Computers and Chemical Engineering 95 (2016) 10–20 Contents lists available at ScienceDirect Computers and Chemical Engineering j our na l ho me pa g e: www.elsevier.com/locate/compchemeng Economic model predictive control of chemical processes with parameter uncertainty Omar Santander, Ali Elkamel, Hector Budman ∗ Chemical Engineering Department, University of Waterloo, Waterloo, ON N2L3G1, Canada a r t i c l e i n f o Article history: Received 7 March 2016 Received in revised form 20 August 2016 Accepted 23 August 2016 Available online 27 August 2016 Keywords: Real time optimization Economic nonlinear predictive control a b s t r a c t This work proposes an EMPC (Economic Model Predictive Control) algorithm that integrates RTO (Real Time Optimization) and EMPC objectives within a single optimization calculation. Robust stability con- ditions are enforced on line through a set of constraints within the optimization problem. A particular feature of this algorithm is that it constantly calculates a set point with respect to which stability is ensured by the aforementioned constraints while searching for economic optimality over the horizon. In contrast to other algorithms reported in the literature, the proposed algorithm does not require terminal constraints or penalty terms on deviations from fixed set points that may lead to conservatism. Changes in model parameters over time are also compensated for through parameter updating. The latter is accomplished by including the parameters’ values as additional decision variables within the optimization problem. Several case studies are presented to demonstrate the algorithm’s performance. © 2016 Elsevier Ltd. All rights reserved. 1. Introduction Chemical Plants are designed with the task of transforming raw materials into more valuable products. These transformations must occur in the most efficient way in order to attain differ- ent goals such as maximization of product yield, minimization of the amount of contaminants or by-products, minimization of the energy employed in the process etc. Furthermore, these transfor- mations have to be carried out under economical, physical and environmental constraints and they must be robust to variations in process settings like temperature, input flows and pressures or variations in raw material quality. To achieve these goals advanced model based controllers such as MPC are widely used since they can optimally deal with multivariable interactions while accounting for process constraints. The conventional hierarchical control structure (see (Findeisen et al., 1980; Luyben et al., 1990)) implemented in most process industries involves an RTO (real time optimization) (Naysmith and Douglas, 1995) level above a multivariate control level realized by an MPC or other multivariable control strategy followed by lower level single-input single-output controllers (e.g. PIDs) to effect con- trol of actuators. The RTO is generally executed to maximize a ∗ Corresponding author. E-mail address: hbudman@uwaterloo.ca (H. Budman). steady state economic cost with respect to steady state values of process variables that are used as set points in the lower level multivariable control strategy. Thus, the RTO provides targets (set- points) and the multivariable controller (e.g. MPC) controls the system around these targets. Although this hierarchical strategy has resulted in good performance in industrial applications there is an opportunity for improvement since chemical processes are rarely at steady state. Hence, the steady state set points calculated by the RTO and enforced by the MPC controller may not be optimal during transient scenarios. There are several additional drawbacks related to this two layer structure. Often the RTO and MPC layers employ different models, with RTO commonly using a detailed steady state model whereas MPC generally uses simplified dynamic models which steady state values may not exactly match those calculated by the RTO algorithm. Hence the set points computed by the RTO may be sometimes unreachable by the MPC layer. Moreover, the frequency of calculation is typically different for the two layers: MPC is opti- mized at every sampling period whereas RTO is optimized once a new steady state has been reached. Thus, the RTO’s sampling period is typically in the order of hours or even days whereas for MPC it is in the order of minutes-seconds (Ellis et al., 2014). Since indus- trial processes are subjected to continuous disturbances the process may never reach a steady state. The fact that the steady state does not always correspond to the optimal economic operation (Budman and Silveston, 2008; Huang http://dx.doi.org/10.1016/j.compchemeng.2016.08.010 0098-1354/© 2016 Elsevier Ltd. All rights reserved.