Model predictive control based on an integrator resonance model applied to an open water channel

• A new simplified model for open water channels is introduced: the integrator resonance model.
• The IR model describes resonance-sensitive channels accurately.
• MPC׳s using different simplified models are compared in a simulation study.
• The IR-MPC outperforms the MPC׳s using commonly used models (ID, IDZ, IDF).
• The IR-MPC is tested on an actual open water channel.

This paper describes a new simplified model for controller design of open water channels that are relatively short, flat and deep: the integrator resonance model (IR model). The model contains an integrator and the first resonance mode of a long reflecting wave. The paper compares the integrator resonance model to the simplified models: integrator delay, integrator delay zero and filtered integrator delay and to the high-order linearized Saint-Venant equations model. Results of using the integrator resonance model in a model predictive controller applied in closed loop on a high-order non-linear Saint-Venant model of the first pool of the laboratory canal at Technical University of Catalonia, Barcelona are compared to the results of using the other simplified models in MPC. This comparison shows that the IR model has less model mismatch with the high order model regarding the relevant dynamics of these typical channels compared to the other simplified models. It is demonstrated that not considering the resonance behavior in the controller design may result in poor performance of the closed loop behavior. In order to demonstrate the validity of the simulation model used in this study, the controller using the IR model is also tested on the actual open water channel and compared to the results of the high-order non-linear Saint-Venant simulation model. The results of this comparison show a close resemblance between simulation model and real world system.