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Design of a self-tuning regulator for temperature control of a polymerization reactor

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Abstract

The temperature control of a polymerization reactor described by Chylla and Haase, a control engineering benchmark problem, is used to illustrate the potential of adaptive control design by employing a self-tuning regulator concept. In the benchmark scenario, the operation of the reactor must be guaranteed under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer. The conventional cascade control provides a robust operation, but often lacks in control performance concerning the required strict temperature tolerances. The self-tuning control concept presented in this contribution solves the problem. This design calculates a trajectory for the cooling jacket temperature in order to follow a predefined trajectory of the reactor temperature. The reaction heat and the heat transfer coefficient in the energy balance are estimated online by using an unscented Kalman filter (UKF). Two simple physically motivated relations are employed, which allow the non-delayed estimation of both quantities. Simulation results under model uncertainties show the effectiveness of the self-tuning control concept.

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... Because of the precise process model and parameter estimations, this feed-forward and feedback hybrid control can guarantee the tracking error to be small. A self-tuning regulator with parameter estimation was proposed in [6], where the unscented Kalman filter is adopted to estimate uncertain parameters of system model without delay and calculate the desired temperature trajectory for the cooling jacket. A novel sensitivity compensating nonlinear control approach within generic model control framework for processes exhibiting input sensitivity was proposed in [7]. ...
... Here just product A is considered. The polymerization process is an exothermic reaction under specific recipe and process [6] which are given below. ...
... The energy balance in (4) gives a dynamic relationship of reactor temperature T (t), and (5) and (6) describe the temperature of cooling jacket outlet T out j and recirculation loop inlet T in j of coolant C, respectively. Furthermore, variables and parameters of reactor model are listed in Table I [6] . ...
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... In a recent study on this system reported by Vasanthi et al. (2012), the master control loop has been defined as a self-tuning controller combined with UKF for estimation to achieve reactor temperature control within the tolerance interval of ±0.6 K from the set point. ...
... K and −0.03 K) for AANNGMC2-PI. Recently, Vasanthi et al. (2012) have applied a self-tuning control based master controller with a PI based slave controller for this system and have reported that the variation of the reactor temperature error lies within ±0.6 K (approx. ±1 • F), which is larger in amplitude compared to the present study. ...
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... Graichen et al. 24 have applied feed forward control with online parameter estimation using EKF based on the first-principles model to find the set point trajectory for jacket temperature. Vasanthi et al. 25 developed a cascade controller with a self-tuning master control loop to obtain the desired control performance for the Chylla and Haase polymerization process maintaining the reactor temperature within the tolerance interval of ±0.6K from the set point. ...
... K and −0.27 K). Recently, Vasanthi et al. 25 have applied a self-tuning control based master controller with a PI based slave controller for this system where they have reported that the variation of the reactor temperature error lies within ±0.6 K (approximately ±1°F), which is larger in amplitude compared to the present study. ...
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... The most promising concepts in the field of adaptive control are [23] to [28]. The authors in [28] developed a self-tuning adaptive control, whose performance meets the required strict temperature tolerances in the polymerization reactor. ...
... The most promising concepts in the field of adaptive control are [23] to [28]. The authors in [28] developed a self-tuning adaptive control, whose performance meets the required strict temperature tolerances in the polymerization reactor. The field of optimal control is represented by [29] to [33] and the field of predictive control by articles [34] to [37]. ...
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... Graichen et al. [26] have applied feedforward control with online parameter estimation using EKF based on a calorimetric reactor model and a nonlinear model of the cooling system. Unscented Kalman filter has been employed to estimate the heat of reaction and heat transfer coefficient in the energy balance equation by Vasanthi et al. [27] in a self-tuning master control loop to maintain the reactor temperature in this problem within a tolerance limit of ±0.6 K. Helbig et al. [28] have proposed a direct control strategy based on a simplified model-based MPC in combination with an EKF for controlling the temperature of the Chylla-Haase problem. ...
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... Graichen et al. [16] have applied feed forward control with on-line parameter estimation using EKF based on a calorimetric reactor model and a nonlinear model of the cooling system. Vasanthi et al. [17] developed a cascade controller with a self-tuning master control loop combined with UKF to obtain the desired control performance for Chylla and Haase polymerization process maintaining the reactor temperature within the tolerance interval of K 6 . 0  from the set point. ...
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... In industrial applications, the temperature control of the reactor is usually carried out with PID controllers in a cascade structure [6,7]. Hence, the disturbances affecting the jacket can be eliminated and the constraints regarding the jacket can be defined. ...
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... Although feed-forward control 6 is used to improve controller performance, it can overcome only a certain type of disturbance. Online estimation 7 may be accomplished using polymerization kinetic models in forms of extended Kalman filter (EKF), 8 unscented Kalman filter (UKF), 9 and artificial neural network (ANN) 10,11 estimating the heat transfer coefficient and the reaction heat in the energy balance. These may be inadequate for the effective control of polymer properties especially in the case when the polymerization reactor exhibits either nonlinear dynamic behavior or strong interactions among the constraints on manipulated variables as well as controlled variables. ...
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This paper points out the flaws in using the extended Kalman filter (EKE) and introduces an improvement, the unscented Kalman filter (UKF), proposed by Julier and Uhlman (1997). A central and vital operation performed in the Kalman filter is the propagation of a Gaussian random variable (GRV) through the system dynamics. In the EKF the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the filter. The UKF addresses this problem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and when propagated through the true nonlinear system, captures the posterior mean and covariance accurately to the 3rd order (Taylor series expansion) for any nonlinearity. The EKF in contrast, only achieves first-order accuracy. Remarkably, the computational complexity of the UKF is the same order as that of the EKF. Julier and Uhlman demonstrated the substantial performance gains of the UKF in the context of state-estimation for nonlinear control. Machine learning problems were not considered. We extend the use of the UKF to a broader class of nonlinear estimation problems, including nonlinear system identification, training of neural networks, and dual estimation problems. In this paper, the algorithms are further developed and illustrated with a number of additional examples
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Recently, in a paper of Chylla and Haase [2], a model of a multiproduct semibatch polymerization reactor has been developed which is representative of those found in the speciality chemical processing industry. One of the aims in these processes is to keep a certain reaction temperature setpoint, in order to fit the quality requirements for the polymer. In the present paper, the optimal solutions of the underlying optimal control problems of the Chylla-Haase reactor, which have been computed by a new direct multiple shooting method, are discussed. It can be shown that the first of the two products for which physical data are given in [2] can be controlled along its required constant reaction temperature setpoint while, for the second product, this cannot be achieved because of certain mathematical and technical reasons.
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This paper considers the temperature control of semi-batch polymerization reactors in which some of the following issues must be considered: (i) production of multiple products in the same reactor; (ii) changing heat transfer characteristics, during a batch and from batch to batch; (iii) time varying and nonlinear reaction rate due to changing monomer concentration and diffusion controlled termination reactions (gel effect); (iv) the absence of detailed kinetic models for the reactors. The industrial challenge problem published by Chylla and Haase [Chylla, R. W. and Haase, D. R. (1993) Temperature control of semi-batch polymerization reactors (with corrected updates). Comput. Chem. Eng.17, 257–264) is used as the simulation basis for evaluating these problems.A nonlinear adaptive controller consisting of a nonlinear controller (based on differential geometric concepts) coupled with an extended Kalman filter (which uses only readily available data and knowledge) is shown to provide excellent control in all the above situations. In particular, the on-line estimation is critical for the strong performance of the nonlinear controller over a broad range of conditions. PID controllers with feedforward terms can perform well at one set of conditions, however, they require retuning as conditions and products change.
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The Chylla–Haase polymerization reactor is used as a benchmark problem to illustrate the potential of feedforward control design by extending the conventional cascade control in the framework of the two-degree-of-freedom control concept. To ensure an accurate temperature control, the feedforward control is adapted to different batch conditions and various products by an extended Kalman filter. The reaction heat and the heat transfer coefficient are estimated online based on simple physically motivated relations applicable to a wider range of batch reactors. Simulation results under model uncertainties show the effectiveness and accuracy of the adaptive feedforward control concept while maintaining the conventional feedback cascade control.
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Design and control of batch reactors provide challenging problems with respect to basic functionality and safety of a process as well as product quality and yield related issues. In this paper examples for the use of modelling, dynamic simulation and advanced control techniques for industrial problems are given. They are evaluated with respect to economic benefit as well as effort for development and implementation.
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An industrial case study appropriate for process control studies is presented. The control problem focuses on the temperature control of a multiproduct semibatch polymerization reactor. Achieving good temperature control in these reactors is often difficult because physical properties of the contents, such as mass, heat capacity and heat transfer coefficient vary from run to run and within a run. Standard PID controllers are unable to perform satisfactorily over the entire range of operation required. Physical data and modeling equations are provided so that process control researchers may test various control strategies. This control problem is representative of those found in the speciality chemical processing industry.
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The measurement and control of polymerization reactors is very challenging due to the complexity of the physical mechanisms and polymerization kinetics. In these reactors many important variables, which are related to end-use polymer properties, cannot be measured on-line or can only be measured at low sampling frequencies. Furthermore, end-use polymer properties are related to the entire molecular weight, copolymer composition, sequence length, and branching distributions. This paper surveys the instrumentation technologies, which are of particular interest in polymerization reactors with emphasis on, for example, measurement of viscosity, composition, molecular weight, and particle size. This paper presents a hierarchical approach to the control system design and reviews traditional regulatory techniques as well as advanced control strategies for batch, semibatch, and continuous reactors. These approaches are illustrated by focusing on the control of a commercial multiproduct continuous emulsion polymerization reactor. Finally, the paper captures some of the trends in the polymer industry, which may impact future development in measurement and reactor control.
Conference Paper
A model based control solution is given for an industrial benchmark problem concerning temperature control of a semibatch polymerization reactor. The original model given by Chylla and Haase (1993) is critically analyzed. The simulation study carried out with a modified benchmark model treats a realistic industrial scenario where process knowledge is incomplete. Reaction kinetics and heat transfer coefficient are assumed to be unknown and measurement information is limited. The proposed control strategy is based on nonlinear model predictive control in combination with an extended Kalman filter. The process model used in both the controller and filter comprises a calorimetric reactor model and a nonlinear model of the cooling system. The control strategy is shown to be robust against parametric uncertainties and batch to batch variations. It is compared to PID control with and without compensation of the estimated heat of reaction.
Adaptive control. second ed. Pearson Education Singapore
  • Astrom Karl
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The unscented Kalman filter for nonlinear estimation. In: Proceedings of symposium on adaptive systems for signal processing, communication and control
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