On SISO and MIMO variable structure control of 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. (C) 2003 Elsevier Ltd. All rights reserved.