On the controllability of activated sludge plants

In this work, the full-state controllability properties of a biological wastewater treatment plant are analysed. Specifically, the five biological reactors in the Benchmark Simulation Model no. 1 are studied. For the task, we represented the activated sludge plant as a dynamical system consisting of 65 states, 7 controls and 27 disturbances as a complex network and we studied its controllability properties from a classical and a structural point of view. By analysing the topology of the network, we show how the system is controllable in the structural sense and thus how it is controllable in the classical sense for almost all realisations of its parameters. Interestingly, we also found that the linearisation around a fixed point commonly used in the literature leads to a realisation of the system that is not full-state controllable in the classical sense. We show how this realisation is controllable if the state variables associated with inert matter are not considered. We quantify the compound and individual control efforts of this reduced-order system in terms of energy-based controllability metrics.