Adrie E. M. Huesman

Nonlinear Model-Based Control of a Semi-Industrial Batch Crystallizer Using a Population Balance Modeling Framework

This paper presents an output feedback nonlinear model-based control approach for optimal operation of industrial batch crystallizers. A full population balance model is utilized as the cornerstone of the control approach. The modeling framework allows us to describe the dynamics of a wide range of industrial batch crystallizers. In addition, it facilitates the use of performance objectives expressed in terms of crystal size distribution. The core component of the control approach is an optimal control problem, which is solved by the direct multiple shooting strategy. To ensure the effectiveness of the optimal operating policies in the presence of model imperfections and process uncertainties, the model predictions are adapted on the basis of online measurements using a moving horizon state estimator. The nonlinear model-based control approach is applied to a semi-industrial crystallizer. The simulation results suggest that the feasibility of real-time control of the crystallizer is largely dependent on the discretization coarseness of the population balance model. The control performance can be greatly deteriorated due to inadequate discretization of the population balance equation. This results from structural model imperfection, which is effectively compensated for by using the online measurements to confer an integrating action to the dynamic optimizer. The real-time feasibility of the output feedback control approach is experimentally corroborated for fed-batch evaporative crystallization of ammonium sulphate. It is observed that the use of the control approach leads to a substantial increase, i.e., up to 15%, in the batch crystal content as the product quality is sustained.

DEGREES OF FREEDOM ANALYSIS OF ECONOMIC DYNAMIC OPTIMAL PLANTWIDE OPERATION

Improving the operation is an attractive option for the process industry to deal with increased competition. In this paper a general dynamic optimization framework is proposed that aims to improve plantwide operation in an economic sense. The term general means that it is based on dynamic operation in which any operational constraints can be accommodated. One would expect economic optimization to utilize all available degrees of freedom. However it is shown that this is normally not the case, so this leaves the possibility open to do further optimization.

Real-time Dynamic Optimization of Batch Crystallization Processes

An on-line optimization strategy is developed and applied to a semi-industrial crystallization process. The seeded fed-batch crystallizer is represented by a nonlinear moment model. An optimal control problem pertinent to maximization of the batch crystal yield is solved using the sequential optimization approach. As the dynamic optimizer requires knowledge of the states of the system, an extended Luenberger-type observer is designed to estimate the unmeasured state variable, i.e. solute concentration. Real-time implementations of the proposed strategy reveal the effectiveness of closed-loop optimal control of the crystallizer. The superior performance of the closed-loop implementation to that of the open-loop implementation is attributed to the distinct role of the observer in the feedback control structure that not only accounts for plant-model mismatch by state adaptation, but also enables disturbance handling. Experimental results also demonstrate that the application of the proposed optimal control strategy leads to a substantial increase in the crystal volume fraction at the end of the batch, while the reproducibility of batches with respect to the product crystal size distribution is sustained.

A Comparison of Nonlinear State Estimators for Closed-loop Control of Batch Crystallizers

Abstract This study investigates the effectiveness of various nonlinear estimation techniques for output feedback model-based control of batch crystallization processes. Several nonlinear observers developed under deterministic and Bayesian estimation frameworks are applied for closed-loop control of a semi-industrial fed-batch crystallizer. The performance evaluation is done in terms of closed-loop behavior of the control strategy and its ability to cope with model imperfections and process uncertainties such as measurement errors and uncertain initial conditions. The simulation results suggest that the extended and the unscented Kalman filters perform best in terms of fulfilling the control objective. Adopting a time-varying process noise matrix, which is particularly suited for batch processes, further enhances the accuracy of state estimates at the expense of a slight increase in computational burden. The results also indicate that model imperfections and process uncertainties rather significantly deteriorate the closed-loop performance of the controller due to inaccurate state estimation.

Towards the systematic design of actuation for process systems

Abstract Currently systematic design of actuation (operational degrees of freedom) for process systems is not possible because (i) the required domain knowledge has not been identified and (ii) it is unclear how to explore the relation between actuation and operational improvement. This paper proposes geometry and flux equations as the required domain knowledge. It is explained that the relation between actuation and operational improvement should be explored in an optimal control setting. By means of an example (distillation) it is illustrated that a spatial actuation extension may result in considerable operational improvement.