PID tuning of a multivariable activated sludge process with nitrification and denitrification with multi-objective optimization

Wastewater treatment plants (WWTPs) are responsible of attenuating the environmental impact that waste in effluent discharged to receiving waters has. As a consequence of this, new techniques for an effective control are valuable, not just for minimising this impact, but also for minimising operational costs using efficiently the energy usage. Such kind of problems, with several objectives to fulfil (and usually in conflict) are termed as multi-objective problems.

Within this context, multi-objective optimisation techniques have shown to be a valuable tool in the control engineering field to tune different kinds of controllers for complex systems. To accomplish this, a simultaneous optimisation approach is carried on, in order to approximate a set of Pareto-optimal solutions. Such solutions differ in the level of trade-off exhibited in two (or more) conflicting objectives.

The multi-objective approach for controller tuning in one-input/one-output processess is well documented in the literature. Nevertheless, that is not the case of multivariable control. This fact is mainly due to the quantity of design objectives required to evaluate the multi-objective performance of several outputs. In this work we elaborate a proposal to handle multi-objective problems for multivariable processes. Performance evaluation is performed (via simulation) in a multivariable benchmark for the PID control of an activated sludge process with nitrification and denitrification.