(687c) Constraint Handling in Inventory Control

Control systems for chemical processes must address restrictions imposed by the equipment and safety constraints.  Constraints may be enforced by alarming and manual intervention or through logic control.  While enforcement of process constraints avoids potentially dangerous operation, the closed-loop stability properties of the process will change.  By including constraints within the control system, the process may be safely steered away to retain the desired closed-loop stability.  Model predictive control includes constraints in the calculation of control inputs.  However, the handling of constraints by local control methods, such as inventory control, in a large chemical process network needs to addressed    

In previous work, we have introduced a formalized approach for inventory control of chemical process networks using extensive variables : internal energy, volume, molar inventories.  However, the inventory control approach has lacked a consistent method to handling process and input constraints.  Most process constraints are in terms of intensive variables such as temperature and pressure rather than the extensive variables.  The  constraints must be converted to the extensive state-space and incorporated into the inventory control law.

In the current work, we propose constraint transformations from the intensive to extensive state-space for a number of example problems.  The extensive variable constraints can be calculated from thermodynamic state relationships.  These constraints are typically nonlinear functions of physical properties, intensive variables, and active intensive variable constraints.  This approach trades nonlinear dynamics with constant constraints in the intensive space for nearly linear dynamics and nonlinear constraints in the extensive variable space. The extensive variable constraints are used to directly calculate setpoints for a particular active set of constraints.  The process control computer system determines the active set and uses the appropriate setpoint relationship.

Even when the process constraints are included in the control system, active input constraints may still cause many problems for inventory control. Passive systems theory has been used to show stability of the extensive variable inventory control laws.  The control laws require feed-forward terms relating to production and process flows.  If the inputs become actively constrained, certain states in the chemical process become uncontrollable and the closed-loop system may no longer be passive.  In the current work, we address input constraints by placing further restrictions on the setpoints of the controlled variables. Motivating examples are used to demonstrate the issues in dealing with steady state process constraints and input constraints in the inventory control framework.