(697a) A Time Scale-Bridging Approach for Integrating Production Scheduling and Process Control
The control and operation hierarchy of the chemical supply chain comprises several layers of functionality, including regulatory and supervisory control, and production scheduling and planning. These functions act over different time horizons, ranging from seconds, in the case of regulatory control, to months, in the case of production planning). Since they all serve the common goal of improving process efficiency, profitability and safety, it is conceivable that carrying out several of these functions in an integrated fashion will yield further economic and/or operational benefits. Indeed, extensive literature studies have been dedicated to the interplay between regulatory and supervisory control, and to the integration of planning and scheduling.
Conversely, the integration of scheduling and control has received far less attention. This is partly due to organizational challenges : the two functions are typically the responsibility of different parts of an organization, with planning and scheduling being carried out by a business arm, and control belonging to an engineering/operations division. However, integrating these two functions also poses significant technical challenges: their time horizons and execution frequencies differ considerably. Moreover, scheduling must account for discrete decisions, in addition to using continuous variables as is typical in control calculations .
In this work, we present a novel framework for integrating short-term scheduling and nonlinear control of continuous chemical processes. We draw our inspiration from scale-bridging techniques used in multi-scale simulation, whereby a reduced-order model of the system characteristics in a faster time scale (or smaller lenghtscale) is used to improve the accuracy of the system model at a higher level in the time/space scale hierarchy. In a similar vein, we develop a low-dimensional dynamic model of the closed-loop input-output behavior of the process under nonlinear control . This low order time scale-bridging model is then incorporated into the scheduling layer as a dynamic constraint. The schedule is computed in the form of a time-varying setpoint signal for the process controller .
We demonstrate the implementation of these concepts using multivariate input-output linearizing feedback control, which imposes a linear and decoupled closed loop behavior on the systems of interest. We then present two illustrative case studies, a multiple product reactor  and a polymerization reactor . We show that the economic performance of the proposed scheduling mechanism is comparable to that of scheduling formulations that rely on the full process model when a perfect model is available, and emphasize the benefits of our approach in the presence of plant-model mismatch.
 S. Engell and I. Harjunkoski. Optimal operation: Scheduling, advanced control and their integration. Comput. Chem. Eng., 47:121–133, 2012.
 M. Baldea and I. Harjunkoski. A systematic review of the integration of production
scheduling and process control. Comput. Chem. Eng., submitted.
 M. Baldea, P. Daoutidis. Dynamics and Nonlinear Control of Integrated Process Systems, Cambridge University Press, 2012.
 J. Du, J. Park, I. Harjunkoski, and M. Baldea. Integrating Production Scheduling and Process Control using Internal Coupling Models. ESCAEP 24, Budapest, Hungary.
 A. Flores-Tlacuahuac and I.E. Grossmann. Simultanous cyclic scheduling and control of a multiproduct CSTR. Ind. Eng. Chem. Res., 45:6698–6712, 2006
 P. Daoutidis, M. Soroush, and C. Kravaris. Feedforward/feedback control of multivariable
nonlinear processes. AIChE J., 36(10):1471–1484, 1990.