Gain-Scheduled Smith Predictor PID-Based LPV Controller for Open-Flow Canal Control

Abstract

In this paper, a gain-scheduled Smith Predictor PID controller is proposed for the control of an open flow canal system that allows to deal with large variation in operating conditions. A linear parameter varying (LPV) control oriented model for open-flow channel systems based on a Second Order Delay Hayami (SODH) model is proposed. Exploiting the second order structure of this model, an LPV PID controller is designed using  H and linear matrix inequalities (LMI) pole placement. The controller structure includes a Smith Predictor, real time estimated parameters from measurements (including the known part of the delay) that schedule the controller and predictor and unstructured dynamic uncertainty which covers the unknown portion of the delay. Finally, the proposed controller is validated in a case study based on a single real reach canal: the Lunax Gallery at Gascogne (France).

Fault detection and isolation in flat navigation canals

“…On the other hand, in order to cope with errors due to uncertainty in transport delays that are present in open-flow canal systems [18], following the ideas in [19], [20], the discrete residual has been computed as…”

On the LPV Control Design and Its Applications to Some Classes of Dynamical Systems

“…As an example, we consider the dam-gallery system analyzed in [8] and we focus on the transfer function between the upstream flow Q U and the downstream flow Q D . By using simplified Saint-Venant's equations, and choosing the downstream flow as scheduling parameter, this transfer function turns out to be, [8],…”

“…By using simplified Saint-Venant's equations, and choosing the downstream flow as scheduling parameter, this transfer function turns out to be, [8],…”

“…A stability analysis, omitted for brevity, shows that, with the polynomial coefficients reported in [8], system (15.24) is LPV stable. Therefore, Theorem 15.3 can be applied.…”

Linear parameter varying modeling and identification for real-time control of open-flow irrigation canals

“…On the other hand, an LPV Hayami model was proposed for fault detection and control purposes in (Blesa et al, 2010) and (Bolea et al 2013) with positive results. An equivalent modeling approach, named stateAuthors are with Automatic Control Department, Technical University of Catalonia (UPC).…”