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.     

Simulation‐Based Design of Dual‐Mode Controller for Non‐Linear Processes

This paper presents a simulation‐based approach for designing a non‐linear override control scheme to improve the performance of a local linear controller. The higher‐level non‐linear controller monitors the dynamic state of the system and calculates an override control action whenever the system is predicted to move outside an acceptable operating regime under the local controller. The design of the non‐linear override controller is based on a cost‐to‐go function, which is constructed by using simulation or operation data. The cost‐to‐go function delineates the admissible region of state space within which the local controller is effective, thereby yielding a switching rule.     

Non‐Linear Long‐Term Tensile Creep of Poly(propylene)/Cycloolefin Copolymer Blends with Fibrous Structure

The tensile deformation of materials with Poisson's ratio smaller than 0.5 generates an additional free volume, which means that tensile creep under constant stress and temperature is a non‐iso‐free volume process. Fractional free volume rising proportionally to the creep strain accounts for a continuous shortening of retardation times. To account for this effect, “internal” time has been introduced which is related to a hypothetical pseudo iso‐free‐volume state. The shift factor along the time scale in the time‐strain superposition is not constant for an isothermal creep curve, but rises monotonically from point to point with the elapsed creep time. The reconstructed compliance dependencies obtained for various stresses approximately obey the time‐strain superposition thus forming a generalised creep curve. A routinely used empirical equation has been found suitable to describe the effects of time and stress on compliance of parent polymers and their blends. The previously proposed predictive format for the time‐dependent compliance of polymer blends has been found applicable also to poly(propylene) (PP)/cycloolefin copolymer (COC) blends with fibrous morphology. As COC shows a tendency to form fibres in a PP matrix, the mixing rule customarily used for fibre composites has been found more appropriate for injection moulded specimens than the equivalent box model for isotropic blends. The predicted compliance curve for a pseudo iso‐free‐volume state can be transformed into a “real” curve for a selected stress σ (in the interval up to the yield stress).

SEM microphotograph of the fractured surface (perpendicular to the injection direction) of the PP/COC blend 60/40.     

Dynamic Optimization and Non‐linear Model Predictive Control to Achieve Targeted Particle Morphologies

An event‐driven approach based on dynamic optimization and nonlinear model predictive control (NMPC) is investigated together with inline Raman spectroscopy for process monitoring and control. The benefits and challenges in polymerization and morphology monitoring are presented, and an overview of the used mechanistic models and the details of the dynamic optimization and NMPC approach to achieve the relevant process objectives are provided. Finally, the implementation of the approach is discussed, and results from experiments in lab and pilot‐plant reactors are presented.     

Practical Consequences of Non‐Linear Effects in Asymmetric Synthesis

The fundamental principles of non‐linear effects (NLE) are reviewed. Particular emphasis is placed on the case of asymmetric amplification, since it allows one to perform useful chemistry with a non‐enantiopure chiral auxiliary. A strong asymmetric depletion in a catalytic reaction may lead to an underestimation of the actual enantioselectivity of the fully resolved ligand. The study of NLE's is also proving useful as a mechanistic tool in asymmetric catalysis. Similar concepts may be extended to chiral reagents or to kinetic resolution. 1. What is a Non‐Linear Effect in Asymmetric Synthesis? 2. The Conditions for Observing a Non‐Linear Effect in Enantioselective Catalysis 3. Some Simple Models of NLE in Enantioselective Catalysis 4. Comparison of the Sizes of Asymmetric Amplifications 5. Rates and Non‐Linear Effects in Asymmetric Catalysis 6. Non‐Linear Effects Involving Chiral Reagents 7. Mechanistic Applications of Non‐Linear Effects 8. Synthetic Applications 9. Concluding Remarks     

Fault Detection of Non‐Linear Processes Using Kernel Independent Component Analysis

In this paper, a new non‐linear process monitoring method based on kernel independent component analysis (KICA) is developed. Its basic idea is to use KICA to extract some dominant independent components capturing non‐linearity from normal operating process data and to combine them with statistical process monitoring techniques. The proposed method is applied to the fault detection in the Tennessee Eastman process and is compared with PCA, modified ICA, and KPCA. The proposed approach effectively captures the non‐linear relationship in the process variables and showed superior fault detectability compared to other methods while attaining comparable false alarm rates.     

Study on the Effect of Interpolation Methods on the Rapidity of Convergence of the Rate Model of Multi‐Component Non‐Linear Liquid Chromatography

The convergence of the rate model of multi‐component non‐linear liquid chromatography is studied in detail. The key step of solving this model is to select the appropriate interpolation method, which determines the rapidity of convergence of the model. Two interpolation methods, the linear interpolation method and the three‐point Lagrange interpolation method, are compared in calculating the model. The results show that when the Lagrange interpolation is used the efficiency of calculation is elevated significantly. The calculation converges quickly at low finite element number.     

Application of Model Predictive Control to a Continuous Multiple‐Effect Crystallizer

An infinite horizon model predictive controller (IHMPC) with zone control is applied to a continuous five‐effect evaporative sodium chloride crystallizer. Firstly, a phenomenological dynamic model of the process is developed considering mass, energy, and moment balances coupled to crystallization kinetics. The developed model plays the role of the real system in order to study the proposed optimization/control strategy. The proposed approach is compared to a classical proportional integral derivative (PID) control system. The control strategy based on the prediction of the future state of the plant provides a faster response, a better stability to the process, and a reduction in energy consumption.     

A Bayesian Non‐Parametric Dynamic AR Model for Multiple Time Series Analysis

In this article, we propose a Bayesian non‐parametric model for the analysis of multiple time series. We consider an autoregressive structure of order p for each of the series and borrow strength across the series by considering a common error population that is also evolving in time. The error populations (distributions) are assumed non‐parametric whose law is based on a series of dependent Polya trees with zero median. This dependence is of order q and is achieved via a dependent beta process that links the branching probabilities of the trees. We study the prior properties and show how to obtain posterior inference. The model is tested under a simulation study and is illustrated with the analysis of the economic activity index of the 32 states of Mexico.     

A Quantitative Measure to Evaluate Competing Designs for Non‐linear Dynamic Process Identification

The strategy for the collection of information (i.e., data) for model development is called experimental design. Optimal design seeks to maximize the information content under constraints of time and sampling. In the system identification literature the dominant strategy has been the method of pseudo random sequences (PRS). However, this work demonstrates that statistical design of experiments (SDOE) can provide greater information content as quantitatively measured by the D‐optimal criterion.     

Neural Optimization of Fed‐batch Streptokinase Fermentation in a Non‐ideal Bioreactor

Microbial fermentations involving two or more kinds of competing cells and operating under realistic conditions are difficult to monitor, model and optimize by model‐based methods. They deviate from ideal behavior in two significant aspects: incomplete dispersion in the broth and the influx of disturbances. The approach here has been to optimize the filtered noise and dispersion on‐line through neural networks. This method has been applied to the fed‐batch production of streptokinase (SK). The culture has two kinds of cells — active (or productive) and inactive — and their growth is inhibited by the substrate and the primary metabolite (lactic acid). Using simulated data, the fermentation was optimized by a system of three neural networks, updated continually during successive time intervals. Such sequential optimization with dynamic filtering of inflow noise generated better cell growth and SK activity than static optimization and even an ideal fermentation.     

Grignard Reagents and Non‐Precious Metals: Cheap and Eco‐Friendly Reagents for Developing Industrial Cross‐Couplings. A Personal Account

Grignard reagents are probably the best organometallics to develop large‐scale eco‐friendly cross‐couplings compatible with the requirements of sustainable development. This account aims to highlight some reactions having an interesting industrial potential and gives the personal point of view of the authors on some attractive fields of research in this area.

     

On Measuring Closed‐Loop Non‐Linearity: A Topological Approach

The focal point of this paper is to develop a measure of closed‐loop non‐linearity. In this work, the Vinnicombe metric and the Quasi‐Linear Parameter Varying representation of a non‐linear system are exploited for this purpose. It is expected that the proposed measure can serve as a decision making tool for control engineers when considering whether a linear or a non‐linear control strategy should be employed to close the loop for a non‐linear system operating in a prescribed range.     

Transition from Batch to Continuous Operation in Bio‐Reactors: A Model Predictive Control Approach and Application

This work considers the problem of determining the transition of ethanol‐producing bio‐reactors from batch to continuous operation and subsequent control subject to constraints and performance considerations. To this end, a Lyapunov‐based non‐linear model predictive controller is utilized that stabilizes the bio‐reactor under continuous mode of operation. The key idea in the predictive controller is the formulation of appropriate stability constraints that allow an explicit characterization of the set of initial conditions from where feasibility of the optimization problem and hence closed‐loop stability is guaranteed. Additional constraints are incorporated in the predictive control design to expand on the set of initial conditions that can be stabilized by control designs that only require the value of the Lyapunov function to decay. Then, the explicit characterization of the set of stabilizable initial conditions is used in determining the appropriate time for which the reactor must be run in batch mode. Specifically, the predictive control approach is utilized in determining the appropriate batch length that achieves stabilizable values of the state variables at the end of the batch. Application of the proposed method to the ethanol production process using Zymomonas mobilis as the ethanol producing micro‐organism demonstrates the effectiveness of the proposed model predictive control strategy in stabilizing the bio‐reactor.     

Non‐dispersive absorption for CO2 capture: from the laboratory to industry

Research on capture and recovery of CO₂ has become a critical topic in the development of technological answers to the greenhouse effect. Conventional industrial processes do not fit into the philosophy of process intensification in which a radically new approach should lead to environmentally friendly methods with minimal use of natural resources and production of secondary waste. Conventional processes involve the use of large amounts of toxic organic solvents, such as diethylamine, and large equipment (e.g. absorption columns). Although CO₂ recovery began in industrial operation more than fifty years ago and, in spite of the clear potential for intensified processes demonstrated in the scientific literature, there is no real evidence that new processes for CO₂ recovery will achieve industrial implementation in the short term. In this perspective, the main limitations of membrane systems based on non‐dispersive absorption using porous membranes are outlined, in order to identify the main challenges that still have to be solved to achieve an industrially attractive process for CO₂ recovery. Copyright © 2011 Society of Chemical Industry     

A Modified Simplex Method for Solving 1‐Norm Minimization Problem in Model Predictive Control

Since the simplex method requires the polyhedron to be in the positive domain, the 1‐norm minimization problems are formulated by substantially increasing the size of the LP problems. This paper presents a simple modification that enables the simplex method to be directly applicable to a polyhedron, which extends into the negative domain. That is, instead of requiring the problem to change, the method is changed to fit the problem. The modification eliminates the need to increase the size of the problem and thus eliminates the associated computational effort. The proposed method skips iterations and Phase 1 of the simplex method. Its computational advantage is verified in two examples.     

Testing Non‐Correlation and Non‐Causality between Multivariate ARMA Time Series

Abstract. Haugh [Journal of the American Statistical Association (1976) Vol. 71, pp. 378–85] developed an approach to the problem of testing non‐correlation (at all leads and lags) between two univariate time series. Haugh's tests however have low power against two series which are related over a long distributed lag when individual lag coefficients are relatively small. As a remedy, Koch and Yang [Journal of the American Statistical Association (1986) Vol. 8, pp. 533–44] proposed an alternative method that performs better than Haugh's under such dependencies. A multivariate extension of Haugh's procedure was proposed by El Himdi and Roy [The Canadian Journal of Statistics (1997) Vol. 25, pp. 233–56], but suffers the same weaknesses as the original univariate method. We develop here an asymptotic test generalizing Koch and Yang's method to the multivariate case. Our method includes El Himdi and Roy's as a special case. Based on the same idea, we also suggest a generalization of the El Himdi and Roy procedure for testing causality in the sense of Granger [Econometrica (1969) Vol. 37, pp. 424–38] between two multivariate series. A Monte Carlo study is conducted, which indicates that our approach performs better than El Himdi and Roy's for a wide range of models. Both procedures are applied to the problem of testing the absence of correlation between Canadian and US economic indicators, and to a brief study of causality between money and income in Canada.     

A Robbins–Monro Algorithm for Non‐Parametric Estimation of NAR Process with Markov Switching: Consistency

We approach the problem of non‐parametric estimation for autoregressive Markov switching processes. In this context, the Nadaraya–Watson‐type regression functions estimator is interpreted as a solution of a local weighted least‐square problem, which does not admit a closed‐form solution in the case of hidden Markov switching. We introduce a non‐parametric recursive algorithm to approximate the estimator. Our algorithm restores the missing data by means of a Monte Carlo step and estimates the regression function via a Robbins–Monro step. We prove that non‐parametric autoregressive models with Markov switching are identifiable when the hidden Markov process has a finite state space. Consistency of the estimator is proved using the strong α‐mixing property of the model. Finally, we present some simulations illustrating the performances of our non‐parametric estimation procedure.