(473d) LMI-Based Multi-Model Predictive Control of An Industrial C3/C4 Splitter

Model Predictive Control (MPC) is nowadays commonly implemented in chemical industries such as oil refineries, paper manufacturing, … The implementation of this control strategy consists in calculating at each time step an open-loop sequence of control moves that minimizes an objective function subject to constraints on the system inputs. Generally the objective function is composed by a term accounting for the difference between the predicted system outputs and their corresponding set points and a term penalizing the input moves. The first calculated control move is implemented and the optimization problem is solved again at the next step.

MPC is based on a linear model which may not be reliable if the real model of the plant is nonlinear, which is often the case in chemical industry. In that case, one unique model is uncertain and may not allow an efficient control of the plant in some operating zones. One way to overcome this disadvantage is to deal with the model uncertainties considering the Multi-plant uncertainty model (Porfírio et al., 2003), for which a discrete set of plants corresponding to different operating points of the system is considered. Defined an objective function for each model of the set, the multi-model predictive controller then results from minimizing the worst case objective function.

Such a controller has already been implemented by (Porfírio et al., 2003) on a real industrial C3/C4 splitter, where it actually showed to have a significantly better performance.

However, a disadvantage of the Multi-Model Predictive Control (MMPC) compared to the MPC is the computational burden involved in the optimization problem resolution, which can be prohibitive for high dimension systems. In this case, the LMI techniques that have been developed over the past decades are of a great interest as they allow to significantly reducing the computational complexity of the optimization problem (Kothare et al., 1996).

In this work, the classical MMPC problem developed for the industrial C3/C4 splitter system that can be found in (Porfírio et al., 2003) is re-casted as an LMI-based problem in order to compare the performances and computational costs of the classical NLP based MMPC and the LMI based MMPC. The simulations show that compared to the NLP based controller, the LMI based controller allows to significantly reducing the computational cost without penalizing the controller performance.

References

Kothare, M. V., Balakrishnan, V. and Morari, M. Robust constrained model predictive control using linear matrix inequalities. Automatica [S.I.], v. 32, n. 10, p. 1361-1379,  1996.

Porfírio, C. R; Almeida Neto, E. and Odloak, D. Multi-model predictive control of an industrial C3/C4 splitter. Control Engineering Practice [S.I.], v. 11, n. 7, p. 765-779,  2003.