Optimizing model predictive control of an industrial distillation column

The main scope of this work is the implementation of an MPC that integrates the control and the economic optimization of the system. The two problems are solved simultaneously through the modification of the control cost function that includes an additional term related to the economic objective. The optimizing MPC is based on a quadratic program (QP) as the conventional MPC and can be solved with the available QP solvers. The method was implemented in an industrial distillation system, and the results show that the approach is efficient and can be used, in several practical cases. (C) 2011 Elsevier Ltd. All rights reserved.

MPC for tracking zone regions

This paper deals with the problem of tracking target sets using a model predictive control (MPC) law. Some MPC applications require a control strategy in which some system outputs are controlled within specified ranges or zones (zone control), while some other variables - possibly including input variables - are steered to fixed target or set-point. In real applications, this problem is often overcome by including and excluding an appropriate penalization for the output errors in the control cost function. In this way, throughout the continuous operation of the process, the control system keeps switching from one controller to another, and even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. From a theoretical point of view, the control objective of this kind of problem can be seen as a target set (in the output space) instead of a target point, since inside the zones there are no preferences between one point or another. In this work, a stable MPC formulation for constrained linear systems, with several practical properties is developed for this scenario. The concept of distance from a point to a set is exploited to propose an additional cost term, which ensures both, recursive feasibility and local optimality. The performance of the proposed strategy is illustrated by simulation of an ill-conditioned distillation column. (C) 2010 Elsevier Ltd. All rights reserved.

A stable MPC with zone control

Several MPC applications implement a control strategy in which some of the system outputs are controlled within specified ranges or zones, rather than at fixed set points [J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, New Jersey, 2002]. This means that these outputs will be treated as controlled variables only when the predicted future values lie outside the boundary of their corresponding zones. The zone control is usually implemented by selecting an appropriate weighting matrix for the output error in the control cost function. When an output prediction is inside its zone, the corresponding weight is zeroed, so that the controller ignores this output. When the output prediction lies outside the zone, the error weight is made equal to a specified value and the distance between the output prediction and the boundary of the zone is minimized. The main problem of this approach, as long as stability of the closed loop is concerned, is that each time an output is switched from the status of non-controlled to the status of controlled, or vice versa, a different linear controller is activated. Thus, throughout the continuous operation of the process, the control system keeps switching from one controller to another. Even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. Here, a stable M PC is developed for the zone control of open-loop stable systems. Focusing on the practical application of the proposed controller, it is assumed that in the control structure of the process system there is an upper optimization layer that defines optimal targets to the system inputs. The performance of the proposed strategy is illustrated by simulation of a subsystem of an industrial FCC system. (C) 2008 Elsevier Ltd. All rights reserved.

Evaluation of plaque composition by intravascular ultrasound ""virtual histology"": the impact of dense calcium on the measurement of necrotic tissue

Aims: We aimed to evaluate if the co-localisation of calcium and necrosis in intravascular ultrasound virtual histology (IVUS-VH) is due to artefact, and whether this effect can be mathematically estimated. Methods and results: We hypothesised that, in case calcium induces an artefactual coding of necrosis, any addition in calcium content would generate an artificial increment in the necrotic tissue. Stent struts were used to simulate the ""added calcium"". The change in the amount and in the spatial localisation of necrotic tissue was evaluated before and after stenting (n=17 coronary lesions) by means of a especially developed imaging software. The area of ""calcium"" increased from a median of 0.04 mm(2) at baseline to 0.76 mm(2) after stenting (p<0.01). In parallel the median necrotic content increased from 0.19 mm(2) to 0.59 mm(2) (p<0.01). The ""added"" calcium strongly predicted a proportional increase in necrosis-coded tissue in the areas surrounding the calcium-like spots (model R(2)=0.70; p<0.001). Conclusions: Artificial addition of calcium-like elements to the atherosclerotic plaque led to an increase in necrotic tissue in virtual histology that is probably artefactual. The overestimation of necrotic tissue by calcium strictly followed a linear pattern, indicating that it may be amenable to mathematical correction.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Identification of protein coding regions using the modified Gabor-wavelet transform

An important topic in genomic sequence analysis is the identification of protein coding regions. In this context, several coding DNA model-independent methods based on the occurrence of specific patterns of nucleotides at coding regions have been proposed. Nonetheless, these methods have not been completely suitable due to their dependence on an empirically predefined window length required for a local analysis of a DNA region. We introduce a method based on a modified Gabor-wavelet transform (MGWT) for the identification of protein coding regions. This novel transform is tuned to analyze periodic signal components and presents the advantage of being independent of the window length. We compared the performance of the MGWT with other methods by using eukaryote data sets. The results show that MGWT outperforms all assessed model-independent methods with respect to identification accuracy. These results indicate that the source of at least part of the identification errors produced by the previous methods is the fixed working scale. The new method not only avoids this source of errors but also makes a tool available for detailed exploration of the nucleotide occurrence.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

ECONOMICAL OCCUPATION OF AGRICULTURAL AREA OF PIRACICABA (SAO PAULO STATE, BRAZIL), INCLUDING RISK THROUGH LINEAR PROGRAMMING

The economic occupation of an area of 500 ha for Piracicaba was studied with the irrigated cultures of maize, tomato, sugarcane and beans, having used models of deterministic linear programming and linear programming including risk for the Target-Motad model, where two situations had been analyzed. In the deterministic model the area was the restrictive factor and the water was not restrictive for none of the tested situations. For the first situation the gotten maximum income was of R$ 1,883,372.87 and for the second situation it was of R$ 1,821,772.40. In the model including risk a producer that accepts risk can in the first situation get the maximum income of R$ 1,883,372. 87 with a minimum risk of R$ 350 year(-1), and in the second situation R$ 1,821,772.40 with a minimum risk of R$ 40 year(-1). Already a producer averse to the risk can get in the first situation a maximum income of R$ 1,775,974.81 with null risk and for the second situation R$ 1.707.706, 26 with null risk, both without water restriction. These results stand out the importance of the inclusion of the risk in supplying alternative occupations to the producer, allowing to a producer taking of decision considered the risk aversion and the pretension of income.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Coding Strategies of Indirect Reported Speech in Typological Perspective

The purpose of this paper is to provide a cross-linguistic survey of the variation of coding strategies that are available for the grammatical distinction between direct and indirect speech representation with a particular focus on the expression of indirect reported speech. Cross-linguistic data from a sample of 42 languages will be provided to illustrate the range of available grammatical coding strategies.