Stochastic model predictive control

In this work an MILP model which achieves the integration of all three Supply Chain (SC) decision levels is developed. Then, the stochastic version of this integrated model is applied as the predictive model in a Model Predictive Control (MPC) framework in order to incorporate and tackle unforeseen events in the SC planning problem in chemical process industries. Afterwards, the validation of the proposed approach is justified and the resulting potential benefits are highlighted through a case study. The results obtained of this particular case study are analyzed and criticized towards future work. 

The state estimation technique can also be incorporated into the design of optimal batch polymerization control system. For example, a batch reaction time is divided into several control intervals, and the optimal control trajectory is updated online using the molecular weight estimates generated by a model/state state estimator. Of course, if batch reaction time is short, such feedback control of polymer properties would be practically difficult to implement. Nevertheless, the online stochastic estimation techniques and the model predictive control techniques offer promising new directions for the improved control of batch polymerization reactors. 

Hence, the aforementioned enterprise-wide model is extended to a stochastic program that takes exogenous uncertainty into account, namely, demand, price and interest rates variability. To tackle the resulting problem, scenario-based multi-stage stochastic mixed integer modeling techniques are applied. Then, the stochastic model is introduced into a model predictive controller to capture the dynamics of SC processes and their environment. The ensuing model can be used as a support tool... 

Many systems of interest to industrial engineers involve randomness or unpredictability for example, in the arrival of jobs requiring processing, or in machine breakdowns. In attempting to understand these systems for the purpose of design or control, a mathematical model is needed. Often, randomness and uncertainty must be captured explicitly in the model in order to represent the system reasonably faithfully. Such a model is called a stochastic model. The value of these models is that they enable us to predict the performance of a new system or the effect of a change in an existing system. 

The second level of control is a model predictive optimisation-based scheme that considers the entire network dynamics, embedding the inventory controllers of the first layer and a stochastic model for demand variation. 

Maybeck PS (1982) Stochastic models, estimation, and control, vol 2. Academic, New York Melchers RE (1999) Structural reliability analysis and prediction, 2nd edn. Wiley, Chichester Nigam NC (1983) Introduction to random vibrations. The MIT Press, Cambridge, MA... 

I/O data-based prediction model can be obtained in one step from collected past input and output data. However, thiCTe stiU exists a problem to be resolved. This prediction model does not require any stochastic observer to calculate the predicted output over one prediction horiajn. This feature can provide simplicity for control designer but in the pr ence of significant process or measurement noise, it can bring about too noise sensitive controller, i.e., file control input is also suppose to oscillate due to the noise of measursd output... 

In this work, therefore we aim to combine the stochastic observer to input/output prediction model so that it can be robust against the influence of noise. We employ the modified I/O data-based prediction model [3] as a linear part of Wimra" model to design the WMPC and these controllers are applied to a continuous mefihyl methacrylate (MMA) solution polymerization reactor to examine the performance of controller. 

One of the goals of the experimental research is to analyze the systems in order to make them as widely applicable as possible. To achieve this, the concept of similitude is often used. For example, the measurements taken on one system (for example in a laboratory unit) could be used to describe the behaviour of other similar systems (e.g. industrial units). The laboratory systems are usually thought of as models and are used to study the phenomenon of interest under carefully controlled conditions. Empirical formulations can be developed, or specific predictions of one or more characteristics of some other similar systems can be made from the study of these models. The establishment of systematic and well-defined relationships between the laboratory model and the other systems is necessary to succeed with this approach. The correlation of experimental data based on dimensional analysis and similitude produces models, which have the same qualities as the transfer based, stochastic or statistical models described in the previous chapters. However, dimensional analysis and similitude do not have a theoretical basis, as is the case for the models studied previously. 

The predictive model within the control algorithm consists in a multistage stochastic MILP. A scenario based approach is applied. Refer to Puigjaner and Lainez for scenario tree description and stochastic formulation indices details (1, hi). 

So far, we have assumed that a change in an equipment-related MEMS-processing parameter set leads to a defined statistical distribution of geometric and material parameters allowing yield predictions based on functional modeling. However, in addition, we need to take stochastic effects into account and develop testing methods to detect defects and anomalies that detract from product quality and which cannot now be traced to their root causes or controlled sufficiently during production. 

Natural attenuation is controlled by numerous processes, which include sorption, intraparticle diffusion as weU as biological and chemical degradation. In order to be able to quantify respectively predict the fate and transport of contaminants, appropriate models that are able to deal with the complexity and interactions of the involved processes need to be developed. Due to insufficient information on the spatial distribution of transport parameters in the subsurface, stochastic methods are a preferred alternative to deterministic approaches. In the present paper a one-dimensional Lagrangian streamtube model is used to describe the reactive transport of acenaphthene as a sample organic compoimd at field scale. As the streamtube model does not consider the heterogeneity of hydrogeochemical parameters but only hydraubc heterogeneity, model results from the streamtube model are compared in a Monte Carlo approach to results of a two-dimensional Eulerian model. 

Hence, the stated above results have shown that molecular weight distribution of polymers, prepared by different modes of synthesis, can be simulated and predicted within the framework of irreversible aggregation cluster-cluster model. MWD curve shape and position are controlled by factors number, which are common for any synthesis method, namely, by the macromolecular coil structure, coil environment stochastic contribution in synthesis process intensity and coil destruction level in the indicated process. The coil mobility in reactionary medium exerts very strong influence on MWD curve shape. 

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