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Keywords:

  • accuracy of state profile approximation;
  • time optimal control;
  • optimal switching behavior;
  • moving finite elements;
  • orthogonal collocation

Abstract

Quasi-sequential methods are efficient and flexible strategies for the solution of dynamic optimization problems. At the heart of these strategies lies the time discretization and approximation of dynamic systems for nonlinear optimization problems. To address this question, we employ a time derivative analysis within the quasi-sequential approach and derive a finite element placement strategy. In addition, methods for direct error prediction are applied to this approach and extended with a proposed time derivative analysis. According to the information for current time derivatives, subintervals are introduced that improve accuracy of state profiles. Since this is only done in the simulation layer, the nonlinear programing solver need not be restarted. An efficient gradient computation is also derived for these subintervals; the resulting enhanced accuracy accelerates convergence performance and increases the robustness of the solution to initialization. A beer fermentation process case study is presented to demonstrate the effectiveness of the proposed approach. © 2011 American Institute of Chemical Engineers AIChE J, 2011