(140b) Fast NMPC Applied to Industrial High Purity Propylene Distillation

Distillation is one of the most used separation processes. Distillation columns are largely studied on process control because they are directly related with product quality, energy consuming and control difficulties due to nonlinearities. With increasing competitiveness, there is a demand to push the process to most profitable operating point, generally closer to the boundary of the admissible operating region, without violating the operating limits and satisfying product specifications.  To guarantee the achievement of these requisites the controller must explicitly consider process nonlinearities and constraints. These problems motivate the use of nonlinear model predictive control (NMPC) with rigorous dynamic models. The NMPC is able to improve operation stability and increase profit.

In this work a detailed propylene distillation model of an industrial unit is derived. The model is represented by tray-by-tray equations consisting of mass balances, energy balances, phase equilibrium, hydraulic and summation equations. This DAE system contains the rigorous description of the plant, bound constraints for the differential, algebraic states and for the manipulated variables. Here, we use a simultaneous collocation-based approach. The infinite dimensional problem was transcribed to a finite element discretization at Radau collocation points.

This industrial-size distillation first principle model incorporates the discretized dynamic as algebraic constraints and has thousands (40,000) of variables which is challenging to solve. One advantage of this dynamic model is that it has a sparse structure. In order to reduce computational complexity, the NLP solver must have the ability to exploit this sparse structure. Another advantage is that the dynamic model is completely algebraic and first and second order derivative information can be obtained directly from modeling platforms. To solve the resulting NLP problem we use the interior-point solver IPOPT (Wächter & Biegler, 2006).  To handle the bound constraints IPOPT add logarithmic barrier terms to the objective function. IPOPT applies Newton’s method to the KKT conditions of system to solve each barrier problem. The factorization of the KKT matrix is the most expensive step at each iteration in the algorithm.  For large systems, this factorization step can take a significant amount of computation time.

A barrier for these optimization-based strategies of NMPC is long time feedback delay due to on-line solution. In order to solve this problem have been developed advanced-step NMPC strategies (Zavala & Biegler, 2007) that use the sensitivity equation to get the fast updated solution.  The control action is extracted from the approximate solution vector and applied on plant. The asNMPC has the same nominal stability properties of the ideal NMPC (Zavala et al, 2008). Success on the application of this strategy for an air separation unit (Huang et al, 2009) leads to the study of other industrial problems.

Industrial data from a propylene unit localized at REVAP (Henrique Lage Refinery, Petrobras-Brasil) were used to determination of system parameters for the propylene distillation model. The main uncertainty sources are the tray efficiencies and heat transfer coefficients. In this work, we are verifying  the performance of the MHE/asNMPC maintaining the composition on desired level and maximizing the valuable product on a modeled industrial case,  dealing with measured  disturbances as plant feed, unmeasured disturbances as well as the  influence of the model-plant mismatch.

References

A. Wächter and L. T. Biegler, On the Implementation of a Primal-Dual Interior Point Filter Line Search Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming 106(1), pp. 25-57, 2006

Zavala, V. M.; and Biegler, L.T. The Advanced Step NMPC Controller. Proceedings of the IEEE Workshop on Advanced Process Control Applications for Industry - Vancouver, Canada. 2007

V. Zavala, C. Laird, L. Biegler, A fast moving horizon estimation algorithm based on nonlinear programming sensitivity, Journal of Process Control 18 (2008) 876–884.

R. Huang, V.M. Zavala and L.T. Biegler. Advanced step nonlinear model predictive control for air separation units. J. of Process Control,19(4) 678-685, 2009.