Trajectory Planning for Grade Transitions: A Restricted Form Approach

Trajectory planning is of great importance as many chemical processes normally operate under transient conditions. Many of the available techniques for trajectory optimization can yield trajectories that are unrealistic and not implementable. Furthermore, many transient processes are operated manually, which further reduces the classes of trajectories that are implementable. In this paper, input trajectories are restricted to step/ramp functions, which are easily implemented by manual control or simple control schemes, through the application of input constraints and input switching times. Direct transcription of the dynamic optimization problem was used to allow the solution to be found using NLP techniques. The proposed method also serves as a useful control policy evaluation tool, where comparison of unrestricted and restricted trajectories leads to valuable insight into the gains associated with adopting a more sophisticated control scheme. The restricted inputs approach is applied to several benchmark problems.