LSTM-based IMC approach applied in Wastewater Treatment Plants: Performance and stability analysis

Wastewater treatment plants are industries where the reduction of residual water pollutant concentrations is performed. These kind of industries are characterised by applying highly complex and nonlinear biochemical and biological processes. Thus, some of the concentrations involved in these processes have to be controlled to assure that they are maintained at a given set-point. For that reason, different control strategies such as Proportional Integral (PI) controllers, Model Predictive Controllers (MPC), Fuzzy Logic or Internal Model Controllers (IMC) have been applied during the last years. However, the appearance of Artificial Neural Networks (ANNs) is changing this scenario. They have been adopted to predict certain WWTP parameters and then feed conventional controllers or even to implement some of them. Here, an IMC approach implemented uniquely with Long Short-Term Memory (LSTM) cells to model the direct and inverse models of the process under control is proposed. Furthermore, its stability conditions are computed adopting a data-based test since no mathematical expressions of the different models are considered. Results show that this approach is stable in the frequency region where it is operating. Besides, control performance shows that this IMC is able to significantly improve the Benchmark Simulation Model No.1 default PI control strategy.