(612h) Dynamic Optimization of Fractional Order Chemical Processing Systems

Flores-Tlacuahuac, A., Universidad Iberoamericana
Biegler, L. T., Carnegie Mellon University

In this work we address the dynamic simulation and optimization of chemical processing systems modeled in terms of fractional order differential equations. Fractional models have been proposed for a wide range of problems, which traditional integer order models cannot cope with. For medium or large scale applications normally no analytical solutions are available and therefore approximated numerical solutions ought to be sought. Unfortunately, little work has been done to solve fractional order differential equations numerically; most of the the existing numerical methods are intended for small scale systems. Therefore, one of the aims of this work is to propose a new numerical method, based on orthogonal collocation on finite elements, to approach this issue. To gain a better appreciation about the performance of the new algorithm we compare its response against a predictor-corrector method recently proposed in the literature. We also extend the proposed method to deal with dynamic optimization fractional order systems, an open research problem that has not received full consideration. We test the performance of the algorithms by deploying three systems embedded with different nonlinear behavior from a simple linear dynamic system to a dynamic multiple steady-states bioreactor. The results indicate better numerical properties of the fractional order orthogonal collocation algorithm both for the dynamic simulation and optimal control issues.