Output feedback control of dissipative PDE systems with partial sensor information based on adaptive model reduction

We address the problem of control of spatially distributed processes in the presence of measurement constraints. Specifically, we assume the availability of sensors that measure part of the state spatial profile. The measurements are utilized for the derivation and on‐demand update of reduced order models (ROM) based on an extension of the adaptive proper orthogonal decomposition (APOD) method using a snapshot reconstruction technique. The proposed Gappy‐APOD methodology constructs locally accurate low‐dimensional ROM thus resulting in a computationally efficient alternative to using a large‐dimensional ROM with global validity. Based on the low‐dimensional ROM and continuous measurements available from point sensors a Lyapunov‐based static output feedback controller is subsequently designed. The proposed controller design method is illustrated on an unstable process modeled by the Kuramoto‐Sivashinsky equation, when the designed controller successfully stabilizes the process even in the presence of model uncertainty. © 2012 American Institute of Chemical Engineers AIChE J, 59: 747–760, 2013     

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     

Feedback control of dissipative PDE systems using adaptive model reduction

The problem of feedback control of spatially distributed processes described by highly dissipative partial differential equations (PDEs) is considered. Typically, this problem is addressed through model reduction, where finite dimensional approximations to the original infinite dimensional PDE system are derived and used for controller design. The key step in this approach is the computation of basis functions that are subsequently utilized to obtain finite dimensional ordinary differential equation (ODE) models using the method of weighted residuals. A common approach to this task is the Karhunen‐Loève expansion combined with the method of snapshots. To circumvent the issue of a priori availability of a sufficiently large ensemble of PDE solution data, the focus is on the recursive computation of eigenfunctions as additional data from the process becomes available. Initially, an ensemble of eigenfunctions is constructed based on a relatively small number of snapshots, and the covariance matrix is computed. The dominant eigenspace of this matrix is then utilized to compute the empirical eigenfunctions required for model reduction. This dominant eigenspace is recomputed with the addition of each snapshot with possible increase or decrease in its dimensionality; due to its small dimensionality the computational burden is relatively small. The proposed approach is applied to representative examples of dissipative PDEs, with both linear and nonlinear spatial differential operators, to demonstrate its effectiveness of the proposed methodology. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

On the attainable region for process networks

In this work the attainable region (AR) concept for process networks with outlet flow rate specifications is introduced for the first time. For process unit models to which the infinite dimensional State‐space conceptual framework is applicable, it is shown that identification of AR boundary membership is equivalent to feasibility assessment of an infinite linear program (ILP). A number of important AR properties are then theoretically established, including AR convexity, and representation of the AR in a concentration state space of reduced dimension. Finite dimensional approximations of the aforementioned ILP are then employed in creating increasingly accurate approximations of the AR. A case study for the vapor‐liquid equilibrium‐based separation of a ternary azeotropic mixture is used to illustrate the proposed method. The quantified two‐ and four‐Dimensional ARs indicate that acetone mole fractions above 0.79 (acetone/methanol azeotrope) are attainable for the considered outlet flow rate ratios. © 2013 American Institute of Chemical Engineers AIChE J, 60: 193–212, 2014     

Delay‐range‐dependent guaranteed cost control for batch processes with state delay

A guaranteed cost control scheme is proposed for batch processes described by a two‐dimensional (2‐D) system with uncertainties and interval time‐varying delay. First, a 2‐D controller, which includes a robust feedback control to ensure performances over time and an iterative learning control to improve the tracking performance from cycle to cycle, is formulated. The guaranteed cost law concept of the proposed 2‐D controller is then introduced. Subsequently, by introducing the Lyapunov–Krasovskii function and adding a differential inequality to the Lyapunov function for the 2‐D system, sufficient conditions for the existence of the robust guaranteed cost controller are derived in terms of matrix inequalities. A design procedure for the controller is also presented. Furthermore, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the optimal guaranteed cost controller that minimizes the upper bound of the closed‐loop system cost. The proposed control law can stabilize the closed‐loop system as well as guarantee H_∞ performance level and a cost function with upper bounds for all admissible uncertainties. The results can be easily extended to the constant delay case. Finally, an illustrative example is given to demonstrate the effectiveness and advantages of the proposed 2‐D design approach. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2033–2045, 2013     

Interaction analysis and geometric interconnection decoupling for networks of process systems

The effects of interactions between nonlinear subprocesses on the stabilizability of plantwide systems via the concept of dissipative systems are studied. Conditions for which controlled variables of each interconnected subprocess can be driven to and maintained at their desired values are established through the application of interconnection decoupling techniques. The resulting decoupling feedback law encodes the interaction effects between subprocesses and determines the required information structure for achieving desired control performance using distributed control laws. The proposed constructive approach leads to new criteria for the selection of manipulated and controlled variables that guarantee plantwide stability. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2795–2809, 2013     

Estimation in Functional Lagged Regression

The paper introduces a functional time series (lagged) regression model. The impulse‐response coefficients in such a model are operators acting on a separable Hilbert space, which is the function space L² in applications. A spectral approach to the estimation of these coefficients is proposed and asymptotically justified under a general nonparametric condition on the temporal dependence of the input series. Since the data are infinite‐dimensional, the estimation involves a spectral‐domain dimension‐reduction technique. Consistency of the estimators is established under general data‐dependent assumptions on the rate of the dimension‐reduction parameter. Their finite‐sample performance is evaluated by a simulation study that compares two ad hoc approaches to dimension reduction with an alternative, asymptotically justified method.     

Lyapunov‐based MPC with robust moving horizon estimation and its triggered implementation

In this work, we consider moving horizon state estimation (MHE)‐based model predictive control (MPC) of nonlinear systems. Specifically, we consider the Lyapunov‐based MPC (LMPC) developed in (Mhaskar et al., IEEE Trans Autom Control. 2005;50:1670–1680; Syst Control Lett. 2006;55:650–659) and the robust MHE (RMHE) developed in (Liu J, Chem Eng Sci. 2013;93:376–386). First, we focus on the case that the RMHE and the LMPC are evaluated every sampling time. An estimate of the stability region of the output control system is first established; and then sufficient conditions under which the closed‐loop system is guaranteed to be stable are derived. Subsequently, we propose a triggered implementation strategy for the RMHE‐based LMPC to reduce its computational load. The triggering condition is designed based on measurements of the output and its time derivatives. To ensure the closed‐loop stability, the formulations of the RMHE and the LMPC are also modified accordingly to account for the potential open‐loop operation. A chemical process is used to illustrate the proposed approaches. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4273–4286, 2013     

Global optimization of reactive distillation networks using IDEAS

In this work, we present a methodology for the global optimization of reactive distillation (RD) networks, through the Infinite DimEnsionAl State-space (IDEAS) approach. Within the IDEAS framework, network synthesis is formulated as an infinite dimensional linear optimization problem. The IDEAS conceptual framework is realized through solution of a series of finite dimensional linear programs whose optimum values converge to the infinite program’s infimum. The proposed optimal design methodology is demonstrated on a case study involving reactive distillation-based synthesis of methyl tert-butyl ether (MTBE) from isobutene and methanol.     

Two–Dimensional Stability of the “Pole” Solutions of the Sivashinsky Equation

The two–dimensional stability of the exact solution of the Sivashinsky equation governing the evolution of a curved flame surface in the hydrodynamic approximation is studied. It is shown that the one–dimensional pole solution of this equation governing a local minimum of the surface is stable with respect to small two–dimensional perturbations. The problem is solved under the assumption that the perturbations are small at a distance from the local minimum. Stable one–dimensional solutions may be used to verify numerical simulation of the surface of a hydrodynamically unstable flame and also to construct two–dimensional solutions of the Sivashinsky equation.     

Minimal perfusion flow for osteogenic growth of mesenchymal stem cells on lattice scaffolds

A modeling approach to identify sets of culture conditions to promote homogeneous growth of cells in perfusion bioreactors equipped with regular shape scaffolds is proposed. We identify cases in which dynamic culturing is necessary using a zero‐dimensional mass transport and reaction model. Then, based on the three‐dimensional (3‐D) rendering of the flow field inside the bioreactor, we identify regions where cellular growth may become critical; finally, using a 1‐D mass transport and reaction model, we calculate the minimal perfusion flow necessary to maintain the cellular growth rate above a target threshold. The developed approach is used to analyze culturing conditions inside an indirect perfusion bioreactor equipped with a lattice scaffold. Regions where the perfusion flow is inadequate to foster cellular growth at the desired rate are identified. The perfusion flow required to maintain the target growth rate inside the bioreactor is calculated. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3131–3144, 2013     

Impacts of PEGylation on the gene and oligonucleotide delivery system

Poly(ethylene glycol) (PEG) is the most widely used polymer and also the gold standard in the field of drug delivery. Therapeutic oligonucleotides, for example, are modified with PEG at the terminus to increases nuclease resistance and the circulating half‐lives. The surface of nanoparticle such as micelle and liposome has been also modified with PEG. At present, one PEGylated therapeutic oligonucleotide has been approved for the market and several more PEGylated products including oligonucleotide and liposome are being tested in clinical settings. This review summarizes the methods and effects of PEGylation on gene delivery. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40293.     

Enhancement of fibroblastic proliferation from photoreactive starch with immobilized epidermal growth factor

Carboxymethyl starch was modified by the incorporation of an azidophenyl group to prepare photoreactive starch, and characterized by Fourier transform infrared reflectance (FT‐IR), proton nuclear magnetic resonance (¹H‐NMR), and ultraviolet (UV) spectroscopy. Photo‐irradiation immobilized the Az‐starch on a polystyrene plate and it was stably retained on the surface. The protein containing immobilized Az‐starch was also immobilized on a stripe micropatterned plate. UV irradiation time and Az‐starch concentration were used to alter the physical properties of Az‐starch and consequently control the rate of epidermal growth factor (EGF) release. The Az‐starch that released growth factor was not cytotoxic to 3T3‐L1 fibroblast cells, and the immobilized EGF maintained its activity and induced cellular proliferation in vitro. These results suggest that Az‐starch could be useful as a clinical synthetic material for medical applications. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

TAT‐modified mixed micelles as biodegradable targeting and delivering system for cancer therapeutics

A mixed micellar system of novel function was designed and synthesized by co‐assembling TAT (cell penetrating peptide)‐modified poly (ethylene glycol)‐poly(l ‐lactide) (PEG‐PLA) copolymer with the drug‐conjugated poly(ethylene glycol)‐b‐poly(l‐ lactide‐co‐2‐methyl‐2‐carboxyl‐propylene carbonate) (mPEG‐b‐P(LA‐co‐MCC)) copolymer. UV‐Vis, Matrix‐assisted laser desorption/ionization time‐of‐flight, and XPS were used to ensure the successful modification of the copolymers with TAT and anti‐tumor drugs. The size of spherical nanomicelles increased from 50 to 60 nm as of empty polymeric micelles to 100–150 nm as of drug‐loaded ones, determined by dynamic light scattering and TEM. Daunorubicin was selected as model drug for in vitro evaluations on different cell lines. 3‐(4,5‐Dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide assay clearly indicated an improved cell growth inhibition of the TAT‐modified mixed micelles. While green fluorescent protein was used as a marker for the mixed micelle, small amount of DMSO was necessary to enhance the accumulation of the mixed micelles in cell lines Caski. Mediated by TAT, mixed micelles containing Apoptin (a tumor‐specific apoptosis drug) showed higher level of tumor cell internalization and growth inhibition than that of mixed micelles without TAT modification. © 2013 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 130: 4598–4607, 2013     

Optimal operation of process plants under partial shutdown conditions

A systematic strategy for optimal plant operation during partial shutdowns is proposed. We consider the situation where one or more process units are shut down due to failure or maintenance but where the remaining units are able to continue operation to some degree. The goal of the strategy is to manipulate the plant degrees‐of‐freedom—during and after the shutdown—such that production is restored in a cost‐optimal fashion while meeting safety and operational constraints. Optimal control trajectories are obtained through the solution of a dynamic optimization problem. A novel multitiered optimization approach allows the prioritization of multiple competing objectives and the specification of trade‐offs between them. Uncertainty in the downtime estimate, a crucial parameter in shutdown optimization, is addressed through reoptimization. We employ a transient predictive control algorithm for implementing the computed control policy under feedback. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4151–4168, 2013