Multicriteria Pole Clustering and H₂/H_inf Control of Regular Singular System

In this paper, a multicriteria control combining H₂/H_inf techniques, and pole clustering under strict linear matrix inequalities (LMI) solving is considered to achieve the design of a static state feedback controller. This robust control targets regular singular systems subject to uncertainties. We have studied the D-admissibility of a pencil matrix, which is an extension of D-stability concept to singular systems, to formulate the clustering pole in LMI regions as an LMI optimization problem. In order to apply this control synthesis strategy, a methaniser process with complex nonlinear model is used. A multivariable representation of an AM2 model for this biological process is determined to study governability. A transformation of the same AM2 model into a singular form allows to study the controllability of the slow and fast subsystems and check the regularity of the system. The simulation results of the controlled methane flow rate shows an important improvement during the methanization phase.