Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Simultaneous Process Scheduling and Control: A Multiparametric Programming-Based Approach

“…Note that additional constraints can be included in eq regarding the needs of the specific problem. The linear state space matrices represent the closed loop dynamics of the system, and acquired through the MATLAB System Identification Toolbox or a model reduction technique, as described by Diangelakis . The multiparametric solution of eq provides explicit affine expressions of the optimal scheduling actions as functions of the system parameters, as defined in eq . …”

“…where x stands for the states of the system, y is the system outputs, u is the optimal control actions, S and Y are the continuous and binary scheduling decisions respectively, d is the measured disturbances to the system and the market conditions, P is the objective function of the system accounting for the short-term and long-term operational costs, f and g are the first principle system equations, and h and m are the Grossmann and co-workers (2006a, 2006b, 2007, 2010, 2011, 2012, 2014), 7,9−14 Gudi and co-workers (2010), 15 Biegler and co-workers (2012, 2015), 16,17 You and co-workers (2013) 18 simultaneous/decomposition (MI)DO or (MI)NLP and open-loop optimal control Pistikopoulos and co-workers (2003a, 2003b), 19,20 You and co-workers (2012) 21 simultaneous/decomposition (MI)DO schedule and P−PI−PID control Allcock and co-workers (2002), 22 Espunã and co-workers (2013), 23 Baldea and co-workers (2014, 2015) 6,24 simultaneous/decomposition algorithms using control/dynamics aware scheduling models Biegler and co-workers (1996), 25 Barton and co-workers (1999), 26 Nystrom and co-workers (2005), 27 Marquardt and coworkers (2008), 28 Ierapetritou and co-workers (2012), 29 You and co-workers (2013) 18 simultaneous/decomposition algorithms via (MI)DO reformulation to (MI)NLP Puigjaner and co-workers (1995), 30 Pistikopoulos and co-workers (2013, 2014, 2016), 3,31,32 Rawlings and co-workers (2012, 2013) 33,34 control theory in scheduling problems Marquardt and co-workers (2011), 35 Pistikopoulos and co-workers (2016, 2017, 2017), 3,36,37 Ierapetritou and co-workers (2016) 38 advanced control and (MI)NLP scheduling schemes Reklaitis and co-workers (1999), 39 Floudas and co-workers (2004, 2007), 40,41 Ricardez-Sandoval and...…”

“…The linear state space matrices represent the closed loop dynamics of the system, and acquired through the MATLAB System Identification Toolbox or a model reduction technique, as described by Diangelakis. 54 The multiparametric solution of eq 6 provides explicit affine expressions of the optimal scheduling actions as functions of the system parameters, as defined in eq 7. Due to approximation of the scheduling model and the large discretization time, there exists a plant-model mismatch that is handled by a surrogate model formulated as a mp(MI)QP.…”