About the classical and structural controllability and observability of a common class of activated sludge plants

In this work, the stability, controllability and observability properties of a class of activated sludge plants are analysed. Specifically, the five biological reactors and the secondary settler in the Benchmark Simulation Model no. 1 (BSM1) are studied. For the task, we represented the plant as a dynamical system consisting of 145 state variables, 13 controls, 14 disturbances and 15 outputs and as a complex networks to study its full-state controllability and observability properties from a structural and a classical point of view. By analysing the topology of the network, we show how this class of systems is controllable but not observable in a structural sense, and thus how it is controllable but not observable in a classical sense for almost all possible realisations. We also show how a linearisation commonly used in the literature is neither full-state controllable nor full-state observable in the classical sense. The control and observation efforts are quantified in terms of energy- and centrality-based based metrics.