Combined Noncyclic Scheduling and Advanced Control for Continuous Chemical Processes

Abstract

Abstract:A novel formulation for combined scheduling and control of multi-product, continuous chemical processes is introduced in which nonlinear model predictive control (NMPC) and noncyclic continuous-time scheduling are efficiently combined. A decomposition into nonlinear programming (NLP) dynamic optimization problems and mixed-integer linear programming (MILP) problems, without iterative alternation, allows for computationally light solution. An iterative method is introduced to determine the number of production slots for a noncyclic schedule during a prediction horizon. A filter method is introduced to reduce the number of MILP problems required. The formulation's closed-loop performance with both process disturbances and updated market conditions is demonstrated through multiple scenarios on a benchmark continuously stirred tank reactor (CSTR) application with fluctuations in market demand and price for multiple products. Economic performance surpasses cyclic scheduling in all scenarios presented. Computational performance is sufficiently light to enable online operation in a dual-loop feedback structure.

Economic Benefit from Progressive Integration of Scheduling and Control for Continuous Chemical Processes

“…This work also utilizes a novel, computationally light decomposed integration method employing continuous-time scheduling and nonlinear model predictive control (NMPC) as the fourth phase of integration. This method is outlined in detail in another work [60]. Although the phases of integration presented in this work are not comprehensively representative of integration methods presented in the literature, the concepts of integration progressively applied in the four phases are applicable across the majority of formulations in the literature.…”

“…The formulation for phase 4 builds on the work of Zhuge et al [49], which justifies decomposing slot-based ISC into two subproblems: (1) NLP solution of transition times and transition control profiles and (2) MILP solution of the slot-based, continuous-time schedule. The formulation in [60] expands the work of Zhuge et al by combining a look-up transition time table with control profiles and transition times between known product steady-state conditions, calculated offline and stored in memory, with transitions from current conditions to each product. The transitions from current conditions or most recently received process measurements are the only transition times and transition control profiles required to be solved at each iteration of combined scheduling and control (Equations (2)- (8)).…”

“…This non-cyclic fixed-horizon approach to combined scheduling and control enables response to market fluctuations in maximum demand and product price, whereas traditional continuous-time scheduling requires a makespan (T M ) to meet a demand rather than producing an optimal amount of each product within a given fixed horizon. Additional details for this formulation are included in another paper [60].…”

“…This formulation, however, does not use simplified dynamic process models for scheduling, but rather maintains nonlinear process dynamics while reducing computational burden via problem decomposition into offline and online components and further decomposition of the problem into computationally light NLP and MILP problems, solvable together without the need for iterative alternation [60].…”

“…This work utilizes the formulation for computationally light online scheduling and control for closed-loop implementation introduced in another work by the authors [60]. As in phase 3, a continuous-time schedule is implemented with NMPC-estimated transition times as inputs to the scheduling optimization; however, the ISC algorithm is implemented not only once at the beginning of the horizon as in phase 3, but triggered by updated market conditions or process disturbances above a threshold (see Figure 4).…”