Development and identification of a reduced-order dynamic model for wastewater treatment plants

Wastewater treatment plants (WWTPs) employ a series of complex chemical and biological processes, to transform an influent stream of contaminated water to an effluent suitable for return to the water cycle. To optimize the performance of WWTP control schemes, appropriate mathematical models capable of accurately simulating the plant dynamic behavior are essential. However, the development of reliable dynamic representations for these large-scale plants is challenging, mainly because of the complex biological reactions taking place and the significant fluctuations in the disturbances that affect the operation of WWTPs. First-principles models, such as the well-known benchmark simulation model no. 1 (BSM1), may be capable of capturing the highly nonlinear nature of WWTPs, but this comes at the cost of employing complex, high-order representations of the reactive units and settling processes. This complexity leads to highly complicated configurations that cannot be efficiently integrated in advanced process control schemes, like model predictive controllers (MPCs). Furthermore, the large number of unknown parameters in these models, along with the non-convex nature of the underlying functions, renders the use of conventional system identification techniques insufficient. To remedy these issues, in this work we introduce a reduced-order first-principles model for WWTPs, incorporating low order mathematical models for the chemical phenomena of the reactive units and the settling procedure. Furthermore, we present a novel system identification scheme, which is based on a customized cooperative particle swarm optimization approach; the scheme effectively handles the high-dimensionality and multimodality of the underlying nonlinear optimization problem, enabling accurate estimation of the model parameters. Comparison results between the dynamic behavior of the original BSM1 and the identified reduced-order model, indicate that the proposed approach is capable of accurately and robustly capturing the highly nonlinear nature of WWTPs, while being simple enough for incorporation in the design of MPC and other advanced control schemes. This represents a significant advancement over traditional models, offering a more practical and efficient approach for WWTP management and control.