A switched system formulation for optimal integration of scheduling and control in multi-product continuous processes

Abstract

Integrating control decisions into scheduling strategies has been shown to improve process economics. Typical integrated formulations consist of mixed-integer optimization models that pose computational challenges. Often, these models describe the scheduling as a static system whereas the production process is considered dynamic over certain time periods. In this work, we propose an alternative formulation that circumvents the need to deal with integer variables. We regard the scheduling as a dynamic system and incorporate the model of the process unit to formulate the integration as a switched system. We address multi-product continuous processes where each product defines a subsystem with different operating conditions. Variable switching instants and sequences are handled using time-scaling transformation and parametrization of the integer decisions. Due dates are also taken into consideration. The resulting formulation is efficiently treated as a nonlinear programming problem that allows to carry out transitions involving stable and unstable steady states. An iterative procedure to improve the transition times is provided. We solve three case studies under different scenarios. Results show that optimal switching sequences and control profiles that maximize the total profit can be obtained at low computational cost. Solutions provide a dynamic description of the scheduling and production process. The proposed framework can be considered as an alternative to mixed-integer models.