Interval State Estimation Based on Ellipsoid for Wastewater Treatment Bioprocess

In this paper, a two-stage state interval estimation method is proposed for the basic process of microbial growth in wastewater treatment based on an
$L_{\infty}$
observer and set-membership technique. Firstly, the continuous-time nonlinear microbial growth model is converted to a discrete time Takagi-Sugeno (T-S) fuzzy system to deal with nonlinearities. Next, an
$L_{\infty}$
T-S fuzzy observer is designed for the generated T-S fuzzy uncertain system to generate the state point estimation, then the interval bounds of state estimation error is calculated by combining with ellipsoidal analysis. Furthermore, the interval estimation of the state for the bioprocess in wastewater treatment can be derived from the point estimate of the state and the range of error in state estimation. Ultimately, the effectiveness of the proposed approach of the interval state estimation for wastewater treatment bioprocess is confirmed through simulation.