Robust Model Predictive Control with Signal Temporal Logic constraints for Barcelona Wastewater System

Abstract

We propose a traceable approach for the control of the Barcelona wastewater system that is subject to sudden weather-change events within the Mediterranean climate. Due to the unpredictable weather changes, lack of appropriate control methodologies may result in overflow in the sewage system, which causes environmental contamination (pollution). In order to improve the management of the wastewater system and to reduce the contamination, we propose robust model predictive control, which is an online control approach that designs the control actions (i.e., flows through network actuators) under the worst-case scenario while minimizing the associated operational costs. We employ signal temporal logic to specify the desired behavior of the controlled system once an overflow occurs and encode this behavior as constraints so that the synthesized controller reacts in time to decrease and eliminate the overflow. We apply our proposed technique to a representative catchment of the Barcelona wastewater system to illustrate its effectiveness.

Model predictive control of urban drainage systems: A review and perspective towards smart real-time water management

“…Some less common objectives include: -Adherence to specific flow references (that is, a desired flow at a specific location in the network) (Cembrano et al, 2004) or a certain basin filling degree (Joseph-Duran et al, 2014b;Mollerup et al, 2016). -Minimization of the operational costs by, for example, minimizing the control action itself (Farahani et al, 2017;Garc ıa et al, 2015;Ocampo-Martinez et al, 2007. This can also be applied to on/off control by using discrete states (Leirens et al, 2010).…”

“…-Preservation of system behaviors that are not included in the internal MPC model, such as ensuring that overflows can only occur from filled basins and that the set-points of local controllers are respected (Pleau et al, 1996) or including transport time in pipes (Fiorelli and Schutz, 2009;Fiorelli et al, 2013). -Duration of overflow (Farahani et al, 2017).…”

“…4) can be used to target peak minimization . Most studies have either applied entirely linear or entirely quadratic terms in the objective function, although some (Cembrano et al, 2004;Farahani et al, 2017;Gelormino and Ricker, 1994;Mailhot et al, 1999;) applied a mixture.…”

“…However, this only includes a fixed decrease in the trust in forecast over time. Farahani et al (2017) also include input uncertainty in the objective function, but in a time-varying manner that allows for the optimization of the "worst case scenario". A complete representation of the time-varying trust in forecasts can be included by, for example, applying stochastic gray-box models (Breinholt et al, 2011(Breinholt et al, , 2012 or by wrapping an uncertainty propagation layer around the existing deterministic models in the form of Monte Carlo simulations (Sch€ utze et al, 2004).…”

Formal controller synthesis for wastewater systems with signal temporal logic constraints: The Barcelona case study

“…This approach incorporates integer variables towards performing a modeling selection within the control structure. In our previous work (Farahani et al, 2017b), we studied a small part of BTC with only 3 tanks. In the current paper, we consider the full model of BTC, as presented in Ocampo-Martinez (2010), to show that our method is both scalable and efficient for formally synthesizing control inputs for the system.…”