Optimal control of eutrophication for a reservoir: The linear quadratic regulation approach

A new approach based on linear quadratic regulation (LQR) method is applied in this study to evaluate control strategies being decided by the optimal load reduction rates of influent nutrient for eutrophication management in a reservoir, Due to dynamic fluctuations occurring in the reservoir, proper adjustment of control strategies to the variations in water quality becomes necessary. Hence, to yield optimum results, a dynamic control strategy for the reservoir is needed. Feitsui Reservoir in northern Taiwan is used as a case study for the the models developed, Monitoring data obtained from Feitsui Reservoir is employed to verify the proposed method. A time invariant state-space eutrophication model is adopted in this study to predict the trophic state in the reservoir. The eutrophication model includes five water quality constituents (chlorophyll-a, NH3-N, NO2-N, NO3-N and PO4-P) and the LQR method is extended to the multi-variable system. Water quality in tl:le reservoir is found to be mainly influenced by pollutants from nonpoint sources, particularly from agricultural activities. Moreover, hydrologic condition is also found to signifiicantly affect the trophic state. The trophic state in the reservoir is predicted by using the eutrophication model in combination with an ARMA (autoregressive/moving average) inflow model. Results of this study show that the state-space eutrophication model can predict water qualities well with limited data. Also, optimal dynamic control enables the reservoir operator to maintain the trophic level below a certain trophic state. The advantages of the proposed approach include: 1) the versatility of dealing with the multi-variable system, and 2) an efficient and economic management through dynamic optimization scheme for the control of reservoir eutrophication.