Integration of Scheduling and Control with Closed Loop Implementation

Traditionally production scheduling and process control problems are considered separately. Scheduling problem results in the optimal production sequence, production time and resources allocation while control problem focuses on dynamic behavior of transition periods between different products. However, the solutions obtained by considering scheduling are certainly suboptimal. Targeting better operating conditions in today’s strict economic environment, a number of efforts have been made towards integration of scheduling and control problems. The integration of scheduling and control results in better modeling of the process operation since transitions are taking into consideration which are ignored in the traditional scheduling approach. With integrated modeling, information can be shared between scheduling and control without delay. Thus, a more economical process operation is achieved.

The existing approaches dealing with the integration of scheduling and control can be broadly categorized into simultaneous modeling approach and decomposition based methods. Using the simultaneous approach the process dynamic model is incorporated into the constraints of scheduling problem. Thus a Mixed Integer Dynamic Optimization (MIDO) problem is formed and then is discretized into Mixed Integer Nonlinear Programming (MINLP) using collocation point method ([1]). Using decomposition method, the control problem is modeled as dynamic optimization (primal problem) and the scheduling part as Mixed Integer Linear Programming (Master problem). The solution procedure proceeds by iterating between these two subproblems until convergence is achieved ([2]).

Most of the simultaneous based approaches however do not implement process control using close loop.  In this study, we consider disturbance in real process and build a closed loop strategy for simultaneous scheduling and control, which can be regarded as real time scheduling and control. We assume that the state variables in both transition periods and production periods are subject to disturbance. We detect the disturbance and generate new solution for the integrated problem at the point of disturbance. As a result, process reacts quickly to eliminate the effects of disturbance. More specifically,  we first solve the integrated problem off-line, and obtain the scheduling solution and control input. Then the solution is implemented in the process. If the real state track the reference (pre-calculated by solving the integrated problem off line) very well (i.e. their difference is within the tolerance), no feedback is needed. If significant disturbance occurs, the difference between state and reference is detected and feedback is activated. With the feedback information, the integrated problem is solved again for the remaining part of the production cycle. Thus both the scheduling solution and control input are updated, which ensure that the operation after the occurrence of disturbance is optimal. Case studies demonstrate that our approach is economically preferable compared to open loop strategy ([1]).

References:

[1] Tlacuahuac, A. Flores, & Grossmann, I.E.. (2006). Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR. Industrial & Engineering Chemistry Research. 45(20), 6698-6712.

[2]  Nystrom, R.H., Franke, R, Harjunkoski, I., Kroll, A. (2005). Production campaign planning including grade transition sequencing and dynamic optimization. Computers & Chemical Engineering. 29(10) 2163-2179.