(244l) Robust Compromise Optimization Tuning Technique for MPC

Abstract

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.

References

Al-Ghazzawi, A., Ali, E., Nouh, A., & Zafiriou, E. (2001). On-line tuning strategy for model predictive controllers. Journal of Process Control, 11(3), 265–284.

Francisco, M., & Vega, P. (2010). Automatic tuning of model predictive controllers based on multiobjective optimization. Latin American Applied Research, 40, 255–265.

García-Alvarado, M. a., Ruiz-López, I. I., & Torres-Ramos, T. (2005). Tuning of multivariate PID controllers based on characteristic matrix eigenvalues, Lyapunov functions and robustness criteria. Chemical Engineering Science, 60(4), 897–905.

Harris, S. L., & Mellichamp, D. A. (1985). Controller tuning using optimization to meet multiple closed-loop criteria. AIChE Journal, 31(3), 484–487.

Lee, J. H., & Yu, Z. H. (1994). Tuning of model predictive controllers for robust performance. Computers & Chemical Engineering, 18(1), 15–37.

Lee, K. H., Huang, B., & Tamayo, E. C. (2008). Sensitivity analysis for selective constraint and variability tuning in performance assessment of industrial MPC. Control Engineering Practice, 16(10), 1195–1215.

Liu, W., & Wang, G. (2000). Auto-tuning procedure for model-based predictive controller. In SMC 2000 Conference Proceedings. 2000 IEEE International Conference on Systems, Man and Cybernetics. “Cybernetics Evolving to Systems, Humans, Organizations, and their Complex Interactions” (Cat. No.00CH37166) (Vol. 5, pp. 3421–3426). IEEE.

Martins, M. A. F., Yamashita, A. S., Santoro, B. F., & Odloak, D. (2013). Robust model predictive control of integrating time delay processes. Journal of Process Control, 23(7), 917–932.

Porfıirio, C. R., Almeida Neto, E., & Odloak, D. (2003). Multi-model predictive control of an industrial C3/C4 splitter. Control Engineering Practice, 11(7), 765–779.

Qin, S. J., & Badgwell, T. A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, 11(7), 733–764.

Reynoso-Meza, G., Garcia-Nieto, S., Sanchis, J., & Blasco, F. X. (2013). Controller Tuning by Means of Multi-Objective Optimization Algorithms: A Global Tuning Framework. IEEE Transactions on Control Systems Technology, 21(2), 445–458.

Santoro, B. F., & Odloak, D. (2012). Closed-loop stable model predictive control of integrating systems with dead time. Journal of Process Control, 22(7), 1209–1218.

Shridhar, R., & Cooper, D. J. (1997). A Tuning Strategy for Unconstrained SISO Model Predictive Control. Ind. Eng. Chem. Res., 36, 729–746.

Vallerio, M., Van Impe, J., & Logist, F. (2014). Tuning of NMPC controllers via multi-objective optimisation. Computers & Chemical Engineering, 61, 38–50.

Yamashita, A. S., & Odloak, D. (2014). Compromise Optimization Tuning Strategy for Model Predictive Controllers. In 14th AIChE Annual Meeting (p. 7). Atlanta.