Distributed model predictive control-oriented network decomposition based on full dynamic response

This article addresses network decomposition for distributed model predictive control (DMPC), which includes two improvements. First, in the weighted input–output bipartite graph construction of a process network, a new measure called frequency affinity is proposed to characterize the input–output interaction considering the full dynamic response and structural information of a process. Then, in community detection, which is used to decompose the process network, the gap metric is added to quantify stability and the loss of control performance of each subsystem. Through the proposed decomposition, the obtained subsystems can be dynamically well-decoupled since both transient and steady-state responses are measured by the frequency affinity. As structural information is considered, the decomposition is consistent with the process physical topology. Furthermore, the utilization of gap metric can facilitate controller design for DMPC. Case studies on a reactor separator process and an air separation process demonstrate the effectiveness of the proposed decomposition method.     

Distributed lyapunov‐based model predictive control with neighbor‐to‐neighbor communication

This work considers distributed predictive control of large‐scale nonlinear systems with neighbor‐to‐neighbor communication. It fulfills the gap between the existing centralized Lyapunov‐based model predictive control (LMPC) and the cooperative distributed LMPC and provides a balanced solution in terms of implementation complexity and achievable performance. This work focuses on a class of nonlinear systems with subsystems interacting with each other via their states. For each subsystem, an LMPC is designed based on the subsystem model and the LMPC only communicates with its neighbors. At a sampling time, a subsystem LMPC optimizes its future control input trajectory assuming that the states of its upstream neighbors remain the same as (or close to) their predicted state trajectories obtained at the previous sampling time. Both noniterative and iterative implementation algorithms are considered. The performance of the proposed designs is illustrated via a chemical process example. © 2014 American Institute of Chemical Engineers AIChE J 60: 4124–4133, 2014     

Control‐relevant decomposition of process networks via optimization‐based hierarchical clustering

A systematic method is proposed for control‐relevant decomposition of complex process networks. Specifically, hierarchical clustering methods are adopted to identify constituent subnetworks such that the components of each subnetwork are strongly interacting while different subnetworks are loosely coupled. Optimal clustering is determined through the solution of integer optimization problems. The concept of relative degree is used to measure distance between subnetworks and compactness of subnetworks. The application of the proposed method is illustrated using an example process network. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3177–3188, 2016     

Low‐order optimal regulation of parabolic PDEs with time‐dependent domain

Observer and optimal boundary control design for the objective of output tracking of a linear distributed parameter system given by a two‐dimensional (2‐D) parabolic partial differential equation with time‐varying domain is realized in this work. The transformation of boundary actuation to distributed control setting allows to represent the system's model in a standard evolutionary form. By exploring dynamical model evolution and generating data, a set of time‐varying empirical eigenfunctions that capture the dominant dynamics of the distributed system is found. This basis is used in Galerkin's method to accurately represent the distributed system as a finite‐dimensional plant in terms of a linear time‐varying system. This reduced‐order model enables synthesis of a linear optimal output tracking controller, as well as design of a state observer. Finally, numerical results are prepared for the optimal output tracking of a 2‐D model of the temperature distribution in Czochralski crystal growth process which has nontrivial geometry. © 2014 American Institute of Chemical Engineers AIChE J, 61: 494–502, 2015     

Subsystem decomposition and configuration for distributed state estimation

Distributed state estimation plays a very important role in process control. Improper subsystem decomposition for distributed state estimation may increase the computational burdens, degrade the estimation performance, or even deteriorate the observability of the entire system. The subsystem decomposition problem for distributed state estimation of nonlinear systems is investigated. A systematic procedure for subsystem decomposition for distributed state estimation is proposed. Key steps in the procedure include observability test of the entire system, observable states identification for each output measurement, relative degree analysis and sensitivity analysis between measured outputs and states. Considerations with respect to time‐scale multiplicity and direct graph are discussed. A few examples are used to illustrate the applicability of the methods used in different steps. The effectiveness of the entire distributed state estimation configuration procedure is also demonstrated via an application to a chemical process example used in coal handling and preparation plants. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1995–2003, 2016     

Graph reduction of complex energy‐integrated networks: Process systems applications

We illustrate the application of a graph reduction method developed recently to analyze complex energy‐integrated process networks. The method uses information on the energy flow structure of the network and the orders of magnitude of the different energy flows to generate, automatically, information on the time scales where the process units evolve, canonical forms of the reduced models in each time scale, and controlled variables and potential manipulated inputs available in each time scale. Representative examples of reactor‐heat exchanger and distillation column networks are considered to illustrate the method and develop insights on effective control strategies for these processes. © 2014 American Institute of Chemical Engineers AIChE J, 60: 995–1012, 2014     

Real‐time economic model predictive control of nonlinear process systems

Closed‐loop stability of nonlinear systems under real‐time Lyapunov‐based economic model predictive control (LEMPC) with potentially unknown and time‐varying computational delay is considered. To address guaranteed closed‐loop stability (in the sense of boundedness of the closed‐loop state in a compact state‐space set), an implementation strategy is proposed which features a triggered evaluation of the LEMPC optimization problem to compute an input trajectory over a finite‐time prediction horizon in advance. At each sampling period, stability conditions must be satisfied for the precomputed LEMPC control action to be applied to the closed‐loop system. If the stability conditions are not satisfied, a backup explicit stabilizing controller is applied over the sampling period. Closed‐loop stability under the real‐time LEMPC strategy is analyzed and specific stability conditions are derived. The real‐time LEMPC scheme is applied to a chemical process network example to demonstrate closed‐loop stability and closed‐loop economic performance improvement over that achieved for operation at the economically optimal steady state. © 2014 American Institute of Chemical Engineers AIChE J, 61: 555–571, 2015     

Flow along and across glass‐fiber wicks: Testing of permeability models through experiments and simulations

A rigorous test of important theoretical models for permeability of glass‐fiber wicks, backed by numerical simulations, is conducted using a novel small‐scale experiment. The models include those for flow along and across aligned fibers and for flow through random fibers. The domains for numerical simulations were created by randomly distributed parallel fibers in a cube‐like unit‐cell using Geodict. Two separate simulations were considered: (1) Stokes‐flow solution using GeoDict, (2) Whitaker's closure‐formulation solution using COMSOL. The falling‐head parameter was adapted to measure the permeability along and across the fibers. Multiple measurements were conducted for each of the wicks to establish repeatability and estimate scatter. The permeabilities obtained through experiments matched with those from the theoretical and numerical methods. But numerical permeabilities for the longitudinal flow were exceptionally accurate. Also, the specialized models for longitudinal and transverse flows were more accurate than the random‐fiber models. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3491–3501, 2018     

A linear model predictive control algorithm for nonlinear large‐scale distributed parameter systems

This work provides a framework for linear model predictive control (MPC) of nonlinear distributed parameter systems (DPS), allowing the direct utilization of existing large‐scale simulators. The proposed scheme is adaptive and it is based on successive local linearizations of the nonlinear model of the system at hand around the current state and on the use of the resulting local linear models for MPC. At every timestep, not only the future control moves are updated but also the model of the system itself. A model reduction technique is integrated within this methodology to reduce the computational cost of this procedure. It follows the equation‐free approach (see Kevrekidis et al., Commun Math Sci. 2003;1:715–762; Theodoropoulos et al., Proc Natl Acad Sci USA. 2000;97:9840‐9843), according to which the equations of the model (and consequently of the simulator) need not be given explicitly to the controller. The latter forms a “wrapper” around an existing simulator using it in an input/output fashion. This algorithm is designed for dissipative DPS, dissipativity being a prerequisite for model reduction. The equation‐free approach renders the proposed algorithm appropriate for multiscale systems and enables it to handle large‐scale systems. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Economic model predictive control of nonlinear time‐delay systems: Closed‐loop stability and delay compensation

Closed‐loop stability of nonlinear time‐delay systems under Lyapunov‐based economic model predictive control (LEMPC) is considered. LEMPC is initially formulated with an ordinary differential equation model and is designed on the basis of an explicit stabilizing control law. To address closed‐loop stability under LEMPC, first, we consider the stability properties of the sampled‐data system resulting from the nonlinear continuous‐time delay system with state and input delay under a sample‐and‐hold implementation of the explicit controller. The steady‐state of this sampled‐data closed‐loop system is shown to be practically stable. Second, conditions such that closed‐loop stability, in the sense of boundedness of the closed‐loop state, under LEMPC are derived. A chemical process example is used to demonstrate that indeed closed‐loop stability is maintained under LEMPC for sufficiently small time‐delays. To cope with performance degradation owing to the effect of input delay, a predictor feedback LEMPC methodology is also proposed. The predictor feedback LEMPC design employs a predictor to compute a prediction of the state after the input delay period and an LEMPC scheme that is formulated with a differential difference equation (DDE) model, which describes the time‐delay system, initialized with the predicted state. The predictor feedback LEMPC is also applied to the chemical process example and yields improved closed‐loop stability and economic performance properties. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4152–4165, 2015     

Liquid‐to‐solid ratio control as an advanced process control solution for continuous twin‐screw wet granulation

Assuring compliance of intermediate and final quality attributes in a continuous pharmaceutical manufacturing campaign is of utmost importance. Application of corrective actions might be required in real‐time. This work exemplifies the steps needed to identify a linear pulse transfer function for the dynamic behavior of the granule liquid‐to‐solid ratio (%w/w) at the end of the granulation unit of a commercial ConsiGma^TM‐25 production line. Near‐infrared spectroscopy was used to monitor the granule composition in‐line. The outcome for both the tracking and regulator problem using either conventional or model predictive control was implemented and evaluated. Dynamic setpoints were correctly followed and an RMSE of 0.25%w/w with respect to the setpoint was obtained when inducing artificial disturbances. Important practical challenges were also tackled. Examples are fouling, computational limitations, and the limited flexibility of the automation software. Applying the proposed advanced process control solution offers an answer to upstream material flow rate deviations. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2500–2514, 2018     

Input–output pairing accounting for both structure and strength in coupling

Input–output pairing is an important problem in control system design and is often performed using the relative gain array (RGA) based approaches. While RGA‐based approaches have been very successful in many applications, they have some well‐known limitations. For example, they may give results which are not consistent with the physical topology since only the strength of interaction between inputs and outputs is taken into account in the RGA. In this work, we propose a new measure for input–output pairing that explores both strength and structural information in input–output coupling. Specifically, we take advantage of the tool of relative degree to measure the physical closeness of input–output pairs and to explore the strength of interaction progressively with respect to the relative degree. We call the proposed measure relative sensitivity array (RSA) between inputs and outputs. Detailed analysis is performed to reveal the relationship between the gain matrix used in the RGA and the sensitivity matrix in the RSA from a mathematical point of view. Since the RSA is an analog of the RGA, many existing pairing guidelines developed for the RGA can be used in the proposed RSA‐based pairing. The proposed RSA‐based approach is applied to two examples. The results show that pairs formed by the proposed approach are consistent with the physical topologies of the processes. Also, the results show that the proposed approach can handle larger systems that cannot be effectively handled by RGA‐based approaches. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1226–1235, 2017     

Thermomechanical and electroactive behavior of a thermosetting styrene‐based carbon black shape‐memory composite

A thermosetting styrene‐based shape memory polymer (SMP) filled with nanoscale (30 nm) carbon black are prepared to reinforce the thermomechanical performances and realize the high‐efficient electronic actuation at macro scale due to the carbon–carbon network morphology at nano/micro scale. The elastic modulus of this thermosetting SMP composite is significant strengthened and can maintain at 1–2.5 GPa at around the room temperature, which is suitable for used as a structural material. The electronic resistivity decreases sharply at a quite low percolation threshold range (2–5%), and maintains at a relatively low and stable level of electronic resistivity. Furthermore, the electronic resistivity also exhibits relative stability in terms of the resistivity–temperature–time relationship and the evolution of resistivity upon heating–cooling cycles. This shape memory styrene‐based composite is suitable to be used as an electroactive functional material in realistic engineering. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45978.     

Non‐Linear Predictive Control of a Three‐Phase Catalytic Reactor

In this work, the predictive control of a three‐phase catalytic reactor is considered. A predictive control algorithm, which has a non‐linear internal model represented by functional link networks, is proposed. This network structure has been shown to have a good non‐linear approximation capability, with the advantage that the estimation of its weight is a linear optimization problem. The results show the potential of the proposed procedure when it is applied to the 2‐methyl‐cyclohexanol production process, which is a non‐linear, distributed parameter and time‐varying process, typical of many important industrial systems.     

Boundary control synthesis for a lithium‐ion battery thermal regulation problem

The thermal regulation problem for a lithium ion (Li‐ion) battery with boundary control actuation is considered. The model of the transient temperature dynamics of the battery is given by a nonhomogeneous parabolic partial differential equation (PDE) on a two‐dimensional spatial domain which accounts for the time‐varying heat generation during the battery discharge cycle. The spatial domain is given as a disk with radial and angular coordinates which captures the nonradially symmetric heat‐transfer phenomena due to the application of the control input along a portion of the spatial domain boundary. The Li‐ion battery model is formulated within an appropriately defined infinite‐dimensional function space setting which is suitable for spectral controller synthesis. The key challenges in the output feedback model‐based controller design addressed in this work are: the dependence of the state on time‐varying system parameters, the restriction of the input along a portion of the battery domain boundary, the observer‐based optimal boundary control design where the separation principle is utilized to demonstrate the stability of the closed loop system, and the realization of the outback feedback control problem based on state measurement and interpolation of the temperature field. Numerical results for simulation case studies are presented. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3782–3796, 2013     

Macro‐economic multi‐objective input–output model for minimizing CO2 emissions: Application to the U.S. economy

Designing effective environmental policies for mitigating global warming is a very challenging task that requires detailed knowledge of the international channels through which goods are traded. This work presents a decision‐support tool that minimizes the environmental impact at a global macroeconomic scale by performing changes in the economic sectors of an economy. Our tool combines multi‐objective optimization, environmentally extended input–output tables and life cycle assessment within a unified framework. Our results on the U.S. economy to minimize CO₂ emissions identify sectors that should be regulated first to reach a given environmental target while maximizing the demand satisfaction. The impact of shale gas on our results is also studied. Our findings show that the application of process systems engineering tools at a macroeconomic level can provide valuable insight for public policy makers into problems of general interest. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3639–3656, 2016     

Subsystem decomposition of process networks for simultaneous distributed state estimation and control

An appropriate subsystem configuration is a prerequisite for a successful distributed control/state estimation design. Existing subsystem decomposition methods are not designed to handle simultaneous distributed estimation and control. In this article, we address the problem of subsystem decomposition of general nonlinear process networks for simultaneous distributed state estimation and distributed control based on community structure detection. A systematic procedure based on modularity is proposed. A fast folding algorithm that approximately maximizes the modularity is used in the proposed procedure to find candidate subsystem configurations. Two chemical process examples of different complexities are used to illustrate the effectiveness and applicability of the proposed approach. © 2018 American Institute of Chemical Engineers AIChE J, 65: 904–914, 2019     

Time‐series clustering via quasi U‐statistics

The problem of time‐series discrimination and classification is discussed. We propose a novel clustering algorithm based on a class of quasi U‐statistics and subgroup decomposition tests. The decomposition may be applied to any concave time‐series distance. The resulting test statistics are proven to be asymptotically normal for either i.i.d. or non‐identically distributed groups of time‐series under mild conditions. We illustrate its empirical performance on a simulation study and a real data analysis. The simulation setup includes stationary vs. stationary and stationary vs. non‐stationary cases. The performance of the proposed method is favourably compared with some of the most common clustering measures available.     

Prediction of the Profit Function for Industrial 2‐Keto‐L‐Gulonic Acid Cultivation

The profit function is the generic criterion to describe the cost effect of a batch process. To focus on the prediction of the profit function for 2‐keto‐L‐gulonic acid (2‐KGA) cultivation, which is potentially applicable for process monitoring and optimal scheduling, rolling learning‐prediction (RLP) based on a support vector machine (SVM) is applied. The RLP implies that the SVM training database is rolling updated as the batch of current interest proceeds, and the SVM learning is then repeated for the prediction. The database is further updated after termination of a batch. The updating procedures are investigated in detail. Pseudo‐online prediction is carried out using the data from industrial‐scale 2‐KGA cultivation under actual and hypothetical inoculation sequences. The results indicate that the average relative prediction error is less than 5 % in the later phase of fermentation in all inoculation sequences.