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Feasible Regions (feasible + regions)
Selected AbstractsLinear time computation of feasible regions for robust compensatorsINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2001M. Sami Fadali Abstract We introduce an application of computational geometry, including figures of merit standard in the analysis of algorithms, to the design of robust control systems. With respect to system transfer function magnitude, we show how to compute feasible regions for compensators whose plant transfer function is the ratio of uncertain interval polynomials. Our solution sweeps the Minkowski quotient set of the corresponding Kharitonov rectangles. Enumerating the winding numbers of Minkowski sum convolution curves, we obtain optimal, linear time algorithms that eliminate three factors from the execution inefficiency of traditional gridding approaches. We illustrate with examples pertinent to quantitative feedback theory (QFT). Copyright © 2001 John Wiley & Sons, Ltd. [source] Studies on the adaptability of different Borgen norms applied in self-modeling curve resolution (SMCR) methodJOURNAL OF CHEMOMETRICS, Issue 6 2009Róbert Rajkó Abstract Lawton and Sylvestre, and later Borgen et al. provided first the analytical solution for determining feasible regions of self-modeling curve resolution (SMCR) method for two- and three-component systems, respectively. After 20 years, Rajkó and István recently revitalized Borgen's method given a clear interpretation and algorithm how to draw Borgen plots using computer geometry tools; later Rajkó proved the existence of the natural duality in minimal constrained SMCR. In both latter cases, 1-norm was used to normalize raw data; however Borgen et al. introduced a more general class of normalization. In this paper, the definition and detailed descriptions of Borgen norms are given firstly appearing in the chemical literature. Some theoretical and practical studies on the adaptability of some Borgen norms used for SMCR method are also provided. Copyright © 2009 John Wiley & Sons, Ltd. [source] A kriging method for the solution of nonlinear programs with black-box functionsAICHE JOURNAL, Issue 8 2007Eddie Davis Abstract In this article, a new methodology is developed for the optimization of black-box systems lacking a closed-form mathematical description. To properly balance the computational cost of building the model against the probability of convergence to global optimum, a hybrid methodology is proposed. A kriging approach is first applied to provide information about the global behavior of the system considered, whereas a response surface method is considered close to the optimum to refine the set of candidate local optima and find the global optimum. The kriging predictor is a global model employing normally distributed basis functions, so both an expected sampling value and its variance are obtained for each test point. The presented work extends the capabilities of existing response surface techniques to address the refinement of optima located in regions described by convex asymmetrical feasible regions containing arbitrary linear and nonlinear constraints. The performance of the proposed algorithm is compared to previously developed stand-alone response surface techniques and its effectiveness is evaluated in terms of the number of function calls required, number of times the global optimum is found, and computational time. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] Using feasible regions to design and optimize reactive distillation columns with ideal VLEAICHE JOURNAL, Issue 5 2006Warren R. Hoffmaster Abstract The design and optimization of reactive distillation columns using feasibility analysis is addressed. Based on the feasible regions identified in previous work, we present two examples to illustrate the benefits of having feasibility information when locating design alternatives for systems with ideal vapor,liquid equilibrium. The examples include a reactive column for the metathesis of 2-pentene and a multifeed reactive column with a constant volatility mixture. In the first example, we use the feasible regions to initialize an optimization-based design strategy. For the second example, we characterize the feasible regions to determine feasible placement strategies for side streams and reactive stages. The design insights gained from feasibility analysis are highlighted for each example. © 2006 American Institute of Chemical Engineers AIChE J, 2006 [source] Simultaneous Controllability of PSD and MWD in Emulsion PolymerisationMACROMOLECULAR REACTION ENGINEERING, Issue 5 2008Stephen J. Sweetman Abstract A sensitivity study of particle size distribution (PSD) and molecular weight distribution (MWD) responses to perturbations in initiator, surfactant, monomer and chain transfer agent in a semi-batch emulsion polymerisation is presented. The objective is to provide a systematic study on the ability to simultaneously control both PSD and MWD, towards inferential control of end-use product properties. This would lead towards identification of the practical feasible regions of operability. All inputs appeared to have an intrinsic and simultaneous influence on end-time PSD and MWD. Trends shown in experimental results have been explained in a mechanistic sense and also compared to simulation results from a combined PSD/MWD population balance model. The preliminary comparison between experiment and simulation highlights areas to be focussed on with respect to model improvement. [source] | ||||||||||