Fault Tolerant Optimal Control of Sewer

Under the city of Barcelona, which has a population of three millions of habitants in an area of 98 Km, there is a complex sewage system with almost 1500 Km of length. That system is characterized for being unitary, that is, its collectors carry rain water and residual water. The yearly rainfall is not very high (600 mm/year), but it includes heavy storms typical of the Mediterranean climate that cause a lot of flooding problems and Combined Sewer Overflows (CSO) to the receiving waters. A control system capable of minimizing flooding and the amount of water going into the sea (pollution) is desirable, especially during important meteorological phenomena [4]. The corresponding actions of control have to be applied over the active components of the sewer system (retain tanks, derivation gates, pump stations). Currently, the Barcelona sewer network has a global control under development. The actuator set points are determined in function of the state of the entire system, that is, the information received from more than one hundred sensors (rain gauges and level sensors). Furthermore, the control strategy is obtained by minimizing flooding and pollution, optimizing other performance aspects (i.e. levels in real tanks) and including fault tolerance in sensors and/or actuators without severe losses in the system performance. The application of global control on the system requires the use of an operative model of the system dynamics and the network constrains to calculate, in a future horizon, optimal strategies to handle actuators taking into account the actual system state information (given by sensors connected to a SCADA) and an adequate rain prediction [4]. One of the aims of this paper is to develop an application of Optimal Control technique over a piece of Barcelona sewer network, which has a total surface of 22,6 Km. An important goal of this global control application is that it works effectively under very strong meteorological conditions. But it is possible that faults could appear in any of their sensors and/or malfunction of any of their derivation gates, retention gates or pump stations if these conditions are presented. Because of that, the sewer network optimal control should be fault tolerant [14]. Fault Tolerant Control (FTC) is a relatively new concept which aims at improving control performance by treating faults and exemptions in the operation of technical processes in a systematic way, see [2]. The robustness of feedback control systems gives rise to an implicit fault tolerance. Faults that occur under closed loop control are often compensated by the control action. The same applies when optimal control techniques are used. It has been furthermore demonstrated that even when knowledge of the fault is not available, when the estimation of external disturbances affecting the loop is performed in a special way and the input levels have hard constraints, the optimization-based controller automatically takes advantage of actuator redundancy when available, see [10]. The paper structure is the following: in Section 2, the fundamental considerations of applying optimal control procedures over a sewer network are presented and discussed. Section 3 discusses the inclusion of the fault tolerance into the optimal control framework. Some computer tools for simulation, analysis and control of sewer networks including fault tolerance are proposed in Section 4. In Section 5 some results obtained from one of these computer tools for the Barcelona sewer network are presented. Finally, conclusions and further work are presented in Section 6.