Trajectory optimization for flat dynamic systems

A number of important chemical engineering processes are operated in a transient manner (e.g., batch processes) and cannot be considered to reach a steady state. Optimizing the operations of such processes requires the solution of a dynamic optimization problem, producing time-based trajectories for process variables, A key characteristic of dynamic optimization problems is that the process model contains differential equations. Numerical solution techniques, which are currently in widespread use, are usually based on discretization schemes and can be computationally expensive. This paper proposes an alternative method for solving dynamic optimization problems in which the nonlinear process model is flat. The approach exploits, as appropriate, either the differential flatness or the orbital flatness of the process model to explicitly eliminate the differential equations from the optimization problem. The resulting optimization problem is solely algebraically constrained and can be solved using readily available optimization codes. The proposed approach is demonstrated on a range of benchmark problems taken from the literature.