(564a) NMPC of Semi-Batch Processes under Uncertainty using Pontryagin's Minimum Principle

 Nonlinear model predictive control (NMPC) is an important tool to perform real-time optimization for batch and semi-batch processes. Direct methods are often the methods of choice to solve the corresponding optimal control problems, in particular for large-scale problems (Wächter and Biegler, 2006; Zavala and Biegler, 2009). However, the matrix factorizations associated with large prediction horizons can be computationally demanding (Cannon, 2004; Cannon et al.,2008)). In contrast, indirect methods can be competitive for smaller-scale problems. Furthermore, the interplay between states and co-states in the context of Pontryagin’s Minimum Principle might turn out to be computationally quite efficient (Cannon et al.,2008; Aydin et al.,2017).

This work proposes to use a novel indirect solution technique within shrinking-horizon in the context of NMPC. In particular, the technique deals with path constraints via indirect adjoining, which allows meeting active path constraints explicitly at each iteration (Hartl et al., 1995). Uncertainties are handled by the introduction of time-varying backoff terms for the path constraints (Srinivasan et al., 2003; Shi et al., 2016). The resulting NMPC algorithm is applied to a two-phase semi-batch reactor for the hydroformylation of 1-dodecene in the presence of uncertainty, and its performance is compared to that of NMPC that uses a direct simultaneous optimization method (Hentschel et al., 2015). The results show that the proposed algorithm (i) can enforce feasible operation for different uncertainty realizations both within batch or from batch to batch, and (ii) it is faster than direct simultaneous NMPC, especially at the beginning of the batch. In addition, a modification of the PMP-based NMPC scheme is proposed that enforces active constraints via tracking and reduces the complexity of the optimization further.

References

Aydin, E., Bonvin, D., & Sundmacher, K. (2017). Dynamic optimization of constrained semi-batch processes using Pontryagin’s minimum principle—An effective quasi-Newton approach. Computers & Chemical Engineering, 99, 135-144

Cannon, M. (2004). Efficient nonlinear model predictive control algorithms. Annual Reviews in Control, 28, 229-237.

Cannon, M., Liao, W., & Kouvaritakis, B. (2008). Efficient MPC optimization using Pontryagin's minimum principle. International Journal of Robust and Nonlinear Control, 18, 831-844.

Hartl, R. F., Sethi, S. P., & Vickson, R. G. (1995). A survey of the maximum principles for optimal control problems with state constraints. SIAM review, 37, 181-218.

Hentschel, B., Kiedorf, G., Gerlach, M., Hamel, C., Seidel-Morgenstern, A., Freund, H., & Sundmacher, K. (2015). Model-based identification and experimental validation of the optimal reaction route for the hydroformylation of 1-dodecene. Industrial & Engineering Chemistry Research, 54, 1755-1765.

Shi, J., Biegler, L. T., Hamdan, I., & Wassick, J. (2016). Optimization of grade transitions in polyethylene solution polymerization process under uncertainty. Computers & Chemical Engineering, 95, 260-279.

Srinivasan, Bonvin, D., Visser, E., & Palanki, S. (2003). Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty. Computers & Chemical Engineering, 27, 27-44.

Wächter, A., & Biegler, L. T. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical Programming, 106, 25-57.

Zavala, V. M., & Biegler, L. T. (2009). The advanced-step NMPC controller: Optimality, stability and robustness. Automatica, 45, 86-93.