Nonlinear model predictive control for the polymorphic transformation of L‐glutamic acid crystals

Polymorphism, a phenomenon where a substance can have more than one crystal forms, has recently become a major interest to the food, speciality chemical, and pharmaceutical industries. The different physical properties for polymorphs such as solubility, morphology, and dissolution rate may jeopardize operability or product quality, resulting in significant effort in controlling crystallization processes to ensure consistent production of the desired polymorph. Here, a nonlinear model predictive control (NMPC) strategy is developed for the polymorphic transformation of L ‐glutamic acid from the metastable α‐form to the stable β‐form crystals. The robustness of the proposed NMPC strategy to parameter perturbations is compared with temperature control (T‐control), concentration control (C‐control), and quadratic matrix control with successive linearization (SL‐QDMC). Simulation studies show that T‐control is the least robust, whereas C‐control performs very robustly but long batch times may be required. SL‐QDMC performs rather poorly even when there is no plant‐model mismatch due to the high process nonlinearity, rendering successive linearization inaccurate. The NMPC strategy shows good overall robustness for two different control objectives, which were both within 7% of their optimal values, while satisfying all constraints on manipulated and state variables within the specified batch time. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

一种基于状态估计的间歇过程模型实时更新预测控制策略简

Nonlinear model predictive control （NMPC） is an appealing control technique for improving the per- formance of batch processes, but its implementation in industry is not always possible due to its heavy on-line computation. To facilitate the implementation of NMPC in batch processes, we propose a real-time updated model predictive control method based on state estimation. The method includes two strategies： a multiple model building strategy and a real-time model updated strategy. The multiple model building strategy is to produce a series of sim- plified models to reduce the on-line computational complexity of NMPC. The real-time model updated strategy is to update the simplified models to keep the accuracy of the models describing dynamic process behavior. The method is validated with a typical batch reactor. Simulation studies show that the new method is efficient and robust with respect to model mismatch and changes in process parameters.     

Integrated B2B‐NMPC control strategy for batch/semibatch crystallization processes

The uncertainty in crystallization kinetics is of major concern in manufacturing processes, which can result in deterioration of most model‐based control strategies. In this study, uncertainties in crystallization kinetic parameters were characterized by Bayesian probability distributions. An integrated B2B‐NMPC control strategy was proposed to first update the kinetic parameters from batch to batch using a multiway partial least‐squares (MPLS) model, which described the variances of kinetic parameters from that of process variables and batch‐end product qualities. The process model with updated kinetic parameters was then incorporated into an NMPC design, the extended prediction self‐adaptive control (EPSAC), for online control of the final product qualities. Promising performance of the proposed integrated strategy was demonstrated in a simulated semibatch pH‐shift reactive crystallization process to handle major crystallization kinetic uncertainties of L‐glutamic acid, wherein smoother and faster convergences than the conventional B2B control were observed when process dynamics were shifted among three scenarios of kinetic uncertainties. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Data‐driven model predictive quality control of batch processes

The problem of driving a batch process to a specified product quality using data‐driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this “missing data” problem by integrating a previously developed data‐driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed‐loop simulations of a nylon‐6,6 batch polymerization process with limited measurements. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2852–2861, 2013     

Real‐time control of a semi‐industrial fed‐batch evaporative crystallizer using different direct optimization strategies

This article presents a model‐based control approach for optimal operation of a seeded fed‐batch evaporative crystallizer. Various direct optimization strategies, namely, single shooting, multiple shooting, and simultaneous strategies, are used to examine real‐time implementation of the control approach on a semi‐industrial crystallizer. The dynamic optimizer utilizes a nonlinear moment model for on‐line computation of the optimal operating policy. An extended Luenberger‐type observer is designed to enable closed‐loop implementation of the dynamic optimizer. In addition, the observer estimates the unmeasured process variable, namely, the solute concentration, which is essential for the intended control application. The model‐based control approach aims to maximize the batch productivity, as satisfying the product quality requirements. Optimal control of crystal growth rate is the key to fulfill this objective. This is due to the close relation of the crystal growth rate to product attributes and batch productivity. The experimental results suggest that real‐time application of the control approach leads to a substantial increase, i.e., up to 30%, in the batch productivity. The reproducibility of batch runs with respect to the product crystal size distribution is achieved by thorough seeding. The simulation and experimental results indicate that the direct optimization strategies perform similarly in terms of optimal process operation. However, the single shooting strategy is computationally more expensive. © 2010 American Institute of Chemical Engineers AIChE J, 57: 1557–1569, 2011     

On‐Line PEMFC Control Using Parameterized Nonlinear Model‐Based Predictive Control

In this work, a fast nonlinear model‐based predictive control (NMPC) strategy is designed and experimentally validated on‐line on a real fuel cell. Regarding NMPC strategies, the most challenging part remains to achieve on‐line implementation, especially when dealing with fast dynamic systems. As previously demonstrated in a recent work, the proposed control strategy is ideally suited to address this problem. Indeed, it is 30 times faster than classical NMPC controllers. This strategy relies on a specific parameterization of the control actions to reduce the computational time and achieve on‐line implementation. Due to its short computational time compared to mechanistic models, an artificial neural network model is designed and experimentally validated. This model is employed as internal model in the NMPC controller to predict the system behavior. To confirm the applicability and the relevance of the proposed NMPC controller varying control scenarios are investigated on a test bench. The built‐in controller is overridden and the NMPC controller is implemented externally and executed on‐line. Experimental results exhibit the outstanding tracking capability and robustness against model‐process mismatch of the proposed strategy. The parameterized NMPC controller turns out to be an excellent candidate for on‐line applications.     

Transition from Batch to Continuous Operation in Bio‐Reactors: A Model Predictive Control Approach and Application

This work considers the problem of determining the transition of ethanol‐producing bio‐reactors from batch to continuous operation and subsequent control subject to constraints and performance considerations. To this end, a Lyapunov‐based non‐linear model predictive controller is utilized that stabilizes the bio‐reactor under continuous mode of operation. The key idea in the predictive controller is the formulation of appropriate stability constraints that allow an explicit characterization of the set of initial conditions from where feasibility of the optimization problem and hence closed‐loop stability is guaranteed. Additional constraints are incorporated in the predictive control design to expand on the set of initial conditions that can be stabilized by control designs that only require the value of the Lyapunov function to decay. Then, the explicit characterization of the set of stabilizable initial conditions is used in determining the appropriate time for which the reactor must be run in batch mode. Specifically, the predictive control approach is utilized in determining the appropriate batch length that achieves stabilizable values of the state variables at the end of the batch. Application of the proposed method to the ethanol production process using Zymomonas mobilis as the ethanol producing micro‐organism demonstrates the effectiveness of the proposed model predictive control strategy in stabilizing the bio‐reactor.     

Dynamic Optimization and Non‐linear Model Predictive Control to Achieve Targeted Particle Morphologies

An event‐driven approach based on dynamic optimization and nonlinear model predictive control (NMPC) is investigated together with inline Raman spectroscopy for process monitoring and control. The benefits and challenges in polymerization and morphology monitoring are presented, and an overview of the used mechanistic models and the details of the dynamic optimization and NMPC approach to achieve the relevant process objectives are provided. Finally, the implementation of the approach is discussed, and results from experiments in lab and pilot‐plant reactors are presented.     

Handling multi‐rate and missing data in variable duration economic model predictive control of batch processes

In the present work, we consider the problem of variable duration economic model predictive control of batch processes subject to multi‐rate and missing data. To this end, we first generalize a recently developed subspace‐based model identification approach for batch processes to handle multi‐rate and missing data by utilizing the incremental singular value decomposition technique. Exploiting the fact that the proposed identification approach is capable of handling inconsistent batch lengths, the resulting dynamic model is integrated into a tiered EMPC formulation that optimizes process economics (including batch duration). Simulation case studies involving application to the energy intensive electric arc furnace process demonstrate the efficacy of the proposed approach compared to a traditional trajectory tracking approach subject to limited availability of process measurements, missing data, measurement noise, and constraints. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2705–2718, 2017     

Integrating data‐based modeling and nonlinear control tools for batch process control

A data‐based multimodel approach is developed in this work for modeling batch systems in which multiple local linear models are identified using latent variable regression and combined using an appropriate weighting function that arises from fuzzy c‐means clustering. The resulting model is used to generate empirical reverse‐time reachability regions (RTRRs) (defined as the set of states from where the data‐based model can be driven inside a desired end‐point neighborhood of the system), which are subsequently incorporated in a predictive control design. Simulation results of a fed‐batch reactor system under proportional‐integral (PI) control and the proposed RTRR‐based design demonstrate the superior performance of the RTRR‐based design in both a fault‐free and faulty environment. The data‐based modeling methodology is then applied on a nylon‐6,6 batch polymerization process to design a trajectory tracking predictive controller. Closed‐loop simulation results illustrate the superior tracking performance of the proposed predictive controller over PI control. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Multistage nonlinear model predictive control for pumping treatment in hydraulic fracturing

Hydraulic fracturing has gained increasing attention as it allows the constrained natural gas and crude oil to flow out of low-permeability shale formations and significantly increase production. Perilous operating states of extremely high pressure also raise some safety concerns, requiring us to formulate an appropriate dynamic model, and provide a careful engineering control to ensure safe operating conditions. Moreover, uncertainties due to spatially varying rock properties increase the difficulties in control of the fracturing process. In this work, we formulate a first-principles model by considering the fracture evolution, mass transport of substances in the slurry, changing fluid properties, and the monitored operating pressure on the ground level. Next, we implement nonlinear model predictive control (NMPC) to control the process under a set of final requirements and process constraints. Our results show that the performance of standard NMPC degrades when the rock uncertainty causes the parameter mismatch between the process and the predictive model in the controller. With standard NMPC, designed with a nominal model, the process fails to meet the terminal requirements of fracture geometry, and pressure is violated in one of the parameter mismatch cases. Therefore, we resort to multistage NMPC, which considers uncertainty evolution in a scenario tree with separate control sequences to address constraint violations. We demonstrate that multistage NMPC presents good performance by showing constraint satisfaction whether the uncertain rock parameter realization is time-invariant or time-variant. We also simulate the process with multistage NMPC including different numbers of scenarios and compare their control performance. Our investigation demonstrates that multistage NMPC effectively manages parametric uncertainties attributed to non-homogeneous rock formation, and provides a promising control strategy for the hydraulic fracturing process.     

Control of a Batch Polymerization System Using Hybrid Neural Network ‐ First Principle Model

In this work, the utilization of neural network in hybrid with first principle models for modelling and control of a batch polymerization process was investigated. Following the steps of the methodology, hybrid neural network (HNN) forward models and HNN inverse model of the process were first developed and then the performance of the model in direct inverse control strategy and internal model control (IMC) strategy was investigated. For comparison purposes, the performance of conventional neural network and PID controller in control was compared with the proposed HNN. The results show that HNN is able to control perfectly for both set points tracking and disturbance rejection studies.     

Fuzzy multi‐model based adaptive predictive control and its application to thermoplastic injection molding

Many chemical processes are inherently nonlinear. A single linear model is ineffective for these processes. Several local linear models may be developed for different operating conditions. A combination of these local models, through a fuzzy logic representation, results in an overall model for a wider operation range. In this paper, on‐line improvements and a fuzzy multi‐model have been proposed for predictive control implementation. Firstly, assuming that the premises of the fuzzy rules keep their original structures, the linear parameters in the rule consequents are on‐line updated by a weighted recursive least squares algorithm at each sample interval. Secondly, a batch learning algorithm is proposed to tune the fuzzy rule premises using a competitive learning algorithm. The effectiveness of the proposed improvements is demonstrated with experimental applications to the filling velocity control of thermoplastic injection molding     

Nonlinear model predictive control for dividing wall columns

Dividing wall columns (DWCs) are practical, effective, and promising among distillation process intensification technologies. Nonlinear model predictive control (NMPC) schemes are developed in this study to control the three-product DWCs. As these systems are intensely interactive and highly nonlinear, NMPC may be more suitable than the traditional PI control. The model is established based on Python and Pyomo platforms. As the original mathematical model of the column section is ill-posed, index reduction is used to avoid a high-index differential-algebraic equation (DAE) system. The well-posed index-1 system after index reduction is employed for the steady-state simulation and dynamic control in this study. Case studies with three DWC configurations to separate the mixture of ethanol (A), n-propanol (B), and n-butanol (C) show that the NMPC performs very well with small maximum deviations and short settling times. This demonstrates that the NMPC is a feasible and very effective scheme to control three-product DWCs.     

Error‐triggered on‐line model identification for model‐based feedback control

In industry, it may be difficult in many applications to obtain a first‐principles model of the process, in which case a linear empirical model constructed using process data may be used in the design of a feedback controller. However, linear empirical models may not capture the nonlinear dynamics over a wide region of state‐space and may also perform poorly when significant plant variations and disturbances occur. In the present work, an error‐triggered on‐line model identification approach is introduced for closed‐loop systems under model‐based feedback control strategies. The linear models are re‐identified on‐line when significant prediction errors occur. A moving horizon error detector is used to quantify the model accuracy and to trigger the model re‐identification on‐line when necessary. The proposed approach is demonstrated through two chemical process examples using a model‐based feedback control strategy termed Lyapunov‐based economic model predictive control (LEMPC). The chemical process examples illustrate that the proposed error‐triggered on‐line model identification strategy can be used to obtain more accurate state predictions to improve process economics while maintaining closed‐loop stability of the process under LEMPC. © 2016 American Institute of Chemical Engineers AIChE J, 63: 949–966, 2017     

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.     

High-order iterative learning model predictive control for batch chemical processes

In order to address two-dimensional (2D) control issue for a class of batch chemical processes, we propose a novel high-order iterative learning model predictive control (HILMPC) method in this paper. A set of local state-space models are first constructed to represent the batch chemical processes by adopting the just-in-time learning (JITL) technique. Meanwhile, a pre-clustered strategy is used to lessen the computational burden of the modelling process and improve the modelling efficiency. Then, a two-stage 2D controller is designed to achieve integrated control by combining high-order iterative learning control (HILC) on the batch domain with model predictive control (MPC) on the time domain. The resulting HILMPC controller can not only guarantee the convergence of the system on the batch domain, but also guarantee the closed-loop stability of the system on the time domain. The convergence of the HILMPC method is ensured by rigorous analysis. Two examples are presented in the end to demonstrate that the developed method provides better control performance than its previous counterpart.     

Dynamic optimization oriented modeling and nonlinear model predictive control of the wet limestone FGD system

Nonlinear model predictive control (NMPC) scheme is an effective method of multi-objective optimization control in complex industrial systems. In this paper, a NMPC scheme for the wet limestone flue gas desulphurization (WFGD) system is proposed which provides a more flexible framework of optimal control and decision-making compared with PID scheme. At first, a mathematical model of the FGD process is deduced which is suitable for NMPC structure. To equipoise the model's accuracy and conciseness, the wet limestone FGD system is separated into several modules. Based on the conservation laws, a model with reasonable simplification is developed to describe dynamics of different modules for the purpose of controller design. Then, by addressing economic objectives directly into the NMPC scheme, the NMPC controller can minimize economic cost and track the set-point simultaneously. The accuracy of model is validated by the field data of a 1000 MW thermal power plant in Henan Province, China. The simulation results show that the NMPC strategy improves the economic performance and ensures the emission requirement at the same time. In the meantime, the control scheme satisfies the multiobjective control requirements under complex operation conditions (e.g., boiler load fluctuation and set point variation). The mathematical model and NMPC structure provides the basic work for the future development of advanced optimized control algorithms in the wet limestone FGD systems.     

Fed‐batch culture of hybridoma cells in serum‐free medium using an optimized feeding strategy

The achievement of high cell density and monoclonal antibody concentration depends on understanding cell metabolism and the control of cell culture. A model of cell metabolism and monoclonal antibody production in hybridoma cell culture is presented. Fed‐batch culture in serum‐free medium was conducted in a bioreactor with an optimized feeding strategy according to the model. In the process, nutrient concentrations, especially glucose and glutamine, were maintained at relatively constant and low levels. The formation of toxic byproducts, such as ammonia and lactate, was greatly reduced in comparison with that in non‐optimized batch culture. The concentration of monoclonal antibody reached 350 mg dm^?3, which was seven times greater than in non‐optimized batch culture. Copyright © 2003 Society of Chemical Industry     

Nonlinear model predictive control of an industrial polymerization process

Nonlinear model predictive control (NMPC) is used to maintain and control polymer quality at specified production rates because the polymer quality measures have strong interacting nonlinearities with different temperatures and feed rates. Polymer quality measures that are available from the laboratory infrequently are controlled in closed-loop using a NMPC to set the temperature profile of the reactors. NMPC results in better control of polymer quality measures at different production rates as compared to using the nonlinear process model with reaction kinetics to implement offline targets for reactor temperatures.