Predictive Process Control Research Articles

Decentralized machine-learning-based predictive control of nonlinear processes

This work focuses on the design of decentralized model predictive control (MPC) systems for nonlinear processes, where the nonlinear process is broken down into multiple, yet coupled subsystems and the dynamic behavior of each subsystem is described by a machine learning model. One decentralized MPC is designed and used to control each subsystem while accounting for the interactions between subsystems through feedback of the entire process state. The closed-loop stability of the overall nonlinear process network and the performance properties of the decentralized model predictive control system using machine-learning prediction models are analyzed. More specifically, multiple recurrent neural network models suited for each different subsystem need to be trained with a sufficiently small modeling error from their respective actual nonlinear process models to ensure closed-loop stability. These recurrent neural network models are subsequently used as the prediction model in decentralized Lyapunov-based MPCs to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. The simulation results of a nonlinear chemical process network example demonstrate the effective closed-loop control performance when the process is operated under the decentralized MPCs using the independently-trained recurrent neural network models, as well as the improved computational efficiency compared to the closed-loop simulation of a centralized MPC system.

Biogas production management systems with model predictive control of anaerobic digestion processes

We developed a biogas production management system to control biogas production by determining the feedstock inputs to the anaerobic digestion process according to fluctuations of the renewable energy supply. The developed system consists of three functions: a prediction model for the anaerobic digestion processes, a parameter-estimation system, and a feedstock-determination controller. A prediction model for the anaerobic digestion processes in a state-space representation was constructed for the input–output relationship of biogas generation from organic compounds and the state of methane fermentation. A parameter-estimation system that estimated the parameters included in the prediction model from actual operating process data was built based on adaptive identification theory. The feedstock-determination controller was established based on model predictive control as a method to control biogas production. From the results of the identification experiment, the least square estimator of the parameters converged as the training data increased, and a reliable parameter was given in 1 week. From the results of the numerical simulation and the control experiment, it was confirmed that the biogas production management system developed in this study had a high prediction accuracy and control performance.

Process structure-based recurrent neural network modeling for model predictive control of nonlinear processes

In this work, physics-based recurrent neural network (RNN) modeling approaches are proposed for a general class of nonlinear dynamic process systems to improve prediction accuracy by incorporating a priori process knowledge. Specifically, a hybrid modeling method is first introduced to integrate first-principles models and RNN models. Subsequently, a partially-connected RNN modeling method that designs the RNN structure based on a priori structural process knowledge, and a weight-constrained RNN modeling method that employs weight constraints in the optimization problem of the RNN training process are developed. The proposed physics-based RNN models are utilized in model predictive controllers and applied to a chemical process network example to demonstrate their improved approximation performance compared to the fully-connected RNN model that is developed as a black box model.

Current and future requirements to industrial analytical infrastructure\u2014part 2: smart sensors

Complex processes meet and need Industry 4.0 capabilities. Shorter product cycles, flexible production needs, and direct assessment of product quality attributes and raw material attributes call for an increased need of new process analytical technologies (PAT) concepts. While individual PAT tools may be available since decades, we need holistic concepts to fulfill above industrial needs. In this series of two contributions, we want to present a combined view on the future of PAT (process analytical technology), which is projected in smart labs (Part 1) and smart sensors (Part 2). Part 2 of this feature article series describes the future functionality as well as the ingredients of a smart sensor aiming to eventually fuel full PAT functionality. The smart sensor consists of (i) chemical and process information in the physical twin by smart field devices, by measuring multiple components, and is fully connected in the IIoT 4.0 environment. In addition, (ii) it includes process intelligence in the digital twin, as to being able to generate knowledge from multi-sensor and multi-dimensional data. The cyber-physical system (CPS) combines both elements mentioned above and allows the smart sensor to be self-calibrating and self-optimizing. It maintains its operation autonomously. Furthermore, it allows—as central PAT enabler—a flexible but also target-oriented predictive control strategy and efficient process development and can compensate variations of the process and raw material attributes. Future cyber-physical production systems—like smart sensors—consist of the fusion of two main pillars, the physical and the digital twins. We discuss the individual elements of both pillars, such as connectivity, and chemical analytics on the one hand as well as hybrid models and knowledge workflows on the other. Finally, we discuss its integration needs in a CPS in order to allow its versatile deployment in efficient process development and advanced optimum predictive process control.

Fractional-Order Predictive Functional Control of Industrial Processes with Partial Actuator Failures

As the actuator faults in an industrial process cause damage or performance deterioration, the design issue of an optimal controller against these failures is of great importance. In this paper, a fractional-order predictive functional control method based on population extremal optimization is proposed to maintain the control performance against partial actuator failures. The proposed control strategy consists of two key ideas. The first one is the application of fractional-order calculus into the cost function of predictive functional control. Since the knowledge of analytical parameters including the prediction horizon, fractional-order parameter, and smoothing factor in fractional-order predictive functional control is not known, population extremal optimization is employed as the second key technique to search for these parameters. The effectiveness of the proposed controller is examined on two industrial processes, e.g., injection modeling batch process and process flow of coke furnace under constant faults, time-varying faults, and nonrepetitive unknown disturbance. The comprehensive simulation results demonstrate the performance of the proposed control method by comparing with a recently developed predictive functional control, genetic algorithm, and particle swarm optimization-based versions in terms of four performance indices.

Accurate Prediction of Nanovoid Structures and Energetics in Bcc Metals

Knowledge on structures and energetics of nanovoids is fundamental to understand defect evolution in metals. Yet there remain no reliable methods able to determine essential structural details or to provide accurate assessment of energetics for general nanovoids. Here, we performed systematic first-principles investigations to examine stable structures and energetics of nanovoids in bcc metals, explicitly demonstrated the stable structures can be precisely determined by minimizing their Wigner-Seitz area, and revealed a linear relationship between formation energy and Wigner-Seitz area of nanovoids. We further developed a new physics-based model to accurately predict stable structures and energetics for arbitrary-sized nanovoids. This model was well validated by first-principles calculations and recent nanovoid annealing experiments, and showed distinct advantages over the widely used spherical approximation. The present work offers mechanistic insights that crucial for understanding nanovoid formation and evolution, provides crucial benchmarks for assessing empirical interatomic potentials, and enables a critical step towards predictive control and prevention of nanovoid related damage processes in structural metals.

Control Lyapunov-Barrier function-based predictive control of nonlinear processes using machine learning modeling

Control Lyapunov-Barrier functions (CLBF) have been adopted to design model predictive controllers (MPC) for input-constrained nonlinear systems to ensure closed-loop stability and process operational safety simultaneously. In this work, a CLBF-MPC using an ensemble of recurrent neural network (RNN) models is proposed with guaranteed closed-loop stability and process operational safety for two types of unsafe regions, i.e., bounded and unbounded sets, for nonlinear processes. The application of the proposed RNN-based CLBF-MPC method is demonstrated through a chemical process example.

Sensitivity-based hierarchical distributed model predictive control of nonlinear processes

Hierarchical distributed model predictive control (HDMPC) is a promising control framework for industrial processes. With the development of efficient solvers for large-scale nonlinear programming (NLP), the implementation of hierarchical distributed control with nonlinear models becomes achievable. However, there is a lack of systematic method that handles the online computational delay in HDMPC which may lead to deterioration of performance or stability. To speed up online computation, an NLP sensitivity-based HDMPC algorithm is proposed in this paper. The implementation strategy is divided into background and online stages. All the local MPC controllers solve their sub-optimization problems iteratively in background based on the predicted future state, and a sensitivity update step is performed online to correct the predicted optimal inputs. The system-wide sensitivity equation is formulated in the upper control level by combining the optimality information of local controllers. The optimality and stability analysis for the proposed method is given. Three case studies are presented to demonstrate the controller performance.

Predictive control of unstable time delay series cascade processes with measurement noise

In this paper, generalized predictive control strategy is applied for unstable time delay series cascade processes. The control structure consists of a secondary loop with a secondary controller designed based on simple internal model control (IMC) method and the primary loop consists of a set-point achievement controller and is designed using synthesis method. Further, a generalized predictor consisting of two filters that deals with time delay, disturbance rejection and noise rejection capabilities is also designed in the primary loop. The filters are designed to ensure internal stability as well. For the predictor, only one tuning parameter is involved, which can be tuned in such a way that a trade-off is attained between disturbances attenuation and performance under uncertainties. In this work, various examples of cascade processes with unstable dynamics and time delay are considered for simulation. Results obtained from simulation reveals that with the suggested predictive control scheme, enhanced closed loop control performances are obtained for both nominal and perturbed conditions both in the presence and absence of measurement noise. The comparison is also verified quantitatively with the literature methods using integral absolute error (IAE) and total variation (TV) measures.

Machine learning‐based predictive control of nonlinear processes. Part I: Theory

AbstractThis article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open‐loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov‐based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed‐loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed‐loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.

Machine‐learning‐based predictive control of nonlinear processes. Part II: Computational implementation

AbstractMachine learning is receiving more attention in classical engineering fields, and in particular, recurrent neural networks (RNNs) coupled with ensemble regression tools have demonstrated the capability of modeling nonlinear dynamic processes. In Part I of this two‐article series, the Lyapunov‐based model predictive control (LMPC) method using a single RNN model and an ensemble of RNN models, respectively, was rigorously developed for a general class of nonlinear systems. In the present article, computational implementation issues of this new control method ranging from training of the RNN models, ensemble regression of the RNN models, and parallel computation for accelerating the real‐time model calculations are addressed. Furthermore, a chemical reactor example is used to demonstrate the implementation and effectiveness of these machine‐learning tools in LMPC as well as compare them with standard state‐space model identification tools.

Health-Aware Model-Predictive Control of a Cooperative AGV-Based Production System.

In the paper, a new scheduling strategy for assembly systems consisting of cooperating Automated Guided Vehicles (AGVs) based on their remaining operational time is developed. The operational time is associated with state of charge and state of health of the AGV battery. While the latter is defined as a possible number of repetitions of a set of given tasks, both are impossible to measure on-line directly with conventional sensors. Therefore, a novel state-of-charge estimator is proposed, which uses battery current and voltage sensor readings. In contrast to the approaches presented in the literature, a comprehensive analysis of its convergence is provided. Subsequently, a state-of-health predictor is developed. With the above measures, a new control strategy for cooperative AGVs is proposed. It is achieved by the allocation of alternative tasks among two cooperating robots referring to the state of the accomplished tasks from the previous stage of the assembly process. The proposed method allows a predictive control of assembly processes with several constraints, e.g., productivity of each assembly station, speed of the communication, or operation capability of the robots involved in the assembling process. The final part of the paper shows an experimental study exhibiting the performance of the proposed approach.

Handling bounded and unbounded unsafe sets in Control Lyapunov-Barrier function-based model predictive control of nonlinear processes

Control Lyapunov-Barrier function (CLBF) has been used to design controllers for nonlinear systems subject to input constraints to ensure closed-loop stability and process operational safety simultaneously. In this work, we developed Control Lyapunov-Barrier functions for two types of unsafe regions (i.e., bounded and unbounded sets) to solve the problem of stabilization of nonlinear systems with guaranteed process operational safety. Specifically, in the presence of a bounded unsafe region embedded within the closed-loop system stability region, the CLBF-MPC is developed by incorporating CLBF-based constraints and discontinuous control actions at potential stationary points (except the origin) to guarantee the convergence to the origin (i.e., closed-loop stability) and the avoidance of unsafe region (i.e., process operational safety). In the case of unbounded unsafe sets, closed-loop stability with safety is readily guaranteed under the CLBF-MPC since the origin is the unique stationary point in state-space. The application of the proposed CLBF-MPC method is demonstrated through a chemical process example with a bounded and an unbounded unsafe region, respectively.

2D Terminal Constrained Model Predictive Iterative Learning Control of Batch Processes With Time Delay

In this paper, a 2D terminal constrained model predictive iterative learning control method of batch processes with time delay is proposed to deal with time delay, input and output constraints, and disturbances in batch processes. Firstly, an iterative learning control law is designed for the given batch process; then the state error and output tracking error are introduced, and the original state-space model is converted to an equivalent 2D-FM model. In the meantime, an optimal performance index with terminal constraints is introduced, and an update law is designed to minimize the objective function under input and output constraints. The robust constraint set is adopted that the system state is converged to this set round the desired point. Then, based on the designed optimal performance index and Lyapunov stability theory, the MPC problem is transformed into a linear matrix inequality problem and a sufficient condition is given to ensure the robust asymptotically stability of the closed-loop system. Finally, the validity of the proposed method is proved by the simulation on a stirred tank.

A Discontinuous-Galerkin Finite-Element Method for Simulation of Packed Bed Chromatographic Processes

Abstract Packed bed chromatography is an important unit operation for purification of product molecules in biopharmaceutical processes. Packed bed chromatographic processes are modeled as advection-diffusion-reaction partial differential equations. The advection term strongly dominates the diffusion term. Therefore, specialized numerical methods must be used for efficient simulation of packed bed chromatographic processes. In this paper, we use a discontinuous-Galerkin method on finite-elements for spatial discretization and low storage explicit Runge-Kutta (LSERK) methods for numerical solution of the resulting system of differential equations. We study the numerical solution of deterministic and stochastic models of packed bed chromatographic processes. The stochastic model and its corresponding numerical solution constitute the first step toward systematic monitoring, fault detection, and optimal predictive control of chromatographic processes. It is also an essential ingredient in uncertainty quantification for efficient and robust design and operation of chromatographic processes.

Demonstration of non-linear model predictive control of post-combustion CO2 capture processes

Nonlinear model predictive control applications have been deployed on two large pilot plants for post combustion CO2 capture. The control objective is formulated in such a way that the CO2 capture ratio is controlled at a desired value, while the reboiler duty is formulated as an unreachable maximum constraint. With a correct tuning, it is demonstrated that the controllers automatically compensate for disturbances in flue gas rates and compositions to obtain the desired capture ratio while the reboiler duty is minimized. The applications are able to minimize the transient periods between two different capture rates with the use of minimum reboiler duty.

Handling sensor faults in economic model predictive control of batch processes

The problem of sensor fault detection and isolation (FDI) and fault‐tolerant economic model predictive control (FT‐EMPC) for batch processes is addressed. To this end, we first model batch processes using subspace‐based system identification techniques. The analytical redundancy within the identified model is subsequently exploited to detect, isolate, and handle the faulty measurements. The reconciled fault‐free measurements are then incorporated in an economic model predictive controller formulation. Simulation case studies involving the application of the proposed data‐driven FDI and FT‐EMPC algorithms to the energy intensive electric arc furnace process illustrate the improvement in economic performance under various fault scenarios. © 2018 American Institute of Chemical Engineers AIChE J, 65: 617–628, 2019

Adaptive Model Predictive Batch Process Monitoring and Control

The present work addresses the problem of loss of model validity in batch process control via online monitoring and adaptation based model predictive control. To this end, a state space subspace-based model identification method suitable for batch processes is utilized and then a model predictive controller is designed. To monitor model performance, a model validity index is developed for batch processes. In the event of poor prediction (observed via breaching of a threshold by the model validity index), reidentification is triggered to identify a new model and thus adapt the controller. In order to capture the most recent process dynamics, the identification is appropriately designed to emphasize more the recent process data. The efficacy of the proposed method is demonstrated using an electric arc furnace as a simulation test bed.

Detecting and Handling Cyber-Attacks in Model Predictive Control of Chemical Processes

Since industrial control systems are usually integrated with numerous physical devices, the security of control systems plays an important role in safe operation of industrial chemical processes. However, due to the use of a large number of control actuators and measurement sensors and the increasing use of wireless communication, control systems are becoming increasingly vulnerable to cyber-attacks, which may spread rapidly and may cause severe industrial incidents. To mitigate the impact of cyber-attacks in chemical processes, this work integrates a neural network (NN)-based detection method and a Lyapunov-based model predictive controller for a class of nonlinear systems. A chemical process example is used to illustrate the application of the proposed NN-based detection and LMPC methods to handle cyber-attacks.

Partitioning for distributed model predictive control of nonlinear processes

A distributed model predictive control (DMPC) strategy brings interesting features of topology, flexibility and maintenance to large-scale nonlinear systems. This work presents contributions in the study of distributed controllers for nonlinear and large-scale systems. Two types of distributed predictive control based on model (DMPC) are proposed: non-cooperative locally linearized DMPC and cooperative locally linearized DMPC. The decomposition is performed based on a local linearized version of the process model by using local matrices representing interactions between controlled outputs, states and inputs. The proposed strategy was successfully evaluated and compared to the centralized control strategy.