Tunable linear feedback control of urban drainage systems using models defined purely from data

Abstract

Real-time and model-predictive control promises to make urban drainage systems (UDS) adaptive, coordinated, and dynamically optimal. Though early implementations are promising, existing control algorithms have drawbacks in computational expense, trust, system-level coordination, and labor cost. Linear feedback control has distinct advantages in computational expense, interpretation, and coordination. However, current methods for building linear feedback controllers require calibrated software models. Here we present an automated method for generating tunable linear feedback controllers that require only system response data. The controller design consists of three main steps: (1) estimating the network connectivity using tools for causal inference, (2) identifying a linear, time-invariant (LTI) dynamical system which approximates the network, and (3) designing and tuning a feedback controller based on the LTI urban drainage system approximation. The flooding safety, erosion prevention, and water treatment performance of the method are evaluated across 190 design storms on a separated sewer model. Strong results suggest that the system knowledge required for generating effective, safe, and tunable controllers for UDS is surprisingly basic. This method allows near-turnkey synthesis of controllers solely from sensor data or reduction of process-based models. HIGHLIGHTS Connectivity is automatically identified among water level sensors and valves solely using response data.; Inferred connectivity and response data are used to train linear feedback controllers.; Controllers built purely from data prevent flooding and greatly improve water treatment.;

Keywords

• causal inference
• data-driven methods
• gray-box models
• linear feedback control
• model discovery
• real-time control