Research

20 pages, 3379 KiB

Open AccessFeature PaperArticle

Recurrent Neural Network-Based Model Predictive Control for Continuous Pharmaceutical Manufacturing

by Wee Chin Wong, Ewan Chee, Jiali Li and Xiaonan Wang

Mathematics 2018, 6(11), 242; https://doi.org/10.3390/math6110242 - 07 Nov 2018

Cited by 103 | Viewed by 9091

The pharmaceutical industry has witnessed exponential growth in transforming operations towards continuous manufacturing to increase profitability, reduce waste and extend product ranges. Model predictive control (MPC) can be applied to enable this vision by providing superior regulation of critical quality attributes (CQAs). For [...] Read more.

The pharmaceutical industry has witnessed exponential growth in transforming operations towards continuous manufacturing to increase profitability, reduce waste and extend product ranges. Model predictive control (MPC) can be applied to enable this vision by providing superior regulation of critical quality attributes (CQAs). For MPC, obtaining a workable system model is of fundamental importance, especially if complex process dynamics and reaction kinetics are present. Whilst physics-based models are desirable, obtaining models that are effective and fit-for-purpose may not always be practical, and industries have often relied on data-driven approaches for system identification instead. In this work, we demonstrate the applicability of recurrent neural networks (RNNs) in MPC applications in continuous pharmaceutical manufacturing. RNNs were shown to be especially well-suited for modelling dynamical systems due to their mathematical structure, and their use in system identification has enabled satisfactory closed-loop performance for MPC of a complex reaction in a single continuous-stirred tank reactor (CSTR) for pharmaceutical manufacturing. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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44 pages, 950 KiB

Open AccessFeature PaperArticle

A Nonlinear Systems Framework for Cyberattack Prevention for Chemical Process Control Systems ^†

by Helen Durand

Mathematics 2018, 6(9), 169; https://doi.org/10.3390/math6090169 - 14 Sep 2018

Cited by 26 | Viewed by 3662

Abstract

Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an [...] Read more.

Recent cyberattacks against industrial control systems highlight the criticality of preventing future attacks from disrupting plants economically or, more critically, from impacting plant safety. This work develops a nonlinear systems framework for understanding cyberattack-resilience of process and control designs and indicates through an analysis of three control designs how control laws can be inspected for this property. A chemical process example illustrates that control approaches intended for cyberattack prevention which seem intuitive are not cyberattack-resilient unless they meet the requirements of a nonlinear systems description of this property. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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19 pages, 583 KiB

Open AccessArticle

Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

by Harwinder Singh Sidhu, Prashanth Siddhamshetty and Joseph S. Kwon

Mathematics 2018, 6(8), 132; https://doi.org/10.3390/math6080132 - 01 Aug 2018

Cited by 34 | Viewed by 5205

Abstract

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside [...] Read more.

Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young’s modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the “curse-of-dimensionality” associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young’s modulus of the rock formation. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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20 pages, 16699 KiB

Open AccessFeature PaperArticle

Forecast-Triggered Model Predictive Control of Constrained Nonlinear Processes with Control Actuator Faults

by Da Xue and Nael H. El-Farra

Mathematics 2018, 6(6), 104; https://doi.org/10.3390/math6060104 - 19 Jun 2018

Cited by 9 | Viewed by 2818

Abstract

This paper addresses the problem of fault-tolerant stabilization of nonlinear processes subject to input constraints, control actuator faults and limited sensor–controller communication. A fault-tolerant Lyapunov-based model predictive control (MPC) formulation that enforces the fault-tolerant stabilization objective with reduced sensor–controller communication needs is developed. [...] Read more.

This paper addresses the problem of fault-tolerant stabilization of nonlinear processes subject to input constraints, control actuator faults and limited sensor–controller communication. A fault-tolerant Lyapunov-based model predictive control (MPC) formulation that enforces the fault-tolerant stabilization objective with reduced sensor–controller communication needs is developed. In the proposed formulation, the control action is obtained through the online solution of a finite-horizon optimal control problem based on an uncertain model of the plant. The optimization problem is solved in a receding horizon fashion subject to appropriate Lyapunov-based stability constraints which are designed to ensure that the desired stability and performance properties of the closed-loop system are met in the presence of faults. The state-space region where fault-tolerant stabilization is guaranteed is explicitly characterized in terms of the fault magnitude, the size of the plant-model mismatch and the choice of controller design parameters. To achieve the control objective with minimal sensor–controller communication, a forecast-triggered communication strategy is developed to determine when sensor–controller communication can be suspended and when it should be restored. In this strategy, transmission of the sensor measurement at a given sampling time over the sensor–controller communication channel to update the model state in the predictive controller is triggered only when the Lyapunov function or its time-derivative are forecasted to breach certain thresholds over the next sampling interval. The communication-triggering thresholds are derived from a Lyapunov stability analysis and are explicitly parameterized in terms of the fault size and a suitable fault accommodation parameter. Based on this characterization, fault accommodation strategies that guarantee closed-loop stability while simultaneously optimizing control and communication system resources are devised. Finally, a simulation case study involving a chemical process example is presented to illustrate the implementation and evaluate the efficacy of the developed fault-tolerant MPC formulation. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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17 pages, 1009 KiB

Open AccessArticle

Model Predictive Control of Mineral Column Flotation Process

by Yahui Tian, Xiaoli Luan, Fei Liu and Stevan Dubljevic

Mathematics 2018, 6(6), 100; https://doi.org/10.3390/math6060100 - 13 Jun 2018

Cited by 8 | Viewed by 3876

Abstract

Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model [...] Read more.

Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model predictive control design for a mineral column flotation process modeled by a set of nonlinear coupled heterodirectional hyperbolic partial differential equations (PDEs) and ordinary differential equations (ODEs), which accounts for the interconnection of well-stirred regions represented by continuous stirred tank reactors (CSTRs) and transport systems given by heterodirectional hyperbolic PDEs, with these two regions combined through the PDEs’ boundaries. The model predictive control considers both optimality of the process operations and naturally present input and state/output constraints. For the discrete controller design, spatially varying steady-state profiles are obtained by linearizing the coupled ODE–PDE model, and then the discrete system is obtained by using the Cayley–Tustin time discretization transformation without any spatial discretization and/or without model reduction. The model predictive controller is designed by solving an optimization problem with input and state/output constraints as well as input disturbance to minimize the objective function, which leads to an online-solvable finite constrained quadratic regulator problem. Finally, the controller performance to keep the output at the steady state within the constraint range is demonstrated by simulation studies, and it is concluded that the optimal control scheme presented in this work makes this flotation process more efficient. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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20 pages, 541 KiB

Open AccessArticle

Enhancing Strong Neighbor-Based Optimization for Distributed Model Predictive Control Systems

by Shan Gao, Yi Zheng and Shaoyuan Li

Mathematics 2018, 6(5), 86; https://doi.org/10.3390/math6050086 - 22 May 2018

Cited by 10 | Viewed by 2883

Abstract

This paper considers a class of large-scale systems which is composed of many interacting subsystems, and each of them is controlled by an individual controller. For this type of system, to improve the optimization performance of the entire closed-loop system in a distributed [...] Read more.

This paper considers a class of large-scale systems which is composed of many interacting subsystems, and each of them is controlled by an individual controller. For this type of system, to improve the optimization performance of the entire closed-loop system in a distributed framework without the entire system’s information or too-complicated network information, connectivity is always an important topic. To achieve this purpose, a distributed model predictive control (DMPC) design method is proposed in this paper, where each local model predictive control (MPC) considers the optimization performance of its strong coupling subsystems and communicates with them. A method to determine the strength of the coupling relationship based on the closed-loop system’s performance and subsystem network connectivity is proposed for the selection of each subsystem’s neighbors. Finally, through integrating the steady-state calculation, the designed DMPC is able to guarantee the recursive feasibility and asymptotic stability of the closed-loop system in the cases of both tracking set point and stabilizing system to zeroes. Simulation results show the efficiency of the proposed DMPC. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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19 pages, 1361 KiB

Open AccessArticle

Safeness Index-Based Economic Model Predictive Control of Stochastic Nonlinear Systems

by Zhe Wu, Helen Durand and Panagiotis D. Christofides

Mathematics 2018, 6(5), 69; https://doi.org/10.3390/math6050069 - 03 May 2018

Cited by 9 | Viewed by 3037

Abstract

Process operational safety plays an important role in designing control systems for chemical processes. Motivated by this, in this work, we develop a process Safeness Index-based economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. A [...] Read more.

Process operational safety plays an important role in designing control systems for chemical processes. Motivated by this, in this work, we develop a process Safeness Index-based economic model predictive control system for a broad class of stochastic nonlinear systems with input constraints. A stochastic Lyapunov-based controller is first utilized to characterize a region of the state-space surrounding the origin, starting from which the origin is rendered asymptotically stable in probability. Using this stability region characterization and a process Safeness Index function that characterizes the region in state-space in which it is safe to operate the process, an economic model predictive control system is then developed using Lyapunov-based constraints to ensure economic optimality, as well as process operational safety and closed-loop stability in probability. A chemical process example is used to demonstrate the applicability and effectiveness of the proposed approach. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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19 pages, 962 KiB

Open AccessFeature PaperArticle

Economic Model Predictive Control with Zone Tracking

by Su Liu and Jinfeng Liu

Mathematics 2018, 6(5), 65; https://doi.org/10.3390/math6050065 - 25 Apr 2018

Cited by 14 | Viewed by 3245

Abstract

In this work, we propose a framework for economic model predictive control (EMPC) with zone tracking. A zone tracking stage cost is incorporated into the existing EMPC framework to form a multi-objective optimization problem. We provide sufficient conditions for asymptotic stability of the [...] Read more.

In this work, we propose a framework for economic model predictive control (EMPC) with zone tracking. A zone tracking stage cost is incorporated into the existing EMPC framework to form a multi-objective optimization problem. We provide sufficient conditions for asymptotic stability of the optimal steady state and characterize the exact penalty for the zone tracking cost which prioritizes zone tracking objective over economic objective. Moreover, an algorithm to modify the target zone based on the economic performance and reachability of the optimal steady state is proposed. The modified target zone effectively decouples the dynamic zone tracking and economic objectives and simplifies parameter tuning. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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21 pages, 6792 KiB

Open AccessFeature PaperArticle

A Novel Distributed Economic Model Predictive Control Approach for Building Air-Conditioning Systems in Microgrids

by Xinan Zhang, Ruigang Wang and Jie Bao

Mathematics 2018, 6(4), 60; https://doi.org/10.3390/math6040060 - 17 Apr 2018

Cited by 5 | Viewed by 3786

Abstract

With the penetration of grid-connected renewable energy generation, microgrids are facing stability and power quality problems caused by renewable intermittency. To alleviate such problems, demand side management (DSM) of responsive loads, such as building air-conditioning system (BACS), has been proposed and studied. In [...] Read more.

With the penetration of grid-connected renewable energy generation, microgrids are facing stability and power quality problems caused by renewable intermittency. To alleviate such problems, demand side management (DSM) of responsive loads, such as building air-conditioning system (BACS), has been proposed and studied. In recent years, numerous control approaches have been published for proper management of single BACS. The majority of these approaches focus on either the control of BACS for attenuating power fluctuations in the grid or the operating cost minimization on behalf of the residents. These two control objectives are paramount for BACS control in microgrids and can be conflicting. As such, they should be considered together in control design. As individual buildings may have different owners/residents, it is natural to control different BACSs in an autonomous and self-interested manner to minimize the operational costs for the owners/residents. Unfortunately, such “selfish” operation can result in abrupt and large power fluctuations at the point of common coupling (PCC) of the microgrid due to lack of coordination. Consequently, the original objective of mitigating power fluctuations generated by renewable intermittency cannot be achieved. To minimize the operating costs of individual BACSs and simultaneously ensure desirable overall power flow at PCC, this paper proposes a novel distributed control framework based on the dissipativity theory. The proposed method achieves the objective of renewable intermittency mitigation through proper coordination of distributed BACS controllers and is scalable and computationally efficient. Simulation studies are carried out to illustrate the efficacy of the proposed control framework. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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17 pages, 3145 KiB

Open AccessFeature PaperArticle

Data Driven Economic Model Predictive Control

by Masoud Kheradmandi and Prashant Mhaskar

Mathematics 2018, 6(4), 51; https://doi.org/10.3390/math6040051 - 02 Apr 2018

Cited by 18 | Viewed by 6106

Abstract

This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven [...] Read more.

This manuscript addresses the problem of data driven model based economic model predictive control (MPC) design. To this end, first, a data-driven Lyapunov-based MPC is designed, and shown to be capable of stabilizing a system at an unstable equilibrium point. The data driven Lyapunov-based MPC utilizes a linear time invariant (LTI) model cognizant of the fact that the training data, owing to the unstable nature of the equilibrium point, has to be obtained from closed-loop operation or experiments. Simulation results are first presented demonstrating closed-loop stability under the proposed data-driven Lyapunov-based MPC. The underlying data-driven model is then utilized as the basis to design an economic MPC. The economic improvements yielded by the proposed method are illustrated through simulations on a nonlinear chemical process system example. Full article

(This article belongs to the Special Issue New Directions on Model Predictive Control)

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