Parallel Distributed Compensation for the Control of Processes in Anaerobic Organic Wastewater Treatment

The aim of the present investigation is to develop a simple approach for the design of a fuzzy logic controller (FLC) based on a derived Takagi-Sugeno-Kang (TSK) plant model using the principle of parallel distributed compensation (PDC) in order to improve the control of the biogas production rate in the anaerobic organic wastewater treatment. A fifth order nonlinear model that fits the experimental data from a laboratory bioreactor is used to study via simulation the plant step responses for two boundary values of the main disturbance - the initial organic load. Two TSK plant models are obtained to approximate the step responses via genetic algorithms minimization of the modelling error. Each TSK model is built of a Sugeno model with plant output as input and three outputs – the membership functions of belonging of the plant output to three linearization zones. The local plant in each zone is modelled by time-lags. Then two PDC on the same Sugeno models are designed with local linear PI controllers tuned with respect to the corresponding local linear plant model. Another Sugeno model with input the concentration of the initial organic waste distributes by weighted average the plant output to the inputs of the Sugeno models of the two PDC. The PDC based system shows via simulation a reduced dynamic error compared to a designed model-free Mamdani PI FLC.