Assuming the flow pattern of aeration tank to be a perfect mixing, the optimal conditions for the design of multistage aeration unit and final sedimentation vessel of the activated sludge process were investigated using a combined method of the discrete maximum principle and the Fibonacci search method. The objective function of the process was taken as the sum of the volumes of multistage aeration unit and final sedimentation vessel, and the control variables were the volumes of the vessels and the amounts of the return sludge to each stage.
The following results were obtained.
1. The sum of the volumes of the aeration unit and final sedimentation vessel could be reduced to 67.6 % and 58.6 % in the case of two-staged and three-staged aeration unit, respectively, compared to that of one-staged aeration unit of the process.
2. The return sludge was to be introduced only to the first stage of the multistage aeration unit according to the optimization calculation, which coincided with the practical operation in the current plants.
3. The volumes of the each stage of the aeration unit were to be almost equal.
The biological basic data used in this paper were taken from the original papers reported by T. Takamatsu and others^2）.