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     

Dynamics and control of aggregate thin film surface morphology for improved light trapping: Implementation on a large-lattice kinetic Monte Carlo model

This work demonstrates the use of feedback control, coupled with a suitable actuator design, in manufacturing thin films whose surface morphology is characterized by a desired visible light reflectance/transmittance level. The problem is particularly important in the context of thin film manufacturing for thin film solar cells where it is desirable to produce thin films with precisely tailored light trapping characteristics. Initially, a thin film deposition process involving atom adsorption and surface migration is considered and is modeled using a large-lattice (lattice size=40,000) kinetic Monte Carlo simulation. Subsequently, thin film surface morphology characteristics like roughness and slope are computed with respect to different characteristic length scales ranging from atomic to the ones corresponding to visible light wavelength and it is found that a patterned actuator design is needed to induce thin film surface roughness and slope at visible light wavelength spatial scales, which lead to desired thin film reflectance and transmittance levels. Then, an Edwards–Wilkinson-type equation (a second-order stochastic partial differential equation) is used to model the surface evolution at the visible light wavelength spatial scale and form the basis for the design of a feedback controller whose objective is to manipulate the deposition rate across the spatial domain of the process. The model parameters of the Edwards–Wilkinson equation are estimated from kinetic Monte Carlo simulations and their dependence on the deposition rate is used in the formulation of the predictive controller to predict the influence of the control action on the surface roughness and slope throughout the thin film growth process. Analytical solutions of the expected surface roughness and surface slope at the visible light wavelength spatial scale are obtained by solving the Edwards–Wilkinson equation and are used in the control action calculation. The cost function of the controller involves penalties on both surface roughness and slope from set-point values as well as constraints on the magnitude and rate of change of the control action. The controller is applied to the large-lattice kinetic Monte Carlo simulation. Simulation results demonstrate that the proposed controller and patterned actuator design successfully regulate aggregate surface roughness and slope to set-point values at the end of the deposition that yield desired levels of thin film reflectance and transmittance.     

Modeling and Control of a Titania Aerosol Reactor

We focus on modeling and control of an aerosol flow reactor used to produce titania powder. We initially present a detailed population balance model for the process which accounts for simultaneous nucleation, Brownian and shearinduced coagulation, and convective transport and describe the spatio-temporal evolution of the aerosol volume distribution. Then, under the assumption of lognormal aerosol volume distribution, the method of moments is employed for the derivation of a model that describes the evolution of the three leading moments of the volume distribution. The moment model, together with the fundamental model that describes the temperature in the reactor and concentrations of the gas-phase species, are subsequently used to synthesize a nonlinear output feedback controller which manipulates the temperature of the reactor wall to achieve an aerosol size distribution in the outlet of the reactor with desired geometric average particle diameter. The nonlinear controller is successfully implemented on the process model and is shown to deal effectively with external disturbances.     

Microstructure and transport properties of porous building materials

To successfully predict the performance of building materials exposed to a degradative environment, transport properties must be either measured or estimated. The development of relationships between microstructure and transport properties for these materials should allow accurate prediction of the latter and an increased understanding of how microstructure influences transport. Here, two microstructural characterization techniques, mercury intrusion porosimetry and scanning electron microscopy, are combined with computer modelling techniques to compute the vapor diffusivity and air permeability of three building materials commonly exposed in building facades, two types of brick and a natural sandstone. In general, the computed values compare favorably to those measured experimentally, thus demonstrating the capability of employing microstructural characterization to predict transport properties.

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Résumé Pour obtenir une prédiction fiable des performances des matériaux de construction exposés à un environnement agressif, leurs propriétés de transport doivent être soit mesurées soit estimées. Le développement de relations entre la microstructure et les propriétés de transport devrait permettre une prédiction exacte de ces dernières et une meilleure compréhension de l’influence de la microstructure sur le transfert. Dans cet article, deux techniques de caractérisation de la microstructure (porosimétrie au mercure et microscopie électronique à balayage) sont combinées avec des techniques de simulation par ordinateur pour calculer la diffusivité à la vapeur d’eau et la perméabilité à l’air de trois matériaux de construction traditionnellement utilisés en facades: deux types de brique et un grès naturel. En général, les valeurs calculées sont proches de celles mesurées expérimentalement. Ces résultats démontrent les possibilités des outils de caractérisation de la structure pour prédire les propriétés de transport.

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Editorial note: Mr. Daniel Quenard is a RILEM Senior Member and a member of TC 123-MME on the Use of Microstructural Models and Expert systems for Cemenitious Materials. He and Mr. K. Xu work at the CSTB (Centre Scientifique et Technique du Batiment), France, a RILEM Titular Member. Mr. Dale P. Bentz is a RILEM Senior Member and participates in the work of TC 159-ETC (Engineering of the Interfacial Transition Zone in Cementitious Composites). He and Mr. Nicos Martys work at the National Institute of Standards and Technology (NIST), USA, a RILEM Titular Member.     

Robust inverse optimal control laws for nonlinear systems

This work proposes a robust inverse optimal controller design for a class of nonlinear systems with bounded, time‐varying uncertain variables. The basic idea is that of re‐shaping the scalar nonlinear gain of an L_gV controller, based on Sontag's formula, so as to guarantee certain uncertainty attenuation properties in the closed‐loop system. The proposed gain re‐shaping is shown to yield a control law that enforces global boundedness of the closed‐loop trajectories, robust asymptotic output tracking with an arbitrary degree of attenuation of the effect of uncertainty on the output, and inverse optimality with respect to a meaningful cost that penalizes the tracking error and the control action. The performance of the control law is illustrated through a simulation example and compared with other controller designs. Copyright © 2003 John Wiley & Sons, Ltd.     

Capacitated Clustering Problems by Hybrid Simulated Annealing and Tabu Search

The capacitated clustering problem (CCP) is the problem in which a given set of weighted objects is to be partitioned into clusters so that the total weight of objects in each cluster is less than a given value (cluster ‘capacity’). The objective is to minimize the total scatter of objects from the ‘centre’ of the cluster to which they have been allocated. A simple constructive heuristic, a R-interchange generation mechanism, a hybrid simulated annealing (SA) and tabu search (TS) algorithm which has computationally desirable features using a new non-monotonic cooling schedule, are developed. A classification of the existing SA cooling schedules is presented. The effects on the final solution quality of the initial solutions, the cooling schedule parameters and the neighbourhood search strategies are investigated. Computational results on randomly generated problems with size ranging from 50 to 100 customers indicate that the hybrid SA/TS algorithm out-performs previous simulated annealing algorithms, a simple tabu search and local descent algorithms.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

Predictive control of switched nonlinear systems with scheduled mode transitions

In this work, a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times. The main idea is to design a Lyapunov-based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed-loop system. This is achieved as follows: For each constituent mode, a Lyapunov-based model predictive controller (MPC) is designed, and an analytic bounded controller, using the same Lyapunov function, is used to explicitly characterize a set of initial conditions for which the MPC, irrespective of the controller parameters, is guaranteed to be feasible, and hence stabilizing. Then, constraints are incorporated in the MPC design which, upon satisfaction, ensure that: 1) the state of the closed-loop system, at the time of the transition, resides in the stability region of the mode that the system is switched into, and 2) the Lyapunov function for each mode is nonincreasing wherever the mode is reactivated, thereby guaranteeing stability. The proposed control method is demonstrated through application to a chemical process example.