Real-Time Optimization of The Wastewater Treatment Process Utilizing a Linear Approximation-Based Extremum Seeking

This paper presents a novel linear approximation-based extremum seeking (ES) scheme applied to real-time optimization of wastewater treatment process, to minimize a certain performance index. Unlike the conventional sinusoidal perturbation-based ES where the influence of the plant delay is disregarded by employing the perturbation extremely slow, and the gradient of the controlled plant map at the current operating point is estimated based on the output measurements only, the proposed ES compensate the plant delay to the input measurements by incorporating a delay compensator, and observes both the input and the output measurements such that an approximated gradient can be obtained via a linear approximation algorithm – Recursive Least Squares (RLS). The effectiveness of the linear approximation-based ES is evaluated through numerical simulations for a complex nonlinear wastewater treatment process model. With the delay compensator incorporated, the linear approximation-based ES performs better than the sinusoidal perturbation-based ES, particularly in some special circumstances (e.g., inflow quality deterioration). This is considered to be due to the faster convergence speed (i.e., the rate at which ES approaches the estimated optimum) and the more accurate convergence value (i.e., the estimated optimum). Meanwhile, without the delay compensator, the control performance degrades noticeably, which indicates the necessity of the delay compensation for the linear approximation-based ES.