horizon control, is the control strategy that depends on empirical (measured or standard) models and also many other models, in particular the mechanistic model obtained by system identification. System identification refers to a process to obtain a model from a data measurement model used to predict output using input. Hence, model predictive controllers use the models and current plant measurements to predict future control moves in input. The MPC then sends this set of control moves into 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 ahead into the future y (tþl), where l ¼ 1, . . . , p. The prediction value y(tþl) depends on the past actuation and the planned m-step ahead actuation: ½Duðt þ jÞ; j ¼ 1; . . . ; m 1; m < p . The planned moves [Du(tþj), j ¼ 1, . . . , m 1] are calculated from minimizing a quadratic cost function. The cost function index incorporates the errors (the

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difference between the future reference trajectory and the predicted process output) and actuation moves. Although the vector of future control moves is calculated, only u(t) is applied to the process. . The prediction is corrected at each stage by comparing the current measured values and its predicted values through a filter. The above steps are repeated at 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 optimal control solution is then found by application of an appropriate optimization routine. As the size of the nonlinear system in question grows, computational speed becomes more of an issue, especially for systems with fast sampling time requirements. The alternative to solving the nonlinear optimization problem is to use an approximation of the nonlinear model. The goal of approximation is to recast the nonlinear model in a linear form that closely matches the original system, while gaining computational savings associated with the simpler linear model. Common methods of approximation include using multiple linear models to span the operating space. Nonlinear models lead to nonlinear prediction, but they need nonlinear optimization; 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 calculate the optimum control moves. The optimization cost function is given by: J¼

N X i¼1

wxi ðri xi Þ2 þ

N X

wxi Du2i

ð1Þ

i¼1

without violating constraints (low=high limits), with xi ¼ i-th control variable (e.g., measured temperature), ri ¼ i-th reference variable (e.g., required temperature), ui ¼ i-th manipulated variable (e.g., control valve), and wxi ¼ weighting coefficient reflecting the relative importance of xi, t 2 E ¼ weighting coefficient penalizing relative big changes in ui.

Figure 1. Receding horizon strategy (Mohammed and Abdulrahman, 2009).



475

Figure 2. Block diagram of model predictive control system (Findeisen and Allgower, 2002).

MPC does not refer to a specific control strategy but to a very ample range of control methods that make explicit use of a model of the process to obtain the control signal by minimizing an objective function. This objective or cost function considers the deviations from a desired trajectory. An advantage of the MPC approach is that to minimize the cost function, constraints can also be taken into account. 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. Feedback is handled by updating the model at each time step. Normally the disturbance term is corrected 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 the future, which involves the application of the first control signal of the sequence calculated at each step. The differences between the various MPC algorithms are the models used to represent 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 an online optimization problem. With a linear model, with polyhedral constraints and a quadratic cost, the resulting optimization problem is a quadratic program (QP). Solving the QP using general-purpose methods can be slow, and this has traditionally limited MPC to applications with slow dynamics, with sample times measured in seconds or minutes. One method for implementing fast MPC is to compute the solution of the QP explicitly as a function of the initial state; the control action is then implemented on-line in the form of a lookup table. The major drawback here is that the number of entries in the table can grow exponentially with the horizon, state, and input dimensions, so that ‘‘explicit MPC’’ can be applied reliably only to small problems.

476


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 first discuss possible objective functions, then possible process models that can be used for MPC. Here, there are several different choices for objectives functions. The first one that comes to mind is a standard least-squares or ‘‘quadratic’’ objective function. The objective function is a ‘‘sum of squares’’ of the predicted errors (differences between the set points and model-predicted outputs) and the control moves (changes in control action from step to step). A quadratic objective function, for example, for a prediction horizon of 3 and a control horizon of 2, can be written as U ¼ ðrkþ1 ^ ykþ1 Þ2 þ ðrkþ2 ^ ykþ2 Þ2 þ ðrkþ3 ^ykþ3 Þ2 þ wDu2k þ wDu2kþ1

ð2Þ

where ^ y represents the model predicted output, r is the set point, Du is the change in manipulated input from one sample to the next, w is a weight for the changes in the manipulated input, and the subscripts indicate the sample time (k is the current sample time). For a prediction horizon of P and a control horizon of M, the least-squares objective function is written U¼

P X

ðrkþ1 ^ ykþi Þ2 þ w

i¼1

M 1 X

Du2kþ1

ð3Þ

i¼0

Another possible objective function is to simply take a sum of the absolute values of the predicted errors and control moves. For a prediction horizon of 3 and a control horizon of 2, the absolute value objective function is U ¼ jðrkþ1 ^ ykþ1 Þj þ jðrkþ2 ^ ykþ2 Þj þ jðrkþ3 ^ykþ3 Þj þ wjDuk j þ wjDukþ1 j

ð4Þ

which has the following general form for a prediction horizon of P and a control horizon of M: U¼

P X

jðrkþi ^ ykþ1 Þj þ w

i¼1

M 1 X

jDukþi j

ð5Þ

i¼0

The optimization problem solved stated as a minimization of the objective function, obtained by adjusting M control moves, subject to modeling equations (equality constraints) and constraints on the inputs and outputs min

U

Duk... DukþM1

ð6Þ

Minimization of objective functions by the least-squares method is by far the most common objective function in MPC. The least-squares method gives analytical solutions for unconstrained problems. It also compensates for relatively larger errors more than for smaller errors. The absolute value objective function is used in few


477

algorithms because linear programming problems result during optimization. Linear programming is frequently solved in large-scale allocation and scheduling problems. For an example, an oil company often uses linear programming to decide how to distribute oil to various refineries. Also, linear programming is useful to decide how much and what product to produce at each plant. However, the linear programming approach is not useful for model predictive control because the manipulated variable often moves from one extreme constraint to another.


Optimization Tools in MPC Optimization provides a management tool for achieving the greatest possible efficiency or profitability in the operation of any given production process. Changes in the operational environment, consisting of current constraints and values for the disturbance variables, will inevitably alter the optimal position. Hence, the optimizing control must be able to cope with change. The most difficult task in the design of an optimization control system is the definition of the problem scope and the subsequent choice of optimization tactics. The need for an on-line optimizing system can be ascertained only following an in-depth feasibility study. Process optimization plays an important role in the efficient use of resources or the minimization of undesired by-products in chemical engineering. Soft constraints allow for violation of process constraints, penalizing measurement limit violation in an attempt to keep the process within specifications. Soft constraints significantly affect the controller objective function when the process output constraints are violated and avoid the creation of infeasible optimization problems. Adequate performance (minimal constraint violation) can be established by tightening the soft output constraints to levels much higher than the actual constraint values. If both set-point tracking and soft constraints are required for a measurement, a new process model with the measurement expressed twice can be used, once for enforcing soft constraints and once for reference tracking. The soft constraints values for a measurement are not required to be equal to each other or the reference value. An MPC controller can be developed that explicitly accounts for process output control objectives. In most situations, specific control objectives are either satisfied or not satisfied. Discrete (binary) variables can be used to represent the value of control objectives.

Linearization-Based MPC Solutions Lack of online measurements and input constraints are two important problems that are sometimes neglected in academic studies. Most nonlinear control techniques proposed are based on feedback linearization or MPC, or, a nonlinear model predictive control based on a piecewise linear Wiener model. Automatic self-tuning within the regulation-optimization loop is not yet a common industrial practice, possibly because human supervisors are reluctant to accept automation systems that have a hidden logic. As a result, performance problems in the regulation layer prevent reaping most of the benefits of implementing real-time optimization. It is worth noting that although a linear MPC can handle very efficiently issues such as loop interaction, constraints, and unknown delays, these types of controllers cannot deal successfully with the problem of significant nonlinearities in process dynamics. On the other hand, nonlinear MPCs (NMPCs) are still too complex and demand significant

478


computing power, which makes them impractical for industrial process control applications. As an alternative, model predictive control philosophy can readily integrate reduced-order process models that incorporate first principles to face nonlinearities. Yet the resulting controller is simple to analyze and implement in industrial control systems even with high sampling rates. The new form of nonlinear predictive control, called parametric predictive control (PPC), avoids the above problems (Assandri et al., 2004).


Advantages of MPC Conventional controllers just make ad-hoc decisions regarding the current error signal, but the predictive controller considers future error signals as well to make a convenient decision. This in turn means that the common proportional-integralderivative (PID) controller uses whatever error from set point as a reference for action. MPC has low computational cost for solving the optimization problem in model development, while leading to a closed-form controller that is much easier to use than empirically tuning an auto-tuned PID. An attractive attribute of MPC technology is its ability to systematically account for process constraints. It has been successfully applied to many various linear, nonlinear systems in process industries and is becoming more widespread. The MPC’s ability to handle process control problems, namely multivariable dynamics, delays, and constraints, in a consistent, systematic manner makes it the one of the most accepted techniques for controlling multivariable constrained systems. There are some features that individualize MPC in the field of control design, making it attractive. In contrast to other feedback controllers that calculate the control action based on present or past information, MPC determines the control action based on the prediction of future dynamics of the system. Due to the future prediction, early control action can be taken accounting for future behavior. MPC is able to obtain better control performance in the presence of constraints since it is able to determine the current control action for minimizing the errors caused by constraints that are predicted to become active in the future. The number of computed values in the manipulated variable sequence is finite (finite input horizon) and discrete in time, accounting for the fact that the involved optimization 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 control performance in the presence of interactions, and MPC can successfully handle such cases. 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 relatively simple 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.


479

4. Its extension to the treatment of constraints is conceptually simple and this can be included systematically during the design process, etc.


Current Issues and Their Solutions Pertaining to Various Chemical Engineering Systems Predictive control, which is a useful advanced industrial control technique, has been accepted worldwide in recent years. It took more than 15 years after MPC appeared in industry as an effective means to cope with constraints on the state or control signal control problems that its mathematical background appeared in a steady framework. The issues of feasibility of on-line optimization, stability, and performance are acceptably understood for systems described by linear models. Many challenges have been dealt with due to these issues for nonlinear systems as well, but there are many questions still remaining about practical applications. This review takes up the systems listed below based on the manner in which MPC has been applied to each individual system and how the systems behave while giving the desired results so as to make the modeling process easy and also overcoming the drawbacks that are generally 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 corresponding solutions proposed by them are discussed in the section following, where various chemical systems are discussed in detail. An important obstacle in the operation of batch reactors that is blocking the widespread use of NMPC is the computational complexity of the associated rigorous dynamic models, which comprise large sets of highly nonlinear differential and algebraic equations (DAEs) that are an issue when larger and more sophisticated process models are considered. Also, the question of closed-loop stability is of great importance. In continuous stirred tank reactors (CSTRs), the plants may be sufficiently nonlinear to hinder the successful application of linear MPC (LMPC). The use of NMPC for plant-wide control is problematic due to complications associated with dynamic modeling, state estimation, and on-line optimization. Large-scale nonlinear models are extremely difficult to obtain using fundamental modeling and available techniques for empirical nonlinear modeling. Another complication is that unmeasured state variables must be estimated from available on-line measurements. This requires the design of a nonlinear observer, which is a difficult task despite recent advances. Even if a suitable nonlinear model is available, a nonlinear programming problem must be solved at each sampling period to generate the control moves. For large-scale systems the optimization problem may be computationally intractable due to the large number of decision variables and the complexity of the constraints resulting from the nonlinear model equations. In case of tubular reactors the formulation of a meaningful objective function is not always easy in terms of the end use properties of produced products. The control system design and implementation have to solve challenging tasks. The multivariable character of the process presenting strong interactions, the nonlinear behavior leading to the need for nonlinear control, and the demand to operate the unit in the presence of material and operating constraints are the main ones. Additionally, the control system has to cope with both large and short time constants and to face changing operating

480


conditions, in the presence of usually unmeasured disturbances. The conventional MPC technique is not designed to exploit the periodic nature of repetitive processes and therefore lacks the ability to improve the control performance as runs are repeated.

Issues and Their Solutions Pertaining to Various Chemical Engineering Systems


Batch Reactors Karer et al. (2007) and Causa et al. (2008) proposed formulations for a hybrid fuzzy model; the former’s model was based on a hierarchical structure and can be written in a compact form, whereas the latter used the design of hybrid fuzzy predictive control based on a genetic algorithm (GA) (HFPC-GA) on a batch reactor for which the prediction model is given by a nonlinear function as a T-S fuzzy hybrid model and the manipulated variable and=or state variable are integer=discrete. Karer et al. (2007) introduced an efficient parameter-estimation method. They proved that a hybrid fuzzy model is suitable for implementation in the MPC of nonlinear hybrid systems with discrete inputs based on a reachability analysis. Their goal was to control the temperature of the ingredients that were stirred in the reactor core so that they synthesized into the final product. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid nonlinear-stiff systems such as batch reactors. Finally, a comparison between 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 results showed that the computation time in the case of the GA remains constant during the whole simulation. Xaumier et al. (2002) used the DAE system that is solved over the prediction horizon at each iterative step of the nonlinear programming (NLP) procedure for the control of a reactive distillation column and for the control of a laboratory-scale fixed-bed water-gas shift reactor. Their main objective was to show experimental results of the application of such a technique on an industrial batch process: a glass-lined 16 L reactor. Their results presented the time evolution of the reactor temperature, the temperature set point, and the manipulated variable corresponding to the heat generation rate profiles and showed that each experiment corresponds to a different temperature set-point profile with the desired temperature of the reaction step. They concluded that an estimation of the dynamic evolution of the heat generation rate over a past finite horizon will permit the addition of feed-forward information in the predictions. Bouchenchir et al. (2006) applied the predictive functional control (PFC) technique to the temperature control of a chemical batch jacketed reactor equipped with a mono-fluid heating=cooling system. The issue they dealt was that batch and fed-batch reactors require good temperature control due to the existence of heatsensitive chemical reactants and=or products and also to the dependency of reaction rate on temperature. They obtained experimental results for the temperature control of an exothermic acid-base neutralization chemical reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH) to test the robustness of the control system when the dynamics change over, due to heat release, during the constant set-point stage.


481


Ruiz Massa and Ruiz Garcıá (2003) performed a feasibility study for the implementation of an advanced control technique (predictive control for temperature control for chemical reactors [PCR]) for a batch reactor for polyol production. Their main objective was to improve reactor temperature control. They found that the control technique they used suited the process equipment (heating and cooling system), so too much work was not necessary to adjust the parameters for all the recipes that run at the same reactor. The solution to the problems faced by the above-mentioned systems is that the developments in large-scale NLP algorithms and dynamic optimization strategies have enabled NMPC to become an attractive alternative. Tables I–V highlight the broad, extensive, and continuing increase in the application of model predictive control approaches in many chemical process control applications, indicating the problems 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 be decomposed into a single linear subsystem and a single nonlinear subsystem. The control objective was to regulate the reactor temperature by manipulating the coolant temperature, assuming the coolant jacket dynamics are negligible. Their problem was that due to the strong reactor nonlinearities, the temperature tracking performance is very poor and the bottom mole fraction deviates significantly from its set point. Hence they overcame this by applying a new class of plant-wide control methods 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 of temperature in the two-stirred-tank reactor used. To achieve this, simulation was carried out using the MATLAB Simulink software package. They used both PID controllers and MPC controllers for the study of control of reactor temperature, and their comparison showed that with the MPC controller the cooling agent consumption was 8% lower than with the PID controllers. Also, they proved that the reactor temperature was better controlled by the MPC controller even when process disturbances were present. Wu (2001) used an extended form of a linear matrix inequality (LMI)-based robust MPC technique for a general class of uncertain linear systems with timevarying, linear fractional transformation (LFT) perturbations to study the constrained control problem for an industrial CSTR. They used the general block diagonal scaling matrices corresponding to the structured uncertainty in the LMI optimization to reduce its conservatism. Their simulation results supported the applicability of this control technique to industrial problems. They also showed that the performance of robust MPC is closely related to the uncertain model derived from an original nonlinear plant. ˚ kesson et al. (2006) used the approach studied by various researchers that is A formulated for constrained MPC-type nonlinear optimal control problems with structural constraints. They represented the control law with a feed-forward neural network with one hidden layer with hyperbolic tangent activation functions. Their simulation used two examples, namely the pH neutralization process and a simulated multivariable non-isothermal with continuous stirred tank reactor, applying an explicit MPC scheme to the process by using a neural network to approximate the

482 Objective was to regulate the reactor temperature by manipulating the coolant temperature Used both PID controllers and the MPC controllers for the study of control of reactor temperature

Cormos and Agach (2005)

CSTR

Batch reactor

Ruiz Massa and Ruiz Garcıá (2003) Zhu (2001)

CSTR

Batch reactor

Chemical batch jacketed reactor

Bouchenchir et al. (2006)

Causa et al. (2008)

Batch reactors require good temperature control due to the existence of heat-sensitive chemical reactants and=or products Hybrid fuzzy predictive control based on a GA (HFPC-GA). The goal was to control the temperature of the ingredients stirred in the reactor core To improve reactor temperature control

Batch reactor

Xaumier et al. (2002)

A hybrid fuzzy model. Goal was to control the temperature of the ingredients stirred in the reactor core so that they synthesize into the final product Dynamic model. Objective was to show experimental results of the application of such a technique on an industrial batch process: a glass-lined 16 L reactor

Batch reactor

Karer et al. (2007)

MPC approach and problem

Chemical system

Reference

Table I. Summary of model predictive control approaches in chemical systems Solution

Application of a new class of plant-wide control methods based on integrating LMPC and NMPC. Showed that in MPC controller the cooling agent consumption was lower by 8% comparison with the PID controllers

Deterimined that the control technique used suited the process equipment

By suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid nonlinear-stiff systems Their results presented the time evolution of the reactor temperature, the temperature set point, and the manipulated variable corresponding to the heat generation rate profiles The evolution of control errors shows that at least an adequate model for the batch reactor permits a better temperature control. Computation time in the case of the GA remains constant during the whole simulation


483

Nonlinear plug-flow tabular reactor

SMB chromatography system

SMB

Natarajan and Lee (2000)

Song et al. (2006)

CSTR

CSTR

CSTR

CSTR

Arefi et al. (2008)

Silva et al. (1999) Lussoń Cervantes et al. (2003)

˚´ kesson and A Toivonen (2006)

Wu (2001)

State space model. to solve the problem of significant transient error caused in conventional feedback controllers, like PID controllers Lumped solid diffusion model. Multiple-input multiple-output (MIMO) control problem.

MPC using the simultaneous solution and optimization strategy Presented a particular realization for the Wiener model. Dealt with problem of uncertainty characterization for application in analysis and design of robust systems Nonlinear model predictive control based on classic optimization methods with nonlinear identification using Wiener model

Used extended form of linear matrix inequality (LMI)-based robust MPC technique Explicit MPC

(Continued )

Set-point tracking behavior of the regulator (closed-loop) system with NMPC, along with the coolant flow signal was compared with the linear MPC and PI controllers; the results prove the higher performance of the NMPC for different operating conditions Repetitive model predictive control (RMPC), which is the combination of repetitive control (RC) and model predictive control (MPC) Objective was to optimize the profit and maintain high product purities

Simulation results supported the applicability of this control technique to industrial problems Simulation results showed that the neural network controller achieves near-optimal control performance for various disturbance types Presented a simpler formulation of the nonlinear programming approach Proved that robust WMPC follows the set point better than the other controllers


484

Three different kinds of MPC strategies: MPC algorithms, a QDMC, and NLMPC First-principles model for dynamic behavior description

Wastewater treatment


Shen et al. (2009)

Cristea and Agachi (2006)

Active set method (projection method) for solving this QP problem

Novelty lies in the inverse of penicillin concentration as a cost function




Fed-batch fermentor

Holenda et al. (2008)

Corriou and Pons (2004)

Mohammed and Abdulrahman (2009) Ashoori et al. (2009)

Used process model to maintain the dissolved oxygen concentration at a given level Extension of dynamic matrix control (QDMC).

Optimal control problem. Aim of the simulation was to assess the flexibility of the proposed scheme

SMB

Alamir et al. (2006)


Chemical system

Reference

Table I. Continued Solution

Nonlinear model is substituted with neuro-fuzzy piecewise linear models

Showed how the controller takes into account sudden changes in the fired auxiliary cost and increases appropriately the corresponding value All the model predictive controllers perform well during the first period of steady influent Objective was the maintenance of the effluent soluble substrate (pollutant) concentration. Found that the set-point tracking performance of the MPC control approach is also very good Results showed that lower prediction horizon reduced significantly the integral of absolute and square error Results showed that in the absence of unmeasured disturbances, the controller performed very well and the set points were followed without problem Proved that MPC algorithm adapts quickly to changing conditions of the water supply network system


485

ALSTOM gasifier

Chemical reactor system

Yu and Yu (2007)

Fermenter

Srinivasarao et al. (2007)

Al Seyab and Cao (2006)

Industrial fed-batch processes

Kova´rova´Kovar et al. (2000)

Biochemical process control

Nonlinear continuous fermentor

Ramasamy et al. (2005)

Silva and Kwong (1999)

Airlift photo bioreactors

Berenguel et al. (2004)

Designed and implemented three decentralized PID controllers to demonstrate the improvement in on-line control performance using the NMPC scheme with PLRBF models

Adaptive scheme ADMC (adaptive dynamic matrix control). Controller objective was to maintain productivity at the closest possible desired level Developed a partially nonlinear Wiener type model

A priori model that was typicallydeveloped from first principles

A combination of predictive control and ANN model

Showed that control of a benchmark system, prevention of batch mode, and minimization of washout occurs only in a narrow operating region

Cost effective model predictive control (MPC) strategy

(Continued )

Proved that the proposed controller was able to control the plant without any constraints violation Results confirmed that the control performance is not significantly deteriorated by the disturbance and the system stability is also well maintained

Showed the improvements obtained when implementing an on-off predictive control scheme Proved that analysis of closed-loop trajectories clearly explained relation between manipulated input and system behavior for different conditions and established regions for optimum controller performance Showed that with riboflavin process product amount and product yield are closely connected and cannot be optimized separately Simulation results applied to a heater-mixer setup. Developed a grey box model for this process as a benchmark for validating the identified models Maintained a high level of closed-loop performance in the servo control problem


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pH neutralization process

UOP type fluid catalytic cracking unit (FCCU)

Fluidized catalytic cracking unit (FCCU) Distillation column

Mahmoodi et al. (2009)

Cristea et al. (2003)

Jia et al. (2003)

Bloemen et al. (2001)

Moderate- to high-purity distillation column simulation model.

Chemical reactor system

Qian et al. (2007)

Abou-Jeyab (2001)

Chemical system

Reference

Table I. Continued

Wiener model–based identification and control technology for dual composition control

Objective was an adequately reduced model to describe important variable variations like pressure effects and use of oversimplified kinetics Objective was to maintain the optimum operating condition

Three-lump model

MPC based Wiener-Laguerre model

BP-ARX model


Solution Results showed that NMPC based on BP-ARX model provides better set-point tracking than RGPC from the point of quickly respond to set-point change and faster settling time Results proved that compared to the Laguerre model the Wiener-Laguerre model modeled the nonlinear gain better Results obtained by dynamic simulation presented a good fit with industrial operating data, simulated variables being situated in a range corresponding to industrial unit behavior Control objective was to maintain the controlled variables at predetermined set points in the presence of typical process disturbances Linear programming (LP) formulation using a simplified model predictive control algorithm Results showed that difference between the measure output and predicted output is hardly distinguishable, indicating Wiener model is able to describe accurately the behavior of the distillation column in a closed-loop setting


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Baotic´ et al. (2003) Thomas et al. (2004)

Borrelli et al. (2003) and Borrelli (2003)

Bemporad et al. (2002b)

Bemporad et al. (2000)

Mahfouf et al. (2002) Bemporad and Morari (1999) and Bemporad et al. (2002a)

Reference

A linear criterion for the proposed algorithm Hybrid predictive controller partitioning in the state-space domain. In every partition some variables change, while the others remain constant

Applied to a gas-supply system that considers quantized manipulated variables

Predictive control scheme for hybrid systems solved by using mixed integer quadratic programming (MIQP). The main problem with MIQP is its computational complexity, which increases the time required to find the solution Predictive control design for piece-wise affine (PWA) systems, as these are models for describing both nonlinear and hybrid systems Hybrid system with the predictive control based on a quadratic objective function and linear constraints that is a subclass of the mixed logical dynamical (MLD) hybrid system A finite-time optimal control solution for PWA systems with a quadratic performance criterion

(Continued )

Result opens up the use of robustness and stability tools developed for hybrid model classes, to study the closed-loop properties of hybrid predictive control. Controller is based on a dynamic programming recursion and a multi-parametric quadratic programming solver. Thus, the optimization problem is solved for each partition of the PWA system Results in reduced computation time Reduces computation time

Reachability conditions are established.

With different fuzzy partitions of the input space

Solution

Takagi-Sugeno (T-S) fuzzy model


Table II. Summary of model predictive control approaches in batch reactors


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Hybrid predictive control strategy based on a fuzzy model. The key element of the fuzzy identification is the detection and estimation of switching regions by combining fuzzy clustering and a principal component analysis To obtain a good solution in a reasonable time for the fuzzy predictive control optimization problem

Nunez et al. (2006)

Sarimveis and Bafas (2003)

Potocnik et al. (2004) Skrjanc et al. (2005)

Hybrid predictive approach based on a temporal decomposition scheme. Duality properties are used to translate the original optimal control problem into a temporal sequence of independent sub problems with a smaller dimension Hybrid predictive control algorithm with discrete inputs based on a reachability analysis Modeling and identification using the interval fuzzy model (INFUMO)


Beccuti et al. (2003)

Reference

Table II. Continued Solution

Specialized GA optimization method for fuzzy predictive control based on Takagi-Sugeno models

Computation time is reduced by building and pruning an evolution tree Useful for describing a family of uncertain nonlinear functions or when systems with uncertain physical parameters are observed The nonlinear NP-hard optimization problem was solved efficiently by using the genetic algorithms, in terms of accuracy and computation time

This solution approximates the optimal, but the computation time is significantly reduced



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Table III. Summary of model predictive control approaches in fermenters


References


Method and solution

Sheng et al. (2002)

The state space formulation of GPC

Amirthalingam and Lee (1999)

A method of identifying a linear fast rate model together with a noise model using the sub-space identification approach. Sub-space identification based approach

For nonuniformly sampled data systems, which include multi-rate sampled data systems as a special case The identified model is further used to develop a multi-rate Kalman filter and an inferential linear MPC scheme For developing a deterministic fast rate model from multi-rate sampled data For the case where the input and output sampling rates are co-prime Feedback linearization is used to induce linear closed-loop input-output behavior, which facilitates the analysis of closed-loop stability and performance in the absence of plant model mismatch Involving free radical polymerization

Li et al. (2001)

Wang et al. (2004)

Fast rate model

Niemiec and Kravaris (2002)

A multi-rate version of nonlinear model algorithmic control for regularly sampled multi-rate systems

Niemiec et al. (2002)

Applicability of the approach on an experimental reactor system Also applied multi-rate NMPC formulations Cybernetic model–based nonlinear multi-rate MPC.

Prasad et al. (2002) Gadkar et al. (2003)

To control polymerization processes Track the maximum achievable productivity in a continuous bioreactor with cell recycle

optimal MPC strategy for the former and both centralized and decentralized neural network model predictive controllers designed for the latter. Their inference was that the training of the decentralized neural network controllers proved to be more demanding both computationally and with respect to the quality of training data required. Silva et al. (1999) developed a new algorithm for model predictive control using the simultaneous solution and optimization strategy. Their objective was to present a simpler formulation of the nonlinear programming approach using a simultaneous strategy. They simulated three control problems of continuously stirred tank

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Table IV. Summary of model predictive control approaches in pH neutralization References


Su and McAvoy Development of RNN (1997) models is considerably more difficult than development of FNN models


Dumont et al. (2004)

Sentoni et al. (1998) Saha et al. (2004)

Model of Wiener-Laguerre type for developing an adaptive predictive control scheme Used ANNs

Method and solution Necessary to evolve a scheme for the development of a black-box model in which the model structure can be selected relatively easily and the resulting model is valid over a wide operating range For controlling SISO nonlinear systems

For constructing a nonlinear state output map. Model completely fails to Wiener-Laguerre model is used for predict the plant nonlinear model predictive control. behavior when the Wiener-Laguerre structure validation data set is improves the quality of modeling used together with the rate of convergence of SQP in a reasonable time. The performance of the controller based on the identified Wiener-Laguerre model shows that this model presents better prediction capabilities thna the identified linear Laguerre model

reactors to demonstrate the effectiveness of the new algorithm. An adiabatic CSTR with an exothermic, first-order irreversible reaction was used as a single-input, single-output (SISO) nonlinear process, a stirred tank reactor was used as an example of a multiple-input, multiple-output (MIMO) nonlinear process where in two versions of the nonlinear MPC algorithm were considered, and finally a continuous fermenter subject to disturbances in the model parameters was simulated. Lussoń 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 presented a strategy to identify Wiener models with PWL functions representing the nonlinear gain. A combination of dynamic as well as stationary data was then used in the evaluation of the uncertainty bounds. They took up a CSTR as their case study. They studied the data distribution in order to estimate the generalization properties of the resulting model. From their results they proved that conservatism was 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 series as the test system. They developed an MPC controller for each model, and the performance of these controllers subjected to a set-point change and an output

491

Population balance model for a non-isothermal styrene emulsion polymerization system

Combined batch-to-batch and within-batch online control approaches based on a partial least squares (PLS) model for the control of the whole PSD in a semi-batch styrene emulsion polymerization system

MPC controller that utilizes a PLS model.

Flores-Cerrillo and MacGregor (2003)

Park et al. (2004)


Meadows et al. (2003)

References

Table V. Summary of model predictive control approaches in drying systems Solution

(Continued )

Temperature profile of the batch affected the breadth of the final PSD along with the surfactant feed to the system. Designed an optimal controller to achieve a target multimodal distribution by manipulating the temperature as a manipulated variable Used midcourse correction (MCC) strategies in a minimum-variance controller framework with batch-to-batch adaptation to improve the performance of the PLS model that predicted the bimodal end-point distribution. Tested the strategy for regulating disturbances arising from uncertainties in the nucleation stage and tracking set-point changes that occurred during the batch Predicted the end-point bimodal PSD in an experimental semi batch emulsion copolymerization reactor.


492

Shi et al. (2006)

Alhamad et al. (2005)

References

Table V. Continued

Designed model-based control algorithms for a continuous and a batch crystallizer, where reduced-order models based on moments of the PSD were utilized.

Applied a dynamic matrix controller (DMC) to an experimental styrene=MMA emulsion copolymerization system.


Solution The average radius, particle size polydispersity index (PSPI), average molecular weight (Mn), and monomer conversion were regulated by the DMC to their optimal trajectories. The optimal trajectories for the outputs were determined by two scenarios, to maximize PSPI and to maximize Mn For the continuous crystallizer, a hybrid predictive controller manipulated the feed solute concentration to regulate the first four moments of the PSD and the solute concentration to an open-loop unstable steady state. In the seeded batch crystallizer case, an MPC controller was designed that manipulated jacket temperature to minimize the third moment of the crystals formed by nucleation



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disturbance provides the basis for comparison. Their results proved that all four models correctly predict the dynamic behavior of the volume. In all cases that were evaluated both reduced nonlinear models provided a closer approximation to the system behavior than the linear model. The solution to the problems faced by the above-mentioned systems is a plant-wide control strategy based on integrating LMPC and NMPC, which is the best option to resolve the issue of decomposing the plant according to the degree of nonlinearity.


Tubular Reactors (Wiener Digesters) Wisnewski and Doyle (1998) applied MPC over a Kamyr digester, which is a two-phase tubular reactor used for the kraft process to convert wood chips to pulp through reaction with a heated caustizing solution ‘‘white liquor.’’ Their objective was to minimize the variations of the kappa number, the measure of the residual lignin, the glue-like substance binding cellulose fiber together, in the presence of measured and unmeasured disturbances. They used a Weyerhaeuser digester problem (WDP), which is a simplified process model to capture the major dynamic characteristics of digester behavior. They used a robust selection procedure to select the ‘‘best’’ manipulated input as well as the ‘‘best’’ set of secondary measurements for the 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 flow rate as the manipulated variable and the secondary measurement set. They found that the use of either trim flow rate provides quick disturbance rejection and set-point tracking for the series of disturbances as well as maintains the kappa number. They also noted that the danger of using the trim flow rates to control the kappa number is that large countercurrent flows of the free liquor can cause the chip flow to stop, increasing their residence time and cooking the chips too long. Arefi et al. (2008) used a nonlinear model predictive control based on classic optimization methods with nonlinear identification using the Wiener model for a highly nonlinear plug-flow tabular reactor. They proposed two methodologies for temperature control of reactor, namely the direct Q model and HYSYS. Their aim was to control the temperature of the output liquid of the reactor by manipulating the coolant flow. Set-point tracking behavior of the regulator (closed-loop) system with NMPC, along with the coolant flow signal, was compared with the linear MPC and PI controllers to find that the results prove the higher performance of NMPC for different operating conditions, especially when it is far from the point where the linear model is identified, thus concluding that the results showed the capability 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 chromatography system, which is a continuous periodic process. To solve the problem of significant transient error caused in conventional feedback controllers like PID controllers or model predictive controllers due to non-minimum-phase dynamics and model errors run after run, they adopted repetitive model predictive control (RMPC), which is the combination of repetitive control (RC) and model predictive control (MPC). Their challenge lay in modeling the complex hybrid dynamics of the process and using


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an appropriate controller that makes use of the periodicity information of the process. Their objective for optimization was to maximize the product yield, which is subject to the constraints that express purity limits. Their results proved that the performance 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 phase movement of the corresponding true moving bed (TMB) process, in which the fluid and solid phases flow countercurrently to each other. They preferred the ‘‘local equilibrium theory of chromatography.’’ They used the lumped solid diffusion model to describe a standard SMB unit with four sections. A case study dealing with separation of the enantiomers of 1-1-bi-2-naphthol was considered with the first principles model as the virtual process to generate input=output data to be used in process identification and to carry out simulation studies for the evaluation of the performance of the designed controller. Their main objective was to optimize profit and maintain high product purities. They evaluated the performance of the controller in two typical control problems of practical interest for the SMB process, namely, rejection of disturbances and tracking of set-point changes. They showed how the process can maintain its productivity while solvent consumption continuously decreases, which brings about continuous reduction of extract and raffinate flow rates. Erdem et al. (2006) proposed an on-line optimization-based SMB control scheme that allows exploiting the full economic potential of the SMB technology on the basis of minimal information. Their work addressed the experimental implementation of the developed control concept on an eight-column four-section laboratory SMB unit that is used to separate the binary mixture of nucleosides uridine and guanosine. The reported results were aimed at demonstrating that the controller is able to deliver products with specified purities and to optimize process performance despite uncertainties in system behavior and disturbances taking place during operation. Alamir et al. (2006) used MPC to control the simulated moving bed (SMB) process by using feedback methodology. They had an optimal control problem that was solved during the system lifetime in the sense that the iterations leading to its solution are distributed in time. The aim of the simulation was to assess the flexibility of the proposed scheme and its reactivity to sudden changes in the auxiliary cost function. They showed how the controller takes into account sudden changes in the fired auxiliary cost and increases appropriately the corresponding value while keeping the purities above the required set points. They also showed the high sensitivity of such high-separation SMB to model uncertainties and suggest using some on-line identification scheme in conjunction with the proposed control. One of the aims is to reduce, during the sampling period, on-line calculation time due 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 the drawbacks of MPC is the computational time aspect, especially when the model becomes more complex and more accurate. Indeed, the model is intended to predict future dynamic behavior of the process output over a finite prediction horizon and has 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 multivariable frame subject to environmental and operational constraints rather than a single problem such as dissolved oxygen control or nitrate control. They actually



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used three different kinds of MPC strategies, namely the dynamic matrix control (DMC) algorithm without constraints, which represents the first generation of MPC algorithms, a quadratic dynamic matrix controller (QDMC) version with hard linear constraints, which is considered to be a representative of the second generation of the MPC algorithms, and an NLMPC version with hard constraints on the inputs and soft constraints on the outputs. The simulation results presented in this article indicate that all the model predictive controllers perform well during the first period of steady influent. Cristea et al. (2006) used model predictive control on the activated sludge process in which biological treatment is to convert soluble organic contaminants into insoluble organic and inorganic constituents or to CO2 and H2O, specifically the way this control algorithm may be used for the control of a suspended growth aerobic system. They used the first-principles model both for the dynamic behavior description of the unit and for building the simulator on which the model-based control strategies were investigated. They found that the set-point tracking performance of the MPC control approach is also very good. Holenda et al. (2008) used a model predictive control to maintain the dissolved oxygen concentration at a certain set point based on a linear state-space model of the aeration process. They chose two internationally accepted models to simulate the processes in the wastewater treatment plant. They used the process model to maintain the dissolved oxygen concentration at a given level. A basic control strategy was proposed to test the benchmark; the aim is to control the dissolved oxygen level in the final compartment of the reactor by manipulation of the oxygen transfer coefficient. The results showed that a lower prediction horizon significantly reduced the integral of absolute and square error; however, input weight had insignificant effect 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 defining a plant layout, a simulation model including influent loads, test procedures, and evaluation criteria. Their aim of the layout was C=N removal and was largely used for full-scale plants. It is composed of a biological reactor and a clarifier. The International Water Association (IWA) activated sludge model was chosen to simulate the biological processes. Also, the double-exponential settling velocity model was selected to describe the behavior of the clarifier. They used the extension of QDMC, and they obtained the results using benchmark FORTRAN implementation. Their results showed that in the absence of unmeasured disturbances, the controller performed very well and the set-points were followed without problem. Mohammed and Abdulrahman (2009) had the objective of controlling a water supply network system using MPC algorithm. They used the active set method (projection method) for solving this quadratic programming (QP) problem supported in the MATLAB software package due to its fast convergence. They developed an SISO 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 system to a desired steady-state value. It was seen that the controller takes the system response to the new values, but from their results the performance is comparable, finally proving that the MPC algorithm adapts quickly to changing conditions of the water supply network system. The MPC structure can be modified to meet possible requirements concerning energy consumption and to handle the constraints applied to the system.

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Fermenters Ashoori et al. (2009) used an unstructured model for penicillin production in a fed-batch fermenter, applying MPC. Their novelty lies in the inverse of penicillin concentration as a cost function instead of a common quadratic regulating one in an optimization block. They compared their results from the displayed controller with that of an auto-tuned PID controller used in previous works. Also, in order to avoid high computational cost, the nonlinear model was substituted with neuro-fuzzy piecewise linear models obtained from a method called the locally linear model tree (LoLiMoT). Berenguel et al. (2004) dealt with the implementation of a cost-effective MPC strategy for closed airlift photo bioreactors used in the production of high-value algal products. Their objective was the control of pH of the culture by means of pure carbon dioxide injection for which the small range of flow injection values that produce nonlinear behavior of the system that is not severe in such a way that a linear model of the pH evolution in spite of changes in CO2 injection and solar radiation was obtained and used within an MPC framework to achieve desired regulation properties, trying to minimize CO2 losses. Their results showed that the MPC control algorithm 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 fermenter. They showed that the control of a benchmark system, prevention of batch mode, and minimization of washout occur only in a narrow operating region. They found from the time series response after implementing MPC on the bioreactor from one initial condition that the system was successfully controlled to the specified set point. They inferred that the controlled bioreactor is not directly driven to the required set point and also the nonlinearities associated with the system result in inefficient control, causing batch or washout conditions along the controlled system response. This is confounded by the fact that most bioreactors, although assumed to be homogeneous, actually exhibit large inhomogeneities. They finally proved that analysis of the closed-loop trajectories clearly explained the relation between manipulated input and the system behavior for different conditions and established regions for optimum controller performance. Kova´rova´-Kovar et al. (2000) used artificial neural networks (ANNs) for on-line optimization of industrial fed-batch processes. They used a combination of predictive control and an ANN model that was used to optimize the industrial fed-batch process for commercial production of riboflavin (vitamin B2) by a recombinant Bacillus subtilis strain. They found that at the beginning of the fed-batch process the specific riboflavin production rate and=or cell growth were maximized; later their impact diminishes in favor of riboflavin production. They showed that with the riboflavin process the product amount and the product yield are closely connected and cannot be optimized separately. Srinivasarao et al. (2007) studied a process where the quality variables are measured on-line, and time delays involved in the measurement assay are significantly large when compared to other process measurements (such as flows, level, temperatures, pressures, etc.) or the rate at which the manipulated input moves are also made. An a priori model that was typically developed from the first-principles model, with the parameters of the noise model used as tuning knobs, could be a solution but using the noise model parameters as tuning knobs can result in suboptimal



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inter-sample estimation and poor quality of inferential control. Their results indicated that it is difficult to make a comparison between the performance of single-rate and proposed multi-rate NMPC on common ground. They gave their simulation results applied to a heater-mixer setup. They developed a grey box model for this process as a benchmark for validating the identified models. Silva et al. (1999) used an adaptive scheme ADMC (adaptive dynamic matrix control) to the biochemical process control for maintaining operational conditions inside a specific optimum range for each process type, microorganism, and medium since it can identify the process on-line periodically under open- or closed-loop conditions. They used SQP (successive quadratic programming) in NMPC; two NMPC algorithms and ADMC were applied to a continuous fermentation process where productivity is the controlled variable and feed substrate concentration is the manipulated variable. These three algorithms were compared with standard DMC. They used an SISO-type control problem for evaluation of the performance of predictive controllers. Their controller objective was to maintain productivity at the closest possible desired level; the superiority of the nonlinear controllers and their results showed that controllers NMPC1 and NMPC2 presented different values for the manipulated variable when compared to ADMC and DMC. They investigated the performance of controller NMPC2, a MIMO-type servo control problem where the control objective was to move the system from the given initial condition to the optimum operational point; the results showed that NMPC2 maintained a high level of closed-loop performance in the servo control problem. Bioprocesses have complicated dynamics, therefore their control is a challenging and delicate task; they also are inherently concerned with nonlinearity and are non-stationary, which makes modeling and parameter estimation particularly difficult. Moreover, the scarcity of on-line measurements of the component concentrations makes this task more sophisticated. Obtaining pure product is the main goal of control. MPC is feasible for on-line optimization and has acceptable performance as well. Chemical Reactors Al Seyab and Cao (2006) used a nonlinear model predictive control based on the Wiener model of the ALSTOM gasifier. They preferred a Wiener structure consisting of a linear MIMO state-space part followed by a partially nonlinear static part to identify a black-box model of the gasifier plant. They showed that the plant=model mismatch was further reduced by developing a partially nonlinear Wiener type model instead of a pure linear model. More specifically, a feed-forward neural network (FFNN) was developed as a nonlinear static gain for one of four output channels, fuel gas pressure (PGAS), to compensate for its strong nonlinear behavior observed in the open-loop simulation. Also, they proved that the proposed controller was able to control the plant without any constraint violations and satisfied all the benchmark challenge requirements. Yu and Yu (2007) used multiple-input single-output neural models with different sample rates in model predictive control of a multivariable process, in order to reduce the number of optimized variables and consequently reduce the dimension of optimization and computing load. They first used three multiple-input single-output pseudo linear radial basis function (PLRBF) models with each representing one output followed by adopting a multi-rate control in the NMPC scheme to cope with


498


significant difference between dynamics for the three variables and a long transmission delay of the heating. They used a neural network model based an NMPC scheme to predict future process response over the specified horizon. On-line control was conducted to assess the NMPC control scheme for the same three aspects as in the simulation. On-line tracking performance proved that the system was stable and tracking was achieved. The tracking results confirmed that the control performance is not significantly deteriorated by the disturbance and system stability is also well maintained. It was finally shown that the overall performance of the multi-rate NMPC scheme based on PLRBF models was better than PID control. Qian et al. (2007) proposed and elaborated a novel nonlinear dynamic model for use in NMPC. The proposed model combines a second-order auto regressive with external 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 the BP-ARX model. They preferred using a three-layer BP network to represent the system static nonlinearity, where a nonlinear mapping between the system steady-state inputs and outputs can be carried out using the static network without feedback elements to describe the mapping. Their results showed that NMPC based on the BP-ARX model provides better set-point tracking than recursive generalized predictive control (RGPC) from the point of quickly responding to set-point change and faster settling time. The control effects of NMPC and RGPC demonstrated that NMPC can track the tank level faster and smoother, thus proving that NMPC has less fluctuation in manipulated variables than RGPC. Solutions to the problems faced by the above-mentioned systems can be found by using MPC As a consequence, MPC proves to be a good candidate for implementing advanced control due to its multivariable structure, direct approach of constraints, and optimal character. pH Neutralization Mahmoodi et al. (2009) made use of the Wiener-Laguerre model, which consists of Laguerre filters and simple polynomials that are used respectively as linear and nonlinear parts to evaluate identification of a pH neutralization process. Based on this model, a nonlinear model predictive controller was designed for a proper operation of the pH process in different set points, and the results were compared with those of a linear model predictive controller based on a linear Laguerre model. Their results showed that the linear Laguerre model captured the dynamics of the process but it cannot model its nonlinear gain; they concluded that adding a nonlinear mapping as the nonlinear gain was necessary to improve model accuracy. Their results proved that compared to the Laguerre model the Wiener-Laguerre model was the better model for nonlinear gain. From the simulation result with the MPC algorithm based on the linear Laguerre model they observed that the MPC based on the Laguerre model performed better than that based on the state-space model, when the operating region is far from the nominal operating conditions (pH 7), also proving that Wiener-Laguerre MPC performed slightly better than the MPC based on the linear Laguerre model. They finally concluded that NMPC based on Wiener-Laguerre showed better performance than the MPC based on the Wiener model but is slightly better than MPC based on the Laguerre model. ˚ kesson et al. (2005) dealt with the computational issues of model predictive A control of nonlinear sampled-data systems. They used a neural network to



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approximate the optimal strategy found by offline calculations. This approach was applied to a simulated highly nonlinear pH neutralization process. A neural network approximator was used for representing the nonlinear control strategy defined by the model predictive controller. Their results showed the system parameters as functions of pH. Robustness with respect to controller approximation was calculated for the pH control system using a small-signal linearized description. They also computed for an idealized situation with a linearized model and no model uncertainty. Kocijan et al. (2004) described an NMPC principle with a Gaussian process model. They obtained a model that describes the dynamic characteristics of a nonlinear system and at the same time provides information about the confidence in these predictions. They took a pH neutralization process as their case study. The pH was controlled by manipulating the base flow rate. The dynamic model of the pH neutralization system was derived using conservation equations and equilibrium relations. The control algorithm was tested for the pH process by simulation. They showed that the closed-loop system response avoids regions with large variance at the cost of steady-state error. Polymerization Reactors ¨ zkan and Kothare (2006) studied the stabilizing multi-model predictive control O strategy for controlling a nonlinear process at different operating conditions. In this research they extend the already formulated multi-model predictive control strategy to incorporate a stabilizing contractive constraint. They analyzed stability of the resulting closed-loop system using the multiple Lyapunov function approach and also proposed two different Lyapunov approaches. They concluded that the use of multiple Lyapunov functions enabled them to relax the monotonically decreasing condition of the Lyapunov function when the control algorithm switches from a quasi-infinite horizon to an infinite horizon strategy. They presented the only their work that dealt with the development of a stabilizing control strategy and stability analysis of the closed-loop system. ¨ zkan et al. (2003) used an MPC algorithm based on multiple piecewise linear O models to study the control of a solution copolymerization reactor of methyl methacrylate (MMA) and vinyl acetate. Their important control objective was to minimize grade transition time, and thereby reduce the amount off-specification product produced during transition, as polymer reactors need to operate in multiple operating regimes to manufacture several different grades of polymers. They developed a multiple model MPC technique using the theory of linear matrix inequalities (LMIs)=semi-definite programming. They illustrated the application of this algorithm on a low-order CSTR model with an exothermic first-order irreversible reaction. They depicted the effect of number of local models on the performance of 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 a piecewise linear Wiener model over it. They used Wiener and Hammerstein models, which are the block-oriented nonlinear models that are obtained by combining linear dynamic models with static or memoryless nonlinear functions. They modeled the static nonlinear element of the Wiener model, which is approximated using the piecewise 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


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were compared to those of a linear MPC. They analyzed the possibilities and the advantages of the use of a specific Wiener approximation to represent the model of the process. A comparison of NMPC and LMPC behavior for a polymerization process when the first output set points have changed shows that the NMPC controller has better performance, with short settling time and without any overshoot changes. All of the simulations showed that the maximum computation time for optimization at each sampling interval is sufficiently below the chosen sampling time and the control signals are feasible due to canonical structure of nonlinear gain. Park and Rhee (2001) used an LMI-based robust model predictive controller in a continuous MMA polymerization reactor with the polytopic uncertain model in order to control the monomer conversion and the weight-average molecular weight of the polymer product. They clearly demonstrated that the RMPC guarantees robust stability by presenting the regulatory performance of the LMI-based RMPC for monomer conversion. The simulation results showed that the controller performed satisfactorily and steadily in the case of the servo problem, although the jacket inlet temperature slightly oscillates while the conversion approaches the set point. Finally, they showed that the LMI-based RMPC gives rise to stable performance for conversion and average molecular weight. Espinosa and Van Brempt (2006) used an MPC for a classical batch process where the MPC controller used was an extended version of the MPC controller INCA (IPCOS novel control architecture). Since the main controlled variable in a batch process is the reactor temperature, the temperature was determined by two mechanisms: the heating and cooling capacity of the heat exchangers and the heat absorbed or generated by the reaction. Models of the heat exchanger tend to be simple and very easy to obtain, either by direct physical modeling or simple identification experiments. On the other hand, the chemical reactions tend to be complex and difficult to observe. Hence, their results showed that the model is kept synchronized with the plant by using a nonlinear observer based on the model. Dokucu et al. (2008) had the challenge of closed-loop regulation of emulsion polymerization systems; this presents a challenging control problem due to the complexity of the process and the lack of reliable high-frequency measurements. They developed a multi-rate MPC controller as a combination of the extended QDMC controller and the linear multi-rate MPC controller. The proposed algorithm was tested against two types of disturbance scenarios. In both cases the controller was able to reject the disturbances successfully. This shows that solids content can be used to infer the states of the system against these disturbances. Kashiwagi and Li (2004) explained the progress on Volterra modeling with a high 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-random M-sequence signal that provides enough excitation and yet is acceptable in an industrial situation. They used a van de Vusse reactor, where they carried out the control of two density components by adjusting the amount of input flow. Their results showed that while all nonparametric NMPC controllers offer zero offsets, the third-order one offers superior performance. They also compared the actual output and the Volterra estimates responding to a sinusoidal input; they found that the third-order model offers the best estimation and should be sufficient to preclude the need for a further higher-order model. They finally concluded that the nonparametric NMPC formulated from the third-order Volterra model offers the best closed-loop performance.



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Da Silva et al. (2008) used MPC for emulsion polymerization processes modeled by nonlinear partial distributed equations. They considered model predictive control of the free surfactant concentration in the aqueous phase, using the surfactant flow rate as a constrained manipulated variable. First, a dynamic model was adapted followed by control of the emulsion polymerization process for the PDE systems to reduce the on-line resolution time. They considered surfactant feed rate as a manipulated variable and free surfactant concentration in the aqueous phase as the controlled variable. Their results showed that the choice of the reference trajectory of the 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 the repetitive model predictive control (RMPC) is a new formulation of MPC in which the basic idea of RC is brought into conventional MPC formulation. The result is a technique 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 catalytic cracking unit (FCCU). They preferred a three-lump model for the global description of the phenomena taking place in the reactor; the reactor had two parts, the riser model and the stripper model. Their results obtained by dynamic simulation presented a good fit with industrial operating data, simulated variables being situated in a range corresponding to industrial unit behavior. Results revealed the superior behavior 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 controlled variables is high and the interactions between them are strong, a multivariable 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 substantially affected by the occurring constraint. Jia et al. (2003) used MPC on an FCCU where the control goals were to maximize the production of one or more products in different seasons. Their objective was an adequately reduced model to describe important variable variations like pressure effects and use oversimplified kinetics, to overcome the largest discrepancies appearing in the modeling of the dense bed in the regenerator, and to overcome disagreement on the necessity of taking into account the spatial character of the bubble phase in the dense bed; FCC models also have strong implications concerning the frequently related instability issues. They modeled the regenerator as a two-phase fluidized bed model, popularly known as K and L model. Their control objective was to maintain the controlled variables at predetermined set points in the presence of typical process disturbances while maintaining safe plant operation and restricting the magnitude per step of the regenerated and spent catalyst slide valves and flue gas butterfly valve stem movements. The plots of the control results showed that all the controlled 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. The reactor bed level has poorer control performance in terms of longer settling time and higher overshoot. Viera et al. (2005) applied neural network-based MPC to an FCCU. They used the first-principles model for simulations. Their main objective was to demonstrate that feed-forward neural network structures that are capable of identifying the


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FCCU and that the resulting MIMO model is a reliable one to be used on-line in a NMPC scheme. An ANN that was used was configured as a fully connected feed-forward network, with one hidden layer. They showed good agreement between the rigorous numerical simulations and the neural model predictions. They also compared the neural network MPC performance to a well-tuned DMC implementation and found that the neural network MPC response was smoother than that obtained from DMC algorithm implementation. Roman et al. (2009) presented simulation results obtained with a complex dynamic model of an FCCU. They developed a model that simulates the dynamic behavior of the reactor-regenerator-fractionator system and predicts the composition of the main products (gasoline and diesel). They developed the FCCU model based on reference construction and operation data from an industrial unit. With the newly developed dynamic simulator they studied the effects of different sets of disturbances. Results obtained with the dynamic simulator presented a good fit with industrial operating data, as simulated process variables are situated in a range corresponding to industrial unit behavior. To guarantee the stability of the closed-loop system even under a finite prediction horizon they used quasi-infinite-horizon nonlinear model predictive control (QIHNMPC), in which the prediction horizon is quasi-extended to infinity by introducing a terminal penalty term in the objective function. They compared QIHNMPC results with the nominal NMPC considered without the penalty term and the terminal constraints and found that the QIHNMPC achieved better control performance than the nominal NMPC, with, however, increased computational burden. They found that the overall performance of the moving horizon estimator (MHE)-NMPC was very good as the temperatures are kept close to the reference values. MPC based on NMPC performed better FCCU control than MPC based on LMPC, and both showed superior control performance over classical PID control. The advantages of a modern NMPC approach, the so-called quasi-infinitehorizon nonlinear model predictive control (QIHNMPC) and moving horizon estimator nonlinear MPC (MHE-NMPC), are shown to achieve better control performance, with, however, increased computational load. Based on a multiple shooting technique, an efficient solution of on-line optimization is obtained even for the case of the high dimensional model. Distillation Columns Abou-Jeyab et al. (2001) used a piecemeal fashion to solve the constrained optimization problem involved in control. Their objective was to maintain the optimum operating condition of a distillation column in the petroleum industry, for which they preferred MPC. Also, to solve the problem without decomposition, they preferred the use of the linear programming (LP) formulation using a simplified MPC algorithm. The LP approach requires a modest computational approach as it involves a very small size optimization problem. The approach led to cycling in the product composition that was present using SISO controllers, which resulted in a 2.5% increase in production rate, 0.5% increase in product recovery, and a significant increase in profit. Jin et al. (2003) dealt with the constrained multivariable control problem of distillation columns. They used the sulfonation of linear alkyl benzene (LAB) process as their case study, which consists of HF acid stripper, benzene column, paraffin



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column, and LAB column. They used MPC controllers by tuning them first and then on-line for three months. They then compared the performance before and after MPC implementation. Norquay et al. (1999) used a distillation column to overcome problems in high-purity columns, which tend to be ill-conditioned, leading to severe input directionality and output coupling. They undertook the case study of a C2-splitter at the Orica Olefins plant, located at Botany in Sydney, Australia. They had the heavy demand of satisfactory performance at a range of operating points, since the process does not have a single operating point about which a controller may be designed, but it must be able to perform equally well at a range of different feed rates and therefore operating points, the reason for which was that the plant throughput, based on customer demand, tends to be changed on a regular basis. Their other problem was that while a significant decrease in feed rate is conducive to a significant decrease in both reboil and reflux rates, the operators were generally uncomfortable with decreasing these rates. Another significant disturbance to the column was the vapor fraction of the feed. To overcome all these problems they proposed a dual composition controller be designed and implemented for the C2-splitter. They used a steady-state deterministic model and developed the simulation of the C2-splitter using the MATLAB Simulink package and used it to test the proposed control strategy in the face of set-point changes, feed changes, unmeasured disturbances, and model mismatch. The results of the data collected during the commissioning of the new control strategy showed much promise. Bloemen et al. (2001) used Wiener model–based identification and control technology for dual composition control of a moderate- to high-purity distillation column simulation model. They compared the direct closed-loop identification of a linear model with indirect closed-loop identification of a Wiener model. For the control part they compared the performance of the MPC algorithm based on the identified linear models and two different approaches to handle the Wiener model within a predictive control framework. Their results showed that the difference between the measured output and predicted output is hardly distinguishable, which indicates that the Wiener model is able to describe accurately the behavior of the distillation column in the closed-loop setting. In the optimization problem of the inverse Wiener MPC (IWMPC) algorithm the nonlinearity is inverted and removed from the control 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 binary packed distillation column simulated using a stagewise approach. They described the models as a set of ordinary differential equations in which the height of the column 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 concluded that a reasonable agreement is obtained. They compared their control results with using integral of the square of the error (ISE) criteria that the top temperature reaches to set point in a minimum time and less oscillation; it was concluded that DMC control has better performance than conventional control strategies. Assandri et al. (2004) used parametric predictive control (PPC), where MPC integrates reduced-order process models that incorporate first principles to face nonlinearities, applied to temperature control of batch reactors. Their main challenge was the bottom temperature in the column, which had significant feed composition variations; the column was to be operated over a broad range of operating conditions. The other issue was that for a linear MPC the need for continuous


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adaptation of model parameters, and possibly structure, prevents its practical use in an industrial setting. Their results showed the step changes in the bottom temperature set point. The performance of the controller also was seen to be very good for a wide range of operating conditions. Karacan (2003) used nonlinear long-range predictive control based on the NARIMAX model for a pilot-scale packed distillation column; in order to control the top temperature of the column experimentally and theoretically, reflux ratio was selected as a manipulated variable. They developed a dynamic model for the packed distillation column. Long-range predictive control (LRPC) was preferred over generalized minimum-variance and pole-placement because of its realistic and practical approach to a wide class of industrial problems. Their aim of the control was to maintain the top product temperature in the packed distillation column at the desired set point against disturbances in the form of varying feed composition and temperature. Their results showed that the second-order model was a reasonable compromise, and the estimated model with no filtering of the top temperature result is not in good agreement with experimental data. Ravi Chandra and Venkateswarlu (2007) proposed to design a multistep MPC strategy for the control of a reactive distillation column. The MPC of their work is based on the auto-regressive moving average (ARX) model structure, whose parameters are updated on-line using the process measurement information. Their objective was to control the desired product purity in the distillate stream despite disturbances in column operation. Their results showed the MPC and PI controller being applied for tracking a series of step changes in ethyl acetate composition. Their ISE results show the better performance of MPC towards the set point changes as well as in stabilizing the operation in the presence of input disturbances. Their results showed the delayed responses in both controllers, however, MPC exhibits better performance than the PI controller. Schwarm and Nikolaou (1999) examined a different aspect of constrained MPC robustness, namely robustness with respect to satisfaction by the actual system of inequality constraints posed in the on-line optimization problem. A method of incorporating model uncertainty into the output constraints of the on-line optimization to improve the robustness of constrained MPC was their goal. They used a high-purity distillation process as their case study. To develop a process model and uncertainty description for the purpose of demonstrating their method, they generated output data from the aforementioned state space model using a pseudo random binary sequence (PRBS) input. They then used standard least-squares techniques to identify multiple-input-single-output finite impulse response (FIR) models for each output using the corrupted data. Drying Systems Dufour et al. (2003) addressed the boundary control of nonlinear parabolic partial differential equation (PDE) systems characterized by complex nonlinearities in the spatial domain and at the boundary as well. Their aim was to provide an MPC framework for such PDE systems to reduce the on-line resolution time at three levels for the control of a catalytic reverse-flow reactor. The control problem considered was the tracking of a reference trajectory for the process temperature, subject to constraints on the infrared flow. The model of the painting film sample infrared drying is composed of two coupled equations: a nonlinear ordinary differential=integral



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equation and a nonlinear parabolic PDE. Hence, from the results one of the properties of the internal model control (IMC) structure (integral action), and the interest of this IMC=MPC strategy, was confirmed by these experimental results: the tracking was effective in spite of the fact that the model output used in the control algorithm 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 longitudinal motion of the mass of gas and solid, the heat transfer from gas to solid, the mass transfer from solid to gas, and the intraparticle effects: water diffusion and heat conduction. He used plant data from a Danish sugar factory as a basis for the simulation studies. Simulations were made with an augmented Kalman filter (AKF) versus process plant data to deal with the problem of evaluating the predictive abilities of the model when the input to the process is not fully known. He simulated with a model-based predictive controller (MPC) configuration. The controller is a standard dynamic matrix control (DMC) algorithm. The disturbances were estimated by the AKF, and the estimated disturbances were used in the MPC. The performance was not quite as good as in the case of measured disturbances, but on the other hand clearly better than the traditional feedback approach. Daraoui et al. (2007) dealt with MPC of the measured surface temperature evolution of a freeze-dried product during the primary stage. They used control software (MPC@CB) allowing solving any other constrained optimal control problems for any processes. Their challenge was the temperature of the product, which must carefully be controlled during the primary drying stage as it cannot exceed the collapse limit of the cake structure or the melting temperature. They preferred the Levenberg-Marquardt algorithm, for which the codes of the MPC@CB software were written with MATLAB. They showed that the measured temperature tracks very well its prescribed time trajectory, due to the on-line optimal tuning of the manipulated variable by MPC@CB, and under input constraints. Panditrao et al. (2005) designed a pilot spray dryer unit for installing in an educational institution. For control purposes they implemented a SISO scheme using conventional instruments. They designed and implemented MPC on the spray dryer, for which they varied process model identification, where model generation was carried out based on a step test and model parameters were calculated. The step test is based on PRBS. Model validation was the next step, where the comparison was between the ARX models with the FIR model; the good match between them indicates good accuracy of the model. This was followed by the development of the MPC operator 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 techniques to perform the plant decomposition, and large-scale process applications. Also, a relevant and worthwhile study, especially from an industrial perspective, would be a comparison of the developed control algorithm with nonlinear MPC techniques on an industrial-scale process. Such a study should consist not only of performance comparisons and disturbance rejection, but also discuss feasibility, stability, and computational features as well. The main advantage of the robust MPC technique is its capability to deal with model mismatch and constraints as well as its stability

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guarantee. This discussion reveals current limitations of robust MPC and possible directions for its future. It should be noted that few experimental validations have been performed for many reasons, including lack of adequate hard or soft sensors, actuators, and process control systems. However, the need for better instrumentation, control, and automation is recognized. There are also possibilities of continuation of current studies. First is the development of the control framework based on a 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 estimation of the stochastic inlet gas concentration acting as a strong input disturbance should be pursued. Future progress also includes analysis of the distributed control problem. Controller performance can be improved by using two different MPC tunings for different areas of the process or by application of a set-point filter.

Conclusions The MPC technique requires modest computational resources, with easy implementation and good performance, thus resulting in significant increase in profit. Here the modest computational resources refer to its needs for real implementation (like hardware issues, etc.). To overcome the computational obstacle of nonlinear models, the prediction model of each MPC is linearized around the current operating point at each step. The results indicate that a neural-based controller can achieve tighter regulatory control than is possible with decentralized single-loop controllers while using multivariable feed-forward=feedback model predictive control. Compared with traditional decentralized PID control, MPC presents better control performance based on its multivariable feature, inherent prediction ability, and capacity to directly handle constraints using an even larger number of manipulated than controlled variables. Nonlinear MPC implementation leads to potential improvement by the use of dynamic sensitivity analysis. The use of a model to predict future behavior based on on-off signals helps to anticipate and account for the delay representing a cycle 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: the skill of the most highly experienced operator has been implementation, then operation and compensation are executed at fairly frequent intervals, and several process variables can be managed in parallel. The advantage of robust MPC technique is its capability to deal with model mismatch and constraints as well as its stability guarantee. The summary of model predictive control approaches in the above-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.

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