A survey of advanced control of polymerization reactors.
A significant amount of work has been developed in the area of modeling, simulation, and control of polymerization reactors. This can be measured by the unusually large number of surveys published in the literature in the last twenty years. Ray (1-5), Ray and Laurence (6) and Gerrens (7-9) discuss how proper modeling of polymerization reactors may be carried out. Martin et al. (10), Nunes et al. (11), and Seitz (12) show how mechanical properties and molecular weight distribution are correlated for a series of polymer materials. Amrehm (13), MacGregor and Tidwell (14), MacGregor et al. (15), Ray (16), Elicabe and Meira (17), and Penlidis et al. (18) discuss aspects related to the proper control of polymerization reactors. Particularly, Elicabe and Meira (17) believe that optimal and adaptive control are the most promising tools for advanced control of polymerization reactors. Meira (19) analyzes how molecular weight distribution may be properly controlled by forced oscillatory operation. MacGregor et al. (15) and Chien and Penlidis (20) present critical reviews on in-line measuring the polymer properties. Kiparissides et al. (21) review the modeling, optimization and quality control of high-pressure ethylene polymerization reactors. The impact caused by advanced control techniques on real industrial environment has yet to be analyzed. With the exception of the paper presented by Schnelle and Richards (22), very little is known about advanced control of actual industrial reactors. The proper characterization of the nature of the technical and academic research that has been done over the last twenty years is still lacking.
Reviews on specific control areas have also been presented. Ray (23) reviews the development of process control theory from a historical point of view. Seborg et al. (24) review the field of adaptive control. Garcia et al. (25) review constrained and unconstrained predictive control. Bequette (26) reviews nonlinear control techniques. Bosley et al. (27) survey model-based control. In all these reviews it is concluded that, in spite of particular difficulties, such as proper state measuring and/or estimation, advanced control techniques shall be of great value in the future. Very little information is given about real implementation of these advanced techniques.
Generically, an advanced control algorithm may be optimal (Section 3) or not (Section 7). An optimal control technique is usually preferred because of its presumed superior performance, although it depends on a process model, which may not be available. This serious limitation led to the development of predictive control (Sections 4 and 5) and geometric control (Section 4), which may be regarded as types of optimal control and are often based on simple process models. These models may be linear (Sections 5 and 6) or nonlinear (Sections 4 and 6) and the choice of which model should be used depends on the need and difficulty of obtaining a nonlinear representation of the process. In spite of that, it may be necessary to estimate some or all of the model parameters in-line, either because they are not known or because they change with time (Section 6). Besides, it may be desirable to control a variable that cannot be measured and whose value has to be estimated or inferred in-line (Section 2). Adaptive controllers (Section 6) are the ones where the estimator is coupled with the control scheme.
The main objective of this paper is to review the application of advanced control techniques in polymerization reactors and characterizing the nature of the research that has been developed in the field. We do not intend to present he mathematical details necessary to allow the implementation of advanced control techniques, as these details may certainly be found in most papers that will be presented here. We also focus more attention on the papers published in the last five years, in order to observe the recent trends in the field. In the next sections it is shown how the advanced control of polymerization reactors has been studied in the literature. It is shown that different theories have mostly been applied to the same processes and that very little experimental work has been carried out to confirm and validate theoretical results.
2. POLYMERIZATION REACTOR MODELING AND CONTROL AND ESTIMATION OF POLYMER PROPERTIES
Detailed modeling of polymerization reactors is characterized by the following:
1-the system dynamics are described by equations that are highly coupled and nonlinear;
2-kinetic parameters are mostly unknown and proper parameter estimation is very difficult;
3-the presence of impurities, which most of the time cannot be measured, may exert extreme influence on the course of the polymerization;
4-difficulties in correlating end-use properties and molecular properties of polymer materials;
5-difficulties in describing the flow of polymer melts and the existence of spatial residence time distributions in reactor vessels;
6-most polymerization reactors are heterogeneous, requiring the proper description of mass transfer between phases, of polymer precipitation and of particle size distribution.
Thus, detailed polymerization models are generally constituted by a set of highly coupled nonlinear ordinary (partial) differential (integro-differential) equations, which require advanced numerical techniques for proper solutions to be obtained in a reasonable amount of time. For these reasons, detailed polymerization reactor models are seldom used for control purposes.
In an excellent paper, Penlidis et al. (18) showed how very simple models can be obtained from detailed models and still keep fair predictive capabilities of the most important process variables, which is stimulating from the point of view of process control. However, for model down-sizing and control to be effective, it should be possible to measure and/or evaluate some of the end-use properties in-line.
Undoubtedly the weakest part in a control loop of a polymerization reactor is the in-line instrumentation; see MacGregor et al. (15) and Chien and Penlidis (20). Although process variables (such as temperature, conversion and pressure) can be easily measured in most polymerization systems, polymer properties (such as molecular weight distribution and copolymer composition) and particle properties (such as particle size distribution) can only be evaluated in-line with the aid of very expensive instrumentation in just few polymer research labs. Even in these cases, end-use polymer properties (such as adhesive tack and hardness) are generally related to the molecular polymer properties through empirical equations, which very frequently are valid in a very narrow range of conditions; see Seitz (12). So, the usual industrial practice is measuring end-use properties off-line, with delays that often are as long as six hours and which may lead to inadequate control schemes.
To cope with all these difficulties, researchers have proposed that state estimation techniques be used for actual implementation of advanced control algorithms. As modeling errors and noise are likely to occur in a real polymerization environment, MacGregor et al. (28) and Dimitratos et al. (29) suggested that deterministic observers should not be used in these systems, although some papers that use deterministic observers have reported successful implementation of control algorithms; see Kravaris et al. (30), Bachman et al. (31), Soroush and Kravaris (32, 33) and Lines et al. (34).
The state estimation techniques mostly used in polymerization reactors are those based on the Extended Kalman Filter (EKF), which is a nonlinear Kalman Filter that has been studied through different approaches since 1962; see Seinfeld (35), Jazwinski (36), MacGregor et al. (28), Elicabe and Meira (17) and Chien and Penlidis (20), Some optimization-based techniques, such as recursive least-squares, have been used less frequently; see McAuley and MacGregor (37) and Kozub and MacGregor (38). Besides estimating the states, ELF algorithms also filter the typical noisy data of polymerization processes. These estimators have also been used to allow the detection of process failures, the estimation of process parameters, and proper sensor selection; Chien and Penlidis (20). Schuler and Schmidt (39) and Schmidt and Reichert (40), McAuley and McGregor (41).
In order for state estimation techniques to be applied successfully, it is necessary that input/output data be available. Moreover, it is necessary that input/output data allow the unique determination of the states of the system; i.e., it is necessary that the system be observable. The concepts of observability and reachability and their application to the theory of polymerization reactor control have been discussed by Elicabe and Meira (17), Ray (16), and Adebekun and Schork (42). Schuler and Suzhen (43) show that polymer properties may not be observed from bulk variables, such as temperature and concentrations. Particularly, Ray (16) presented a Table that shows how polymer properties can be observed from bulk measurements (see Table 1). Details on how to implement [TABULAR DATA FOR TABLE 1 OMITTED] EKF algorithms may be found in Chien and Penlidis (20).
According to Adebekun and Schork (42), even if the process is not observable (a process is observable if all of its modes can be observed) it is usually possible to design estimation procedures when the process is detectable (a process is detectable if its unstable modes can be observed). According to Ray (16), state estimation of detectable processes is adequate only at [TABULAR DATA FOR TABLE 2 OMITTED] steady-state conditions. So, process observability is much more desirable than process detectability. Nevertheless, some papers have shown that successful state estimation is possible even when the process is not observable; see Schuler and Suzhen (43), Adebekun and Schork (42) and Kozub and MacGregor (38).
Table 2 shows a collection of papers recently published on state estimation in polymerization reactors. Jo and Bankoff (44) were the first to report the use of EKF in these reactors. Comparing experimental and theoretical results obtained for the vinyl acetate solution polymerization, they concluded that simulation results would usually lead to very optimistic conclusions about the performance of state estimation techniques.
If measured and estimated data in Tables 1 and 2 are compared, it will be seen that in some cases the estimated data cannot be observed with the measurements available. When this occurs, non-observable states are either estimated with the integration of a reactor model, which can be considered a mixed EKF/open-loop observer strategy [see Schuler and Suzhen (43), Schuler and Papadopoulou (45), and Adebekun and Schork (42)] or estimated simultaneously with the other observable states by the EKF; see Adebekun and Schork (42) and Kozub and MacGregor (38, 46). Adebekun and Schork recommended that the first strategy be used, while Kozub and MacGregor recommend the use of the second one.
Time delays of 24 hours between data sampling and the moment when results are available are not unusual. If infrequent data are available, Adebekun and Schork (42) and Chien and Penlidis (20) recommend that they be used for state estimation, instead of simply integrating the reactor model. Ellis et al. (47) and Choi and Khan (48) show that good state estimation is possible even in the presence of huge time delays. Ogunnaike (49) used an EKF to estimate and control the states of an industrial polymerization reactor where data were measured infrequently.
An interesting point is presented by MacGregor et al. (28), Kozub and MacGregor (38, 46), and Gagnon and MacGregor (50), who proposed the introduction of stochastic states, which would represent the possible presence of impurities in the reaction medium. Actually, if these stochastic states had not been introduced, models would have not been able to describe the reaction course when non-stationary stochastic perturbations were present. Dimitratos et al. (29, 51) suggested that the noise covariance should be estimated with the other states and observed that the simultaneous estimation of a process parameter (average number of radicals per particle in an emulsion reactor) does not lead to a significant improvement of the state estimates. Jo and Bankoff (44) observed just the opposite: the introduction of an additional process parameter (inhibition lag time in a solution reactor) leads to better state estimation. McAuley and MacGregor (41) used an EKF to estimate process parameters (including kinetic rate constants) and an inference scheme to estimate polymer properties. The EKF provided integral action to the coupled control scheme, through the inclusion of stochastic states, as suggested by Kozub and MacGregor (38, 46). Finally, Schmidt and Reichert (40) used EKF to estimate the heat released by reaction and to detect dangerous operation conditions that might lead to runaway, and Elicabe and Georgakis (52) used a linear Kalman filter to estimate reaction rates, assuming that reactant concentrations were known in an emulsion polymerization reactor.
A closed-loop deterministic observer, which may be classified as a hybrid deterministic observer/EKF procedure, was introduced by van Dootingh et al. (53) and used to estimate the states of a continuous styrene solution free radical polymerization reactor. As shown by the authors, their procedure is more robust to noise and modeling errors, although it can be applied to a narrower range of polymerization problems, owing to strong observability requirements.
Each different type of estimator has its own advantages and disadvantages, and so, it is difficult to choose the best from a general perspective. Meanwhile, the Kalman filter has a long history of success and is now becoming popular in the process engineering area. It depends on a dynamic, nonlinear, stochastic model of the process to calculate the unmeasurable variables. These values are corrected as a function of the errors between calculated and measured values, for some measurable variables. Through an increasing number of practical implementations, this technique is taking its place as an efficient tool for state and parameter estimation, particularly in the polymerization area. Perhaps one disadvantage of the Kalman filter is the need for a model relating measurable and unmeasurable variables, a requirement that may be difficult to fulfill in practice. Another disadvantage is the complex designing and tuning of EKFs. However, based on the successful applications described in the previous paragraphs (which include closed-loop and open-loop estimation, analysis on nonstationary disturbances, simultaneous state and parameter estimation, analysis of infrequent data, etc.), EKF may be certainly recommended as an appropriate state estimation technique for most polymerization reactors.
3. OPTIMAL CONTROL AND STEADY-STATE OPTIMIZATION OF POLYMERIZATION REACTORS
Research in the area of optimal control and steady-state optimization of polymerization has been particularly rich and has centered around three lines of investigation:
a) selection of the best steady-state control settings (steady-state optimization);
b) selection of the best control strategy that leads the system from certain initial conditions to final specified conditions (optimal servo control); and
c) selection of the best control strategy that reduces the effects of undesirable disturbances of process conditions (optimal regulatory control).
It is interesting to note that few papers have been concerned about steady-state optimization of polymerization reactors when compared to those devoted to optimal control of such reactors. This probably results from the fact that most polymerization reactors are still operated in batch mode, although important Ziegler-Natta and emulsion processes are operated continuously. Brandolin et al. (54) studied the high pressure tubular ethylene polymerization and proposed temperature and initiator concentration steady-state profiles in order for certain objectives to be reached. They aimed to maximize conversion while keeping molecular weight distribution and branching frequency around specified values. Ray and Gupta (55, 56) and Srivastava and Gupta (57) studied the steady-state optimization of tubular nylon 6 reactors. Their main objective was the maximization of monomer conversion and simultaneous minimization of the amount of cyclic dimer at the outlet of a tubular reactor, while keeping average molecular weight of polymer at specified values. The manipulated variable was the jacket temperature, and the results were not very sensitive to changes of process parameters, but the reactor length and desired average molecular weight. Particularly, Tsoukas et al. (58) used a multi-objective optimization algorithm, which has been used by many authors to solve optimization problems in the area of polymerization control successfully. Using such an algorithm, Farber (59) studied continuous MMA/VA and styrene/acrylonitrile (SAN) copolymerizations and showed how temperature and residence time might be manipulated in order for conversion, molecular weight, and polymer composition to reach specified values.
The second line of investigation may be split into two different streams. In the first, which is generally called "chemical control," optimal policies are developed in order to keep some variables, such as polymer composition and reaction rate, constant throughout the batch. In the second, which deals with the optimal control theory, optimal policies are developed in order to minimize/maximize certain objective functions, such as the minimization of batch time and/or maximization of polymer production.
Table 3 lists some papers published recently about chemical control of polymerization reactors. Takamatsu et al. (60) show that temperature profiles may be designed in order for polymer with specified average molecular weight and polydispersity to be obtained. Couso et al. (61) and Alassia et al. (62) design monomer feed and reactor withdrawal policies in order [TABULAR DATA FOR TABLE 3 OMITTED] to obtain specified molecular weight distribution in a styrene anionic polymerization reactor. Budde and Reichert (63) and Pinto (64) show how constant rate polymerization may be obtained with the proper design of initiator feed and temperature policies. Choi (65), Arzamendi and Asua (66-68), Arzamendi et al. (69) and Van Doremaele et al. (70) show how initiator and monomer feed policies may be defined in order for polymer composition to be constant throughout the operation. It is important to emphasize that Pinto (64) showed that very frequently, optimal control policies cannot be implemented because of the existence of real operation constraints, such as finite cooling capacity and maximum pump feed rates.
Table 4 lists papers recently published on the application of optimal control theory to polymerization reactors. Louie and Soong (71) presented a short review on optimal control of polymerization reactors, and studied different strategies for minimization of polymer polydispersity, namely, manipulation of reactor temperature, monomer and solvent feed rates, and rate of initiation. They concluded that manipulation of solvent addition would lead to better results, in spite of the slightly longer reaction times. Ponnuswamy et al. (72, 73) developed experimental and theoretical initiator feed and temperature profiles in order to reach specified average molecular weight and conversion in a minimum time and with minimum polydispersity in an MMA polymerization reactor. A good agreement was reached between experimental and theoretical results, although it was shown that the optimal temperature and initiator feed policies would not lead to results much better than those obtained with optimal isothermal policies. Similar results were obtained by Hsu and Chen (74) for a solution styrene polymerization reactor, by Jang and Yang (75) for a VA emulsion reactor and by Jang et al. (76) for an acrylamide solution reactor, although significant differences between theoretical and experimental polydispersity were observed in the first paper. Secchi et al. (77) studied optimal control problems similar to the previous ones, but included process constraints in the model. They concluded that optimal policies are generally [TABULAR DATA FOR TABLE 4 OMITTED] of no value if constraints are not taken into consideration and that the optimal operation time of the real constrained reactor is usually much longer than predicted when constraints are not considered. Optimal control policies have also been studied by Chen and Lee (78, 79), O'Driscoll and Ponnuswamy (80), Vaid and Gupta (81), Jang and Lin (82), Chang and Lai (83), and Carafilakis (84) for similar problems. An interesting paper was presented by Huang and Lee (85) on the optimal control of styrene casting, which is a distributed parameter system. The objective was to develop wall temperature profiles in order to minimize polydispersity and reaction time and reach specified monomer conversion and average molecular weight. They concluded that optimal trajectories would not lead to significant reduction of reaction time and product polydispersity when compared to isothermal monomer casting.
Multi-objective optimization has been studied by Tsoukas et al. (58), Cawthon and Knaebel (86), Choi and Butala (87), and Butala et al. (88). In the first three papers it is desired to control monomer conversion, copolymer composition, and molecular weight distribution simultaneously in a minimum batch time. In the fourth paper, a mixture of different initiators is used to allow the control of the molecular weight distribution in a minimum batch time for styrene bulk reaction. McAuley and MacGregor (89) developed optimal control strategies in order to reduce the time necessary to change the grade of polyolefins in continuous heterogeneous Ziegler-Natta reactors.
The third line of investigation is the least exploited. Optimal control policies are not guaranteed to work in a real environment unless control schemes are designed to reject disturbances and noise and cope with model uncertainties. Usually, researchers have used proportional integral derivative (PID) controllers to keep track of the optimal designed dynamic trajectory. However, whenever the process is deviated from its optimal trajectory, the new optimal control policy that should be designed from the actual process condition may differ from the original control policy significantly. Kozub and MacGregor (46) developed a feedback control scheme that, at each sampling time, re-evaluates the optimal control, following a chemical control approach, in order to deal with process disturbances in a semibatch emulsion styrene butadiene robber (SBR) copolymerization reactor. They aimed to control the copolymer composition, conversion, and molecular weight distribution, and used an EKF to estimate the states of the system. They showed that results obtained were better than those obtained when a simpler optimal policy without a feedback scheme was used.
Optimal control and steady state optimization generally lead to results that are strongly dependent on a process model and often require a huge amount of computer work. These are the main obstacles for successful real implementation and are the main reasons for the weak impact by modern control theory on industrial practice. The problem was solved by the introduction of predictive control techniques, where the optimization problem is continuously reformulated for new performance criteria (objectives or constraints) and a new model (based on measured variables). The idea of updating the optimization problem, studied by Kozub and MacGregor (46) is similar to predictive control and should help in reducing the difference between simulation and real results.
4. NONLINEAR CONTROL OF POLYMERIZATION REACTORS
Although it is hard to define properly what nonlinear control means, we say here that nonlinear control schemes are those that are explicitly based on a nonlinear representation of the system. Table 5 lists a collection of papers recently published about nonlinear control of polymerization reactors. Nonlinear control strategies may be grouped in two different classes: control strategies based on optimization procedures and control strategies based on the theory of differential geometry.
Nonlinear model predictive controllers (NMPC), where model predictions over a given time horizon (prediction horizon) are used at each sampling time to generate optimal control policies over another time horizon (control horizon), are included in the first class. Although optimal control strategies might also be included in the first class, they were presented separately because the area of optimal control is very well established. Actually, predictive control is an open-loop optimal control strategy where feedback action is provided by optimization procedures at each sampling time.
Garcia (90) implemented an NMPC to control the production of block synthetic rubbers in a semibatch reactor and obtained excellent experimental results. In order to make predictions, the nonlinear model was [TABULAR DATA FOR TABLE 5 OMITTED] linearized at each sampling time. Monomer and cooling water feed rates were manipulated to control the reactor temperature. Gattu and Zafiriou (91) extended the work developed by Garcia and used a Kalman Filter to estimate the states and control unstable emulsion reactors. They also showed that the strategy would lead to better disturbance rejection. Hidalgo and Brosilow (92) used a similar strategy to control the operation of an unstable styrene solution polymerization reactor. The full nonlinear model was used to make predictions, though, and not a linearized model. Peterson et al. (93) used a similar technique to control a nonlinear multi input multi output (MIMO) semi-batch solution MMA reactor, where both reactor temperature and average polymer weight were controlled. An NMPC was also used by Souza et al. (94) to stabilize the operation of a chaotic VA solution polymerization reactor. The nonlinear model was based on a neural network, which was identified off-line. The NMPC performed much better than traditional PID controllers.
Results from differential geometry have been used successfully to allow the analysis of nonlinear processes. Briefly, the differential geometry based control deals with the idea of finding an inverse (generally an analytical one) of a nonlinear process. Usually nonlinear transformations of the state and/or control variables are sought so that the transformed process description is linear. Surveys on control strategies based on differential geometry were presented by Kantor (95), Kravaris and Kantor (96, 97), and Henson and Seborg (98). Among these strategies, the GLC (globally linearizing control) [see Kravaris and Chung (99)] seems to be the most developed one. Its basic philosophy is building a state feedback structure so that the original nonlinear process becomes input/output linear and classical linear theory can be applied.
In a series of papers, Kravaris and co-workers applied the GLC to control different variables and polymerization processes. Kravaris et al. (30) used the GLC to control the copolymer composition of a SAN batch reactor, keeping the reactor temperature at its optimal trajectory. Kravaris and Soroush (100) showed that the GLC could be used successfully to control the copolymer composition and average molecular weight in a VA/MMA semibatch solution reactor. They also analyzed the performance of the GLC experimentally [see Soroush and Kravaris (32, 33, 101, 102)] in batch and continuous MMA solution reactors. In the first case the GLC was used to keep the reactor temperature on its optimal trajectory and behaved much better than standard PID controllers, performing well even in the presence of modeling errors, process disturbances, and noise. In the second case, the GLC was used to control reactor temperature and conversion. Soroush and Kravaris (102) showed that reactor control is effective even when the characteristic matrix is singular. Daoutidis et al. (103) also used the GLC to control the reactor temperature and the average molecular weight of MMA continuous solution reactors, introducing a feed forward action in the GLC structure. The authors concluded that the control algorithm performed well in the presence of modeling errors and noise.
Other control strategies based on differential geometry have also been used in the polymerization field. Adebekun and Schork (42, 104) studied MMA continuous solution polymerization reactors and developed an algorithm that would lead to proper control of steady-state conditions, even when they were open-loop unstable, by proper manipulation of feed conditions. The use of state estimation techniques would not lead to significant control deterioration. Alvarez et al. (105, 106) developed a feedforward-feedback algorithm, based on differential geometry, to reject process disturbances and allow the operation at open-loop unstable steady-state conditions. The algorithm was used to control an MMA continuous bulk reactor. Singstad et al. (107) studied the control of industrial polyethylene reactors with a model reference approach. They compared the nonlinear control with a PID and concluded that the advanced strategy provided an improvement of the reactor performance: reduction of temperature variance and amount of off-specification product. McAuley and MacGregor (41) used a similar approach to control the same system studied by McAuley and MacGregor (89). They compared the controller with a linear internal model control (IMC), a control strategy based on the inversion of the plant, and observed that the major benefit of the nonlinear algorithm was allowing a successful grade transition, a task that was performed inadequately by the linear controller. Moreover, in the nonlinear case a unique controller could be used for all the different operation conditions that were linked to the different grades produced, which was not possible in the linear one.
Nonlinear predictive and differential geometry control are the two main techniques used for the solution of nonlinear process control problems. During the last ten years, both were thoroughly studied, and it is now clear that:
a) because of its strong dependence on process model and conditions that must be satisfied, differential geometry control techniques are difficult to implement in real process, although they are useful for nonlinear process analysis; and
b) nonlinear model predictive control techniques are potentially useful as an extension of the successful linear model predictive techniques, a recursive optimization problem. One of the main areas of research interest at he moment is nonlinear model identification, a key problem in NMPC. In the near future, we believe that the development of both GLC and NMPC will depend strongly on the development of adequate techniques for nonlinear identification, based on nonlinear empirical models such as artificial neural networks.
5. LINEAR PREDICTIVE CONTROL
Linear predictive controllers (LPC) are predictive controllers that use a linear model to represent the process. Among predictive controllers, linear predictive controllers are certainly the most popular and successful ones in industry; see Richalet et al. (108), Cutler and Ramaker (109), Garcia et al. (25) and Houk et al. (110). Table 6 lists some papers that used such controllers in polymerization systems. Inglis et al. (111) used the LPC to control the reactor temperature and conversion in MMA solution reactors, in batch and continuous mode respectively, and analyzed the performance and robustness of the control scheme. Kelly et al. (112) showed that a LPC might be used to reduce the variance of output variables (conversion and average molecular weight) in a train of butadiene continuous solution Ziegler-Natta catalyst reactors. Dittmar et al. (113) also used predictive controllers successfully to control the reactor temperature at open-loop unstable conditions in a SAN continuous copolymerization reactor. They showed that compared with standard PID controllers, predictive controllers presented better performance and robustness. Ohshima et al. (114, 115) also showed that predictive controllers improved the control of copolymer composition in ethylene/propylene rubber heterogeneous Ziegler-Natta reactors, when compared with standard control techniques. Lines et al. (34) used LPC to control polymerization conditions and polymer properties in industrial linear polyethylene and ethylene copolymer reactors. The control strategy led to much faster grade transitions and reduced off-specification material, and allowed the increase of production. More recently, Ogunnaike (49) used an LPC to control the copolymer composition, average molecular weight and monomer conversion of an industrial Ziegler-Natta copolymerization reactor successfully. State variables were estimated in-line with an EKF algorithm.
[TABULAR DATA FOR TABLE 6 OMITTED]
Linear predictive control techniques have been successfully implemented as efficient control tools in many different real processes. Polymerization reactors are not exceptions. Because of the use of linear models, which can be identified in-line with well-established identification techniques, implementing LPCs in actual applications is generally easier than implementing nonlinear control algorithms. Besides, the properties of linear controllers are better understood than the properties of more sophisticated nonlinear controllers, which enhances confidence in the control scheme. The main disadvantage of using LPCs in the polymerization area is the strong nonlinear behavior of polymerization reactors, which may lead to poor control performance and may require the identification of different models to be used at different operation conditions.
6. ADAPTIVE CONTROL OF POLYMERIZATION REACTORS
Adaptive controllers are those where control parameters are continuously updated in order to cope with process changes. Adaptive controllers are always implemented with process parameter estimation routines in order to keep track of process conditions. Table 7 lists a collection of papers recently published where adaptive controllers were applied to polymerization reactors.
Niederlinski et al. (116) used an adaptive controller to control the temperature of a batch suspension polyvinyl/chloride (PVC) reactor and showed that its performance was much better than the performance of standard PI/PID controllers. Farber and Ydstie (117) studied the performance of adaptive controllers to control the reactor temperature during startup and setpoint change operations of continuous styrene polymerization and concluded that its performance did not depend on control design parameters significantly. Takamatsu et al. (118) implemented adaptive techniques to control the average molecular weight of styrene and isobutylene solution reactors and showed that such controllers could be used to stabilize unstable steady-state conditions that could not be stabilized by standard PI controllers. Takamatsu et al. (60, 119) also studied the performance of adaptive controllers to keep the temperature of a styrene suspension reactor at its optimum calculated trajectories and showed that the performance of the adaptive control scheme was similar to the performance of a standard PI controller. Tzouanas and Shah (120, 121) studied the batch solution MMA polymerization reactor and used adaptive controllers to control conversion and average molecular weight. They concluded that the proper tuning of the adaptive controller was very sensitive to process conditions, process constraints, and initial parameter values. They also observed that its performance depended on the availability of frequent data, which is not very common in polymerization systems. Temeng and Schork (122) studied continuous emulsion MMA polymerization reactors and used adaptive controllers to control monomer conversion and particle size. They observed that the controller would present excellent performance even in the presence of huge perturbations in the process. Elicabe and Meira (123) used adaptive controllers to keep the process conditions oscillating at specified oscillatory trajectories in continuous anionic reactors in order to produce polymers with special molecular weight distributions. Mendoza-Bustos et al. (124, 125) used adaptive controllers to control monomer conversion in continuous solution MMA reactors. They analyzed the effects caused by the presence of impurities in the feed stream and concluded that adaptive and nonadaptive controllers would effectively keep the process conditions under control. From their results it may be observed that the existence of process constraints can significantly alter the controller tuning and performance. Kiparissides et al. (126) studied the batch [TABULAR DATA FOR TABLE 7 OMITTED] MMA bulk polymerization and used adaptive controllers in order to control monomer conversion and average molecular weight when there are uncertainties about the amount of initiator added to the system. Manipulating a single variable (the reactor temperature) to control two variables, the authors concluded that disturbances could not be completely removed, although they could be significantly reduced. They also showed that the controller performance was very sensitive to the frequency of available data. Toledo (127) studied the temperature control of free radical bulk polymerization reactors by reflux condensers and concluded that a nonadaptive LPC controller would perform better than its adaptive version. Defaye et al. (128) studied the temperature control of free radical solution copolymerization reactors, evaluated the performance of adaptive and nonadaptive controllers (some of which are commercially available), and concluded that the "improvement brought out by our [their] adaptive controllers is indisputable."
The use of adaptive techniques still leads to actual implementation problems, although these techniques have been considered as promising tools for nonlinear and time varying process control problems since the late 1950s. Robustness, convergence, and tuning of adaptation techniques may constitute complex problems in many applications. Identification is normally the most difficult step for actual implementation, although progress in this area is creating more confidence for industrial implementation. Our belief is that adaptation is one of the most important control strategies and that implementation problems will soon be overcome.
7. RESULTS ON CLASSICAL CONTROLLERS AND ALTERNATIVE CONTROL SCHEMES
The application of advanced control techniques in real polymer industrial environments has grown very slowly. This reflects the lack of robustness of many of these advanced techniques and the efficiency of standard PID controllers in the great majority of process conditions; see Ray (23) and Luyben (129). As shown in previous sections, a large number of investigations showed that the performance of advanced control strategies would not be better than the performance of standard PID controllers at various process conditions. It was also mentioned that many researchers observed that the performance of advanced controllers is very sensitive to process and tuning parameters. Table 8 lists a collection of papers recently published that show that such simple control schemes may perform very well even in complex polymerization systems.
Choi and Ray (130) analyzed the performance of PI controllers in controlling the temperature of an olefin Ziegler-Natta fluidized bed polymerization reactor. Congalidis et al. (131, 132) analyzed different control designs in order to control conversion, molecular weight distribution, polymer composition, and temperature [TABULAR DATA FOR TABLE 8 OMITTED] of an MMA/VA continuous solution reactor. They showed that PI controllers would allow the proper control of such variables for both servo and regulatory control problems. Choi and Ray (133) showed that a PID controller might be used to stabilize the operation of a olefin Ziegler-Natta fluidized bed polymerization reactor at open-loop unstable steady-state conditions. Bachmann et al. (31) showed that PI controllers might be used to control molecular weight distribution, where the states were estimated with an open-loop observer. Lontra (134) analyzed the performance of nonadaptive and adaptive PID controllers in controlling the reactor temperature of an industrial batch suspension styrene reactor. He concluded that the nonadaptive PID controller would not allow the proper reactor control, while the adaptive version of the PID controller would lead to adequate process operation. Estrella (135) studied the reactor control of an ethylene/vinyl acetate autoclave copolymerization reactor and showed that PID controllers would lead to proper control operation. Kim and Choi (136) used a PI controller to control the temperature of a continuous ethylene/butene-1 soluble Ziegler-Natta catalyst reactor. They concluded that the temperature control would not allow the proper control of final polymer properties. Chan et al. (137) showed that a PID controller might be used to stabilize an open-loop unstable steady state of a continuous ethylene autoclave reactor. More recently, Kwag and Choi (138) showed that the nonlinear behavior of a high-pressure ethylene polymerization process may pose serious control problems if a constant parameter PI controller is used to keep reactor temperature under control.
Less popular alternative control schemes have also been studied in the field of polymerization reactors. Prasad et al. (139) used the CMBC (conservative model-based control) to control the molecular weight distribution, conversion, and temperature of an MMA solution reactor successfully. The CMBC is a control algorithm that, considering the open-loop behavior as the worst closed-loop response, uses an extra first order lead factor to incorporate desirable properties of robustness and dead-time compensation. The resulting algorithm has only one adjustable parameter and has shown good performance for both setpoint and load changes. Kawata et al. (140) used a sliding-mode controller to control the temperature of a semibatch reactor and showed that this strategy led to results that were better than those obtained with standard PI controllers. The sliding-mode controller is based on an optimal law that takes the trajectory on the process state space to a (switching) straight line and slides on it towards the equilibrium point (setpoint) by an appropriate switching; see Utkin (141). Roffel and Chin (142) used a fuzzy controller, based on heuristic rules, to control a continuous reactor. MacGregor (143) analyzed the impact of the theory of statistical process control on the polymerization industry. A very interesting study was developed by Penlidis et at. (144) in order to remove the natural oscillations frequently present in continuous emulsion polymerization reactors. They introduced a small reactor before the usual large process reactor in order to allow the stabilization of particle nucleation and observed that oscillations could be eliminated and that conversion and particle size distribution could be controlled more efficiently. Temeng and Schork (122) proposed a similar solution, but used a small tubular reactor instead.
8. DISCUSSION AND CONCLUSIONS
Table 2 shows that a significant amount of work has been developed in order to allow the estimation of the states of polymerization reactors, which also shows that efforts have been concentrated in order to solve the common measurement problems in polymer systems. It may be seen in Table 2 that 50% of the papers are somehow linked to industrial practice and that approximately 60% of the publications deal with actual experimental data, which certainly is stimulating. Approximately 40% of the papers included variables that are not measured very frequently in the estimation procedures. Among those variables that can be measured frequently, 85% of the publications chose conversion-related variables, viscosity, refractive index, and/or temperature. These numbers show a real interest in analyzing industrial practice. On the other hand, more than 70% of the papers study some sort of [TABULAR DATA FOR TABLE 9 OMITTED] free radical polymerization, 50% in solution reactors, and 65% of the paper study the polymerization of styrene, VA, MMA, or ethylene. It is also interesting to observe that less than 45% of the papers study the state estimation and the reactor control simultaneously and that less than 25% of the articles estimate process parameters and states simultaneously. Among these, none of them studies the reactor control, which means that no work has been published on adaptive control with state estimation. These numbers show that the scope of state estimation in polymerization reactors has to be enlarged, in order to include other important polymerization systems and allow a deeper analysis of the performance of simultaneous estimation and control of polymerization reactors.
Tables 3 to 7 show that typical papers on the advanced control of polymerization reactors are simulations (60%) carried out by academicians (75%) about the free radical (85%) homopolymerization (65%) of MMA, VA, styrene or acrylonitrile (75%) in bulk or solution (80%) stirred tank reactors (90%, with almost 60% in batch mode). Those Tables also show that most papers may be divided into two groups: 1) development of control policies, based on relatively simple models, in order to produce polymers with desired properties; 2) development of feedback control schemes in order to control bulk reactor variables, such as temperature. In the first group, temperature, initiator feed, and monomer feed policies are usually designed in order to allow the production of polymer with desired average molecular weight and/or composition in a minimum time (if the optimal control theory is used). In the second group, reactor temperature and conversion are usually controlled by manipulating the rate of heat exchange, the initiator feed and/or the monomer feed. Because of the difficulties of in-line measurement and estimation of polymer properties, few papers of the second group analyze the feedback control of these variables (actually, studies on the control of molecular properties are much more frequent, although almost all are of simulation nature). It is also interesting to note that only 35% of the papers of the second group analyze MIMO control problems. So, it may be said that the knowledge available on advanced control of polymerization reactors is still scarce and mostly theoretical, concentrated on polymerization systems that can be easily described by published data.
It is interesting to note that if the LPC is analyzed as a separate group (excluding the papers that use LPC only to analyze the performance of other control strategies), from a total of six papers, five of them may be considered experimental, five are somehow linked to industrial practice, four deal with Ziegler-Natta catalyst reactors, five analyze copolymerization or terpolymerization reactors, four study MIMO control problems, and three analyze the control of polymer properties. This picture is completely different from the one that was presented before. It seems that the application of LPC controllers has been stimulated by the Ziegler-Natta polymerization industry, which has applied such controllers to solve some of its problems successfully.
Table 9 presents a summary of the last paragraphs. A particular point was made by Richard and Schnelle (145). They believe that feedforward techniques will probably be the most effective way to regulate polymerization reactors, rejecting perturbations that are common in these systems. Such techniques have not been well studied in the literature analyzed.
Finally, in spite of the huge number of papers recently published, it may be said that very little is known about the actual implementation of advanced control techniques in real industrial polymerization process environments. This is not different from what happens in other areas. In order for advanced control techniques to be applied successfully, efforts will still have to be made to develop efficient measuring devices and identification schemes in the near future, especially regarding the measurement and identification of molecular weight and particle size distributions. Theoretical and simulation results show that if polymer properties are evaluated properly, optimal control and nonlinear control techniques may be useful in the polymerization industry. We believe, though, that linear adaptive predictive controllers will be the most important advanced control technique used in polymerization processes, as they are based on a simple linear representation of the process. LPCs have also been applied to other processes successfully and are becoming a popular control tool of the Ziegler-Natta industry, which probably is the one with the highest concentration of advanced technology among polymerization industries and is capable of exerting the most influence on the development of other polymerization technologies.
We thank CNPq-Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, for supporting our work. We also thank COPENE-Companhia Petroquimica do Nordeste, for giving Marcelo Embirucu a scholarship.
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