On SISO and MIMO variable structure controlo f non linear distributed parameter systems: application to fixed bed reactors

This paper deals with the design of variable structure control of distributed parameter systems. The control problem is discussed in relation to a model consisting of a set of non-linear, time varying partial differential equations of hyperbolic type. A formulation of a Single Input–Single Output (SISO) variable structure controller based on the distributed parameter model (late lumping control) is given. An extension to the Multiple Input–Multiple Output (MIMO) case is derived when the control variables are coupled and located on boundary conditions. A theoretical proof of DPS convergence in sliding mode is given. A fixed bed bioreactor in which drinkable water is treated, was used as a simulated example to prove the effectiveness of the control design. The bioreactor must control the harmful component concentrations in such a way that the quality of water fulfils international standards.