A method for improving condition number of chemical processes by sensitivity analysis

Simple and effective method for improving Euclidean Norm Condition Number for chemical processing system is presented. The singular value sensitivities of Freudenberg et. al. (1982) is used to estimate the behavior of singular values of process transfer function matrix when design is changed, then the condition number can be calculated straightforwardly. The method requires explicit dependencies of each transfer function matrix elements on design parameters. These dependencies can be obtained either by symbolic differentiation in the form of explicit function of design parameters, or by numerical perturbation studies for units with large and complicated models. Gerschgorin-type lower bound for minimum singular value is introduced to detect the large discrepancies near singular point due to linear limitation of sensitivities. The case study is performed to show the efficiency of the proposed method.