A Novel Numerical Strategy for Computing Flexibility Index of Dynamic Systems with Piecewise Constant Manipulated Variables

Abstract

The chemical processes designed on the basis of nominal operating conditions and parameters have traditionally been evaluated according to economic criteria This approach often ends up with a plant which may become inoperable in realistic environment if some of the conditions/parameters significantly deviate from their nominal values Thus in addition to the financial feasibility it is equally important to consider the operational flexibility in a practical design The dynamic flexibility index (FId) have already been well defined to characterize the batch or unsteady operations and the corresponding dynamic programming models have also be rigorously derived for computing such metrics However at the present time it is still very difficult to apply the traditional vertex method or the active set method to numerically compute FId for even moderately complex systems This is often due to an overwhelmingly large number of vertices in the former case On the other hand since the Karush–Kuhn–Tucker conditions must be included into the mathematical programming model in the latter case the huge number of real and binary variables usually causes convergence failure In addition notice that it is really impractical to allow instantaneous and continuous control adjustments in computing the original version of FId It is actually more realistic to assume that the manipulated variables are piecewise constant Together with the above assumption and constraints for incorporating additional insights the above two traditional solution methods are integrated with the genetic algorithm in this work to overcome the aforementioned numerical difficulties Specifically the following three-step compotation strategy is proposed: 1 Identify the approximate region(s) of candidate vertexes by using the dynamic active-set method the dynamic vertex method solved with genetic algorithm or the dynamic vertex method solved with exhaustive enumeration 2 Use a refined time interval to discretize the constraints in vertex method and carry out the corresponding computation procedure by fixing the identified regions of candidate vertexes 3 Use a refined time interval to discretize the constraints in KKT conditions and fix the time profiles of control variables and uncertain parameters identified in the previous step to carry out dynamic active set method again The above optimization computations can be readily implemented with MATLAB and GAMS This strategy not only retains the advantages from traditional vertex method and the active set method but also avoid their shortcomings The numerical results obtained in several case studies are reported in this thesis to demonstrate the feasibility and accuracy of the solution strategy

Date of Award	2019
Original language	English
Supervisor	Chuei-Tin Chang (Supervisor)