(712e) Integrating RTO with Stabilizing Economic MPC

Authors: 
Allan, D. A., University of Wisconsin Madison
Rawlings, J. B., University of Wisconsin-Madison
Integrating RTO with stabilizing economic MPC
Douglas A. Allan and James B. Rawlings
April 17, 2017

Model predictive control (MPC) is an advanced control algorithm that combines a system
model with an objective function and numerical optimization to provide improved control
performance. Traditionally, the objective functions used in MPC have been tracking objective
functions that penalize deviations from a target steady-state combination of system
states and inputs. Recently, a new form of MPC that optimizes other performance criteria,
termed economic MPC has been proposed (Diehl, Amrit, and Rawlings, 2011).

This type of MPC has the possibility of directly optimizing important performance
criteria, such as maximizing plant profit or minimizing pollution or carbon dioxide emissions,
rather than optimizing a surrogate tracking cost. However, in general this type of MPC does
not stabilize any particular steady state unless the system and stage cost satisfy a certain
dissipation inequality (Angeli, Amrit, and Rawlings, 2012); if this inequality is not satisfied,
then (under a reachability condition) it is more profitable to operate the system periodically
(Muller, Angeli, and Allgower, 2015). However, industrial systems are often not designed to
operate in such a fashion. Periodic operation may cause excess fatigue on equipment, and
periodic operation may meet resistance from process operations personnel.

There are conditions under which economic MPC is known to be stabilizing. In particular,
if a problem has a linear model and convex objective function, economic MPC stabilizes
the optimal steady state under mild assumptions (Diehl et al., 2011). Typically industrial
dynamic models are linear, but profit functions typically have both linear and bilinear terms.
We propose a method to obtain a local convex approximation of the profit function from
the real-time optimization (RTO) layer and use it in Economic MPC. We compare this
technique to both the current industrial practice of RTO combined with tracking MPC and
fully nonlinear economic MPC in a case study.

References

D. Angeli, R. Amrit, and J. B. Rawlings. On average performance and stability of economic
model predictive control. IEEE Trans. Auto. Cont., 57(7):1615-1626, 2012.

M. Diehl, R. Amrit, and J. B. Rawlings. A Lyapunov function for economic optimizing
model predictive control. IEEE Trans. Auto. Cont., 56(3):703-707, 2011.

M. Muller, D. Angeli, and F. Allgower. On necessity and robustness of dissipativity in
economic model predictive control. Automatic Control, IEEE Transactions on, 60(6):
1671-1676, June 2015. ISSN 0018-9286. doi: 10.1109/TAC.2014.2361193.
1