Repository logo

Optimal control of flow in combined sewer systems




Bell, Peter Warren Wentworth, author
Water Resource Systems Program, Department of Civil Engineering, Colorado State University, publisher

Journal Title

Journal ISSN

Volume Title


This study examines the development of a suitable control logic for the real time control of flow in combined sewer systems. The approach followed is based on continuous time optimal control theory. The combined sewer system is modelled as a series of interconnected reservoirs having both weir and orifice controls. Using this model as a basis the state equations and inequality constraints of the system are then presented. The objective function chosen is that of minimizing weighted flow diversions from the system. Application of the calculus of variations to the minimization problem yields necessary conditions for an optimal control. These necessary conditions are examined and solution forms for the optimal control strategies for several configurations and system inflows are derived. The problem of numerical solution of the necessary conditions is examined and it is concluded that in general their solution is too cumbersome for practical use. An alternative control solution is proposed, based on operating rules derived from the common factors shown to exist in the previously examined solution forms. When combined with a first order gradient search technique these operating rules yield an optimal control strategy. Results of application of this technique to systems of four reservoirs and ten reservoirs are presented. They show that a satisfactory control strategy for up to twenty control points can be obtained within the time limits imposed by real time operation. A further example is presented showing the effects of information errors on the true optimality of a computed control strategy. Finally the necessary modification to the necessary conditions for an optimal control in which there are time delays in the flow routing are presented. It is shown that the change in operating rules amounts to a shift in time scales between reservoirs. It appears that the approach outlined herein is a feasible solution to the problem of real time control of flow in combined sewers.


May 1974.

Rights Access


Combined sewers
Fluid dynamics -- Mathematical models


Associated Publications