A controlled sewer system should be treated as a sampled data system with events

Arguments are presented in favor of modeling sewer systems and in particular Dutch sewer systems as a sampled data system with events. Basic limitations on controlling these systems when ignoring their hybrid nature are stated. The traditional control scheme for the Dutch systems is given as an example of event driven local control. Basic limitations on systems using a sampled data approach without an event driven component are derived. To provide context a brief description of a sampled data controller for a sewer system based on set-point tracking is given. This is followed by an explanation of how the absence of event driven control limits its effectiveness.Water Resource

Stability of a Class of Controllers for a Sequence of Canals and Structures

Networks of open channels form an important category of environmental systems. They are used not only to transport irrigation and drainage water, but also as highways for barges transporting raw materials and goods. Automatic control of these systems poses specific problems. A local stability analysis for an open canal that is split into several parts by sluice gates under discrete time control is proposed. Theoretical justification is provided, and the method is tested for a simple controller. The method allows the examination of local stability of a series of canals when equipped with a controller from a large class, linear and non-linear. The analysis is based on the analysis of the eigenvalues of a matrix derived from the controlled system that is small enough to allow for parameter optimization.Water ResourcesTeam DeSchutte

Graph theory algorithms for real time control of a sewer network

Many Dutch sewer networks are combined sewer systems, they carry both stormwater and foul water. They consist of multiple sub-networks, linked by pumps into a tree structure with the Waste Water Treatment Plant as its root. Within sub-networks sewage transport is by gravity driven flow. Usually the original design assumed local control. Later changes, additions and extensions sometimes reduced the effectiveness of the original design. In these cases central control can improve the performance of the system without costly new construction. We apply two algorithms from graph theory, one is based on stable flows in time, the other on quickest evacuation flows. Results on local control are included to provide a lower bound on performance. A linear programming problem based of a perfect forecast of the whole event provides an upper bound on performance.Water Resource

Capturing the uncertainty about a sudden change in the properties of time series with confidence curves

The representation of uncertainty in results is an important aspect of statistical techniques in hydrology and climatology. Hypothesis tests and point estimates are not well suited for this purpose. Other statistical tools, such as confidence curves, are better suited to represent uncertainty. Therefore three parametric methods to construct confidence curves for the location of a sudden change in the properties of a time series, a change point (CP), are analyzed for three distributions: log-normal, gamma, and Gumbel. Two types of change are considered: a change in the mean and a change in the standard deviation. A question that confidence curves do not answer is how likely the null hypothesis of ‘no change’ is. A possible statistic to help answer this question, denoted by Un, is introduced and analyzed. It is compared to the statistic that underlies the Pettitt test. All methods perform well in terms of coverage and confidence set size. One method is based on the profile likelihood for a CP, the other two, first defined in this article, on the pseudolikelihood for a CP. The main advantage of the pseudolikelihood over the profile likelihood lies in the much lower computational cost. The confidence curves generated by the three methods are very similar. In a limited test on time series of measurements found in the literature, the methods gave results that largely matched those reported elsewhere. Some results are also given for an order one autoregressive series with a lognormal marginal distribution.</p

Balancing Waste Water Treatment Plant Load Using Branch and Bound

The problem of smoothing dry weather inflow variations fora Waste Water Treatment Plant (WWTP) that receives sewage frommultiple mixed sewer systems is presented, together with a first roughsolution algorithm. A simplification followed by a naive translation intoa zero-one linear programming problem results in 1152 inequalities for480 binary variables.Water Resource

Realizing Steady Supply to a Treatment Plant from Multiple Sources

In sewer systems sewage from different areas is often treated in a shared Waste Water Treatment Plant (WWTP). Currently the flows from different areas are usually determined by needs local to that area. During dry weather this may result in large variations in the flow into the WWTP. There are two reasons why this may be undesirable. Due to design peculiarities of some WWTP’s this may disrupt the treatment process and necessitate the use of additional energy and chemicals. In other cases areas are connected to the same pressurized transport pipe line, so energy costs may be higher when multiple stations use the line at the same time. Due to the daily variation in the sewage flow from domestic and light industrial sources, limits on temporary in system storage and due to limitations on the range of discharges the pumps can deliver, minimizing the flow variations can be a complex problem. Under the assumption of a periodic inflow sufficient conditions for the existence of a solution are given. The conditions imply the existence of a repeatable pattern of a length less than a day.Water Resource

Water System Examples for Control Education

Management of water systems is becoming more and more complex; this creates opportunities for the application of control theory. These opportunities are the subject of a course on operational water management given to students of the water management department, Delft University of Technology, over the past 15 years. Traditional examples in control theory courses are taken from industry and do not easily map to water systems, so examples were developed that use water systems to illustrate control theory concepts. This provided the students with a link between control theory and water management practice.Water ResourcesTeam DeSchutte

A test of stability rules for a series of identical canals

Water Resource

The properties of negation and zero in ringoids as defined by Kulisch

In [1,2] Kulisch defines (ordered) ringoids and vectoids to provide a theoretical basis for computer arithmetic and interval arithmetic. One interesting aspect of his treatment is the search for necessary and sufficient conditions for a meaningful notion of negation and zero. In this paper we consider this both from the point of view of functions on the underlying set and from a category theoretical standpoint. It turns out that the conditions provided by Kulisch can be restated in other forms, but that the original form is probably both necessary and sufficient for the intended purpose.Water Resource