Robust multivariable tracking control for biological wastewater treatment process with external disturbances and uncertainties

This paper proposes a robust multivariable tracking control (RMTC) strategy to address tracking control of the biological wastewater treatment process (BWWTP) with external disturbances and uncertainties. Primarily, the system of BWWTP, attributed to an ill-defined nonaffine nonlinear system, is directly expanded with Taylor series expansion in the neighborhood of the nominal control law (NCL). To achieve NCL, the RMTC is drawn with a direct controller and an approximate controller. The direct controller is introduced with sliding-mode theory while the structure of the system is unknown and no prior knowledge about external disturbances/uncertainties is available. The approximate controller is employed to compensate for the uncertainties of BWWTW with a suitable-sized fuzzy neural network that is tuned by a self-organizing mechanism. Then, an adaptive strategy is established to optimize the control gain and parameters of fuzzy neural network to hold the steady-state control performance under different operational conditions by suppressing the negative impacts of external disturbances and approximation errors. Finally, the stability of RMTC is established to ensure successful applications. The RMTC is evaluated in an actual BWWTP. The results including tracking performance, controlinputs, and adaptive parameters have shown that RMTC can provide effective control performance with the external disturbances and uncertainties under different operational conditions.