(301d) A State-Space Model and Advanced Control Methods for Chemical Production Scheduling

A State-space Model and Advanced Control Methods for Chemical Production Scheduling
Kaushik Subramanian, Christos T. Maravelias and James B. Rawlings
Department of Chemical and Biological Engineering, University of Wisconsin Madison
1415 Engineering Dr., Madison, WI 53706, USA
Traditionally, scheduling is considered as a static optimization problem. We optimize at the beginning of the scheduling horizon, implement the schedule, and optimization is performed again for the next scheduling horizon. In case of disturbances affecting the schedule, various heuristic and recipe based methods are employed to locally correct the schedule within the current scheduling horizon. In reality, however, scheduling is a dynamic process, in which the optimal schedule can drastically change on observing a disturbance. Advance model based controllers are a natural choice to deal with dynamic processes. Accordingly, to facilitate the use of advanced process control methods to scheduling, we first develop a state-space form of the standard state task network (STN) model and then discuss how concepts from model predictive control (MPC) can be used to effectively address scheduling problems.
In developing the state-space STN model, we identify the inputs and introduce new state variables, via input lifting, to fully describe the state of the system. Then, we model typical scheduling disturbances that lead to rescheduling (e.g., shipment/delivery disturbances, unit breakdowns, and processing delays) using disturbance variables in the state-space model. We discuss how a wide range of scheduling models, with different types of decisions and processing constraints, can be expressed in state-space form. The state-space form of the STN model allows researchers to study scheduling models from a process control perspective, using existing theory (e.g., hybrid MPC) or developing new results to study the dynamics of the scheduling problem.
Furthermore, we discuss how concepts from control can be used in scheduling. Specifically, we discuss: (i) if and what input/state trajectories can be used in scheduling; and (ii) what stability and operability mean in the context of scheduling problems. Finally, we discuss two methods to achieve recursive feasibility for the scheduling problem that is responding to a nominal demand scenario. We achieve recursive feasibility using terminal constraints, that is constraints at the end of the scheduling horizon, which is the standard method used to ensure recursive feasibility (and stability) for dynamic control problems. First, we develop periodic schedules and use them as the terminal constraint, thus, developing a sub-optimal infinite horizon schedule for the plant. Second, we develop a safety state (that includes constraints on the inventories in the STN as well as the tasks). We also present some ideas to develop safety stocks that ensure recursive feasibility and terminal conditions that are robust to multiple demand-scenarios.