(179a) A Methodology for the Simultaneous Design, Scheduling and Control of Multi-Product Processes Under Uncertainty

Chemical process industry has been reinforced time to time by development of methodologies that strengthen the various aspects of the industry. The competitive environment makes the industry vulnerable to non-optimal operations. The overall cost of plant has always been the classical measure of the optimality of the operations in the industry. This may include the capital cost, the operating cost, the cost associated with the control system, etc. An important section of the chemical industry produces various grades of products (multi-product) and scheduling of the production of these grades plays an important role in the economy of the operations. The presented work focuses on the development of a methodology that can address three aspects of the economy of multi-product plants; i.e. process design, control and scheduling. The approaches proposed in the literature to address this challenging problem can be classified in two groups: i) the sequential approach, which generates overall optimal solution by sequentially solving an optimization problem for each of the aspect separately; i.e. one of the three aspects at a time, and ii) the simultaneous approach, which adds more degrees of freedom by generating optimal solution of an optimization problem for all aspects simultaneously. Studies have been presented on integration of the aspects, where some of them present the integration of process design and control^1,4 ,while the other integrates scheduling and control² . There also have been studies which address integration of optimal transitions of grades with design and control with fixed sequence of production³, while others have integrated design, scheduling and optimal control, where control decisions involve transition times⁶  but not the controller tuning parameters. The work presented here involves the development of simultaneous design, scheduling and control (SDSC) approach. The integration of the three aspects is one of the novel features of the work, as sequence of production remains part of decision variables as opposed to fixed sequence considered in previous works³. Key contributions of the work also include determination of tuning parameters as decision variables and the integration of the three aspects under continuous influence of disturbances and uncertainty in product demands.

The optimization framework developed aims to minimize an overall cost function, which includes capital cost, operating cost, variability cost and transition cost, while taking into account various operational constraints. The decision variables consist of the design of process equipment’s, the tuning parameters for the control system in place and the scheduling parameters. Scheduling parameters include optimal sequence of production and optimal transition trajectories. The proposed approach takes into account the influence of disturbances in the system by the identification of critical frequency from the disturbances, which is used to quantify the worst-case variability in the controlled variables. The uncertainty in the demands of products has also been addressed by creating critical demand scenarios with different probabilities of occurrence. These features foster the robustness of the approach to uncertainty. System stability analysis is performed at each optimal solution to ensure feasibility of the solution to achieve stable operation. To demonstrate the effectiveness of the SDSC approach, a multi-product continuous stirred-tank reactor (CSTR) system is considered⁵, which produces 4 different grades of a product. A comparison study has been performed to prove an edge of simultaneous approach over the traditional sequential method and effect of demand uncertainty is demonstrated via a case study involving different demand scenarios.

References

(1)   Flores-Tlacuahuac,  A.,  Biegler, L. T. Simultaneous mixed-integer dynamic optimization for integrated design and control, Computers & Chemical Engineering, 31, 588–600, 2007

(2)   Flores-Tlacuahuac, A., & Grossmann, I. E. Simultaneous cyclic scheduling and control of a multiproduct CSTR, Industrial & Engineering Chemistry Research,  45(20), 6175–6189, 2006.

(3)   Flores-Tlacuahuac, A., Biegler, L. T. Integrated control and process design during optimal polymer grade transition operations, Computers and Chemical Engineering, 32 (11), 2823-2837, 2008.

(4)   Ricardez-Sandoval, L. A., Douglas, P. L., & Budman, H. M. A methodology for the simultaneous design and control of large-scale systems under process parameter uncertainty, Computers and Chemical Engineering, 35(2), 307–318, 2011.

(5)   Ricardez-Sandoval, L. A. Optimal design and control of dynamic systems under uncertainty: A probabilistic approach, Computers and Chemical Engineering, 43, 91–107, 2012.

(6)   Terrazas-Moreno, S., Flores-Tlacuahuac, A., Grossmann, I.E. Simultaneous design, scheduling, and optimal control of a methyl-methacrylate continuous polymerization reactor, AIChE Journal. 54 (12), 3160–3170, 2008.