Two-stage dynamic real-time optimization framework using parameter-dependent differential dynamic programming

The purpose of chemical process control includes proactive adjustment of the operation to make the most profit out of it. Within this context, real-time optimization (RTO) is proposed and extended to dynamic RTO (DRTO) in the hierarchical control structure, usually having model predictive control (MPC) below. However, online tractability confined the model complexity of RTO and MPC, which results in model inconsistency and, even, incompatible solutions. Here we use parameter-dependent differential dynamic programming (PDDP) to incorporate the closed-loop behavior of the controller in an RTO layer to reduce problem complexity and online computation time. The adaptive control performance of PDDP and the efficacy of closed-loop DRTO formulation with PDDP is demonstrated with the reaction–storage–separation network system control. Consequently, PDDP provides a useful parameterization method to express closed-loop system dynamics, which enables fast feedback control and integrated plant optimization.