Zoltan K. Nagy

Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations

Abstract Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented.

Nonlinear Model Predictive Control: From Theory to Application

While linear model predictive control is popular since the 70s of the past century, only since the 90s there is a steadily increasing interest from control theoreticians as well as control practitioners in nonlinear model predictive control (NMPC). The practical interest is mainly driven by the fact that todays processes need to be operated under tight performance specifications. At the same time more and more constraints, stemming for example from environmental and safety considerations, need to be satisfied. Often, these demands can only be met when process nonlinearities and constraints are explicitly taken into account in the controller design. Nonlinear predictive control, the extension of the well established linear predictive control to the nonlinear world, is one possible candidate to meet these demands. This paper reviews the basic principle of NMPC, and outlines some of the theoretical, computational, and implementational aspects of this control strategy.

Advances and New Directions in Crystallization Control

The academic literature on and industrial practice of control of solution crystallization processes have seen major advances in the past 15 years that have been enabled by progress in in-situ real-time sensor technologies and driven primarily by needs in the pharmaceutical industry for improved and more consistent quality of drug crystals. These advances include the accurate measurement of solution concentrations and crystal characteristics as well as the first-principles modeling and robust model-based and model-free feedback control of crystal size and polymorphic identity. Research opportunities are described in model-free controller design, new crystallizer designs with enhanced control of crystal size distribution, strategies for the robust control of crystal shape, and interconnected crystallization systems for multicomponent crystallization.

Model based robust control approach for batch crystallization product design

The paper presents a novel control approach for crystallization processes, which can be used for designing the shape of the crystal size distribution to robustly achieve desired product properties. The approach is based on a robust optimal control scheme, which takes parametric uncertainties into account to provide decreased batch-to-batch variability of the shape of the crystal size distribution. Both open-loop and closed-loop robust control schemes are evaluated. The open-loop approach is based on a robust end-point nonlinear model predictive control (NMPC) scheme which is implemented in a hierarchical structure. On the lower level a supersaturation control approach is used that drives the system in the phase diagram according to a concentration versus temperature trajectory. On the higher level a robust model-based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modelled using the population balance equation (PBE), which is solved using a novel efficient approach that combines the quadrature method of moment (QMOM) and method of characteristics (MOC). The proposed robust model based control approach is corroborated for the case of various desired shapes of the target distribution.

Worst-case and distributional robustness analysis of finite-time control trajectories for nonlinear distributed parameter systems

A novel approach is proposed that quantifies the influence of parameter and control implementation uncertainties upon the states and outputs of finite-time control trajectories for nonlinear lumped and distributed parameter systems. The worst-case values of the states and outputs due to model parameter uncertainties are computed as a function of time along the control trajectories. The algorithm can also compute the part of the optimal control trajectory for which implementation inaccuracies are of increased importance. An analytical expression is derived that provides an estimate of the distribution of the states and outputs as a function of time, based on simulation results. The approaches require a relatively low computational burden to perform the analysis, compared to Monte Carlo approaches for robustness analysis. The technique is applied to the crystallization of an inorganic chemical with uncertainties in the nucleation and growth parameters and in the implementation of the control trajectory.

Model Based Control: Case Studies in Process Engineering

Filling a gap in the literature for a practical approach to the topic, this book is unique in including a whole section of case studies presenting a wide range of applications from polymerization reactors and bioreactors, to distillation column and complex fluid catalytic cracking units. A section of general tuning guidelines of MPC is also present.These thus aid readers in facilitating the implementation of MPC in process engineering and automation. At the same time many theoretical, computational and implementation aspects of model-based control are explained, with a look at both linear and nonlinear model predictive control. Each chapter presents details related to the modeling of the process as well as the implementation of different model-based control approaches, and there is also a discussion of both the dynamic behaviour and the economics of industrial processes and plants. The book is unique in the broad coverage of different model based control strategies and in the variety of applications presented. A special merit of the book is in the included library of dynamic models of several industrially relevant processes, which can be used by both the industrial and academic community to study and implement advanced control strategies.

Nonlinear model predictive control of a four tank system: An experimental stability study

There are well-known theoretical examples that show that stability constraints in nonlinear model predictive control (NMPC) are necessary in order to guarantee closed loop stability. In this paper it is shown that these stability constraints, derived from theory, are also essential in practice. In particular, an experimental study is carried out on a four tank system that illustrates the stability behavior of NMPC.

The TriLab, a novel ICT based triple access mode laboratory education model

This paper introduces a novel model of laboratory education, namely the TriLab. The model is based on recent advances in ICT and implements a three access modes to the laboratory experience (virtual, hands-on and remote) in one software package. A review of the three modes is provided with highlights of advantages and disadvantages of each mode. It is shown that recent literature on laboratory education recommends hybrid structures. Some literature has reported on the use of two modes hybrid structures, however, it is seldom reported to have triple access mode laboratory. This paper probably the first to report empirical findings of using the three components together. The virtual component of the TriLab has been mainly used in a preparation session for undergraduate students, while the remote component has been mainly used for demonstrating theory applicability in postgraduate courses. The empirical findings shows clearly the positive impact of the hybrid approach on students learning and motivation, these are discussed in light of pedagogical and cognitive psychology theories.

Automated direct nucleation control for in situ dynamic fines removal in batch cooling crystallization

Secondary nucleation (e.g. due to attrition) and accidental seeding (e.g. from crust on the wall of vessels) are undesired events that often take place during industrial crystallization processes. The crystal size distribution is greatly affected by these events. The typically used open loop control strategies fail to respond to these dynamic changes resulting in undesired end product properties. Variations in seed quality during seeded operations (e.g. initial breeding) can also result in undesired product quality. The automated direct nucleation control (ADNC) approach presented in this paper automatically detects any changes in the system and removes fines in situ. The approach is tested for external seed additions and accidental seeding scenarios. The results show that the ADNC approach is able to detect any changes in the metastable zone width and drive the system accordingly to dissolve unwanted fines providing an automatic in situ fines removal mechanism.

Enhancing crystalline properties of a cardiovascular active pharmaceutical ingredient using a process analytical technology based crystallization feedback control strategy

Pharmaceutical regulatory bodies require minimal presence of solvent in an active pharmaceutical ingredient (API) after crystallization. From a processing point of view bigger crystals with minimal agglomeration and uniform size distribution are preferred to avoid solvent inclusion and for improved downstream processing. The current work addresses these issues encountered during the production of the potential anti-arrhythmic cardiovascular drug, AZD7009. This paper demonstrates that by applying the automated direct nucleation control (ADNC) approach problems with agglomeration and solvent inclusion were resolved. This model free approach automatically induces temperature cycles in the system, with the number of cycles, temperature range and adaptive heating and cooling rates determined to maintain the number of particles in the system, as measured by a focused beam reflectance measurement (FBRM) probe, within a constant range during the crystallization. The ADNC approach was able to produce larger and more uniform crystals and also removed the residual solvent trapped between the crystals compared to the typical crystallization operation using linear cooling profile. The results illustrate the application of process analytical technologies, such as FBRM and ATR-UV-vis spectroscopy, for the design of optimal crystallization operating conditions for the production of pharmaceuticals, and demonstrate that the ADNC approach can be used for rapid crystallization development for APIs exhibiting problems with agglomeration and solvent inclusion.