Model Predictive Controllers (MPC) are widely used in the oil processing and petrochemical industries because the algorithm formulation is straightforwardly applicable to both SISO and MIMO systems, moreover, it accommodates restrictions on the inputs, outputs and control actions directly in the control problem formulation (Qin & Badgwell, 2003). There is a set of parameters that affect the closed-loop performance of the MPC, which varies according to the MPC formulation. It is possible to improve the performance of the MPC by properly selecting the tuning parameters. Most of the attempts to tune MPCs in industry are based on trial and error (Al-Ghazzawi, Ali, Nouh, & Zafiriou, 2001; Liu & Wang, 2000). Nonetheless, there are tuning techniques available in the literature that take into account simplifications of the system dynamics and heuristic definition of parameters to develop analytic equations for the tuning parameters (Shridhar & Cooper, 1997); that take the sensitivity functions of the control cost function, with respect to the tuning parameters, to calculate analytical equations for the tuning parameters (K. H. Lee, Huang, & Tamayo, 2008); or that pose the tuning problem as a multi-objective optimization problem (Harris & Mellichamp, 1985; Reynoso-Meza, Garcia-Nieto, Sanchis, & Blasco, 2013; Vallerio, Van Impe, & Logist, 2014).
The classic MPC approach uses a linear model of the real process to predict the output values over the prediction horizon. Therefore, the operating range in which the liner model is valid is tight, and the operating point of the process usually changes either because of process disturbances, or due to economic optimization. It is considered in this work a multi-plant uncertainty description, in which a set of multiple linear models of the plant is available, and the plant might behave as any model throughout its operation.
The literature has proposed different approaches to deal with multi-plant uncertainty. One is to change the MPC formulation, allowing for robustness guarantees (Martins, Yamashita, Santoro, & Odloak, 2013), another is to tune the MPC considering the uncertainty model (Francisco & Vega, 2010; García-Alvarado, Ruiz-López, & Torres-Ramos, 2005; J. H. Lee & Yu, 1994). The latter however, is mostly carried on in the frequency domain.
In this work, a time-domain robust tuning technique for MPC is proposed. It is an extension of the compromise optimization based tuning technique developed in (Yamashita & Odloak, 2014) that takes into account multi-plant uncertainty and calculates optimum tuning parameters to deal with the trade-off between robustness and performance. The robust tuning strategy in applied to tune an adapted version of the Infinite Horizon MPC proposed in (Santoro & Odloak, 2012), in closed-loop with a C3/C4 splitter model, identified in six operational points (Porfıirio, Almeida Neto, & Odloak, 2003). A simulation illustrates how the robust tuning improves closed-loop performance in model mismatch scenarios, comparing the IHMPC tuned using both the nominal and robust version of the technique. A second simulation compares the robustly tuned IHMPC to the Robust IHMPC developed in (Martins et al., 2013).
Even though the robust tuning strategy is not capable of ensuring robust performance, the results showed that it successfully calculated a set of parameters capable of compromising robustness and performance in multi-plant uncertainty scenarios. Moreover, the time-domain robust tuning strategy for nominal MPC yielded an alternative to the RIHMPC in model-mismatch applications.
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