Control Logic for Real Time Control of Flow in Combined Sewers

This paper presents a method for determining an optimal control strategy for the real time control of flow in combined sewer systems. The objective of this control is to minimize weighted flow diversions from the sewer system to the receiving waters during storm periods. The elements of a control system for combined sewers are described first. This is followed by a development of a reservoir model for combined sewer systems having weir and orifice controls at the regulator structures. An example, verified by the variational calculus, is given of an optimal control strategy that will minimize the weighted overflows from a system of three reservoirs. Examination of this optimal strategy and others presented in the literature shows that the optimal control strategy for this type of problem typically falls on constraint boundaries and includes jumps in the orifice controls from maximum to minimum positions. By formulating these common operating procedures into a set of rules it is shown that if the times at which the jumps in the orifice controls occur are known, then for a given set of inflow hydrographs the control strategy is completely defined. The determination of an optimal control is then reduced to finding the optimal times for the jumps in the orifice controls to occur. A procedure for this optimization is outlined and the results of its application to a system of ten reservoirs are presented. It is concluded that the method presented for the determination of an optimal control logic would be suitable for a system containing up to twenty control points and would ensure maximum utilization of available system storage capacity.