(699a) Economic Model Predictive Control Using Nonlinear Empirical Models

Significant strides have been made in the last five years to unify economic process optimization and feedback control. Economic model predictive control (EMPC) is a feedback control technique that attempts to tightly integrate economic optimization and feedback control since it is a predictive control scheme that is formulated with an objective function representing the process economics. Key theoretical developments on stability, performance, and robustness of EMPC have been presented as well as numerous demonstrations of improved economic performance of closed-loop systems under EMPC [1]-[3] (for an overview of recent results on EMPC see, also, [4]). As its name implies, EMPC requires the availability of a dynamic model to compute its control actions. However, in industrial processes, it may be difficult to obtain an accurate first-principles model of the process. Furthermore, EMPC may dictate a possibly time-varying operating policy, that is, it may not force convergence of the closed-loop state to a pre-defined operating steady-state. A consequence of such operating strategy is that the operating region in state-space under EMPC may be sufficiently large such that the effect of nonlinearities is significant (i.e., a linear model cannot adequately capture the process dynamics in the region of operation). For the cases where the development of a sufficiently accurate first-principles dynamic model is not possible, system identification techniques may need to be used to obtain an accurate empirical input/output model of the process dynamics. In particular, nonlinear autoregressive moving average with exogenous inputs (NARMAX) models may be one type of nonlinear system identification techniques employed and used to construct an empirical model [5].

In this work, EMPC schemes using NARMAX models are investigated and discussed. In this direction, EMPC schemes are formulated with NARMAX models and the applicability of using these models with EMPC is discussed. In the first part, a nonlinear system identification methodology is presented that can be used to identify model structure and parameters to construct a NARMAX model capable of adequately describing the process dynamics. Since EMPC may dictate a time-varying operating strategy, being able to construct a NARMAX model that can describe the process transients is especially important. In the second part, the advantages and disadvantages of the using various NARMAX models in the context of EMPC are discussed. Finally, the EMPC schemes are demonstrated through several chemical process examples.

[1] Angeli D, Amrit R, Rawlings JB. On average performance and stability of economic model predictive control. IEEE Transactions on Automatic Control. 2012;57:1615-1626.
[2] Huang R, Harinath E, Biegler LT. Lyapunov stability of economically oriented NMPC for cyclic processes. Journal of Process Control. 2011;21:501-509.
[3] Heidarinejad M, Liu J, Christofides PD. Economic model predictive control of nonlinear process systems using Lyapunov techniques. AIChE Journal. 2012;58:855-870.
[4] Ellis, and  M, Durand H, Christofides PD. A tutorial review of economic model predictive control methods. Journal of Process Control, in press.
[5] Billings SA. Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Chichester, West Sussex, United Kingdom: John Wiley & Sons, 2013.