Discussion on synthesis of non linear spatio-temporal systems with unstable zeros dynamics

Abstract

This paper deals with multivariable control problem of spatio-temporal systems modelled by non linear partial differential equations (PDEs). SISO control of distributed parameter systems (DPS) can be achieved either by late or by early approaches. In practice, there are mainly two reasons why MIMO control of DPS, which can provide an analytical law of a distributed controller, could be impossible by late approach. The reasons are: coupled input variables located in boundary conditions and tracking problems caused by unstable zero dynamics. Early approach allows approximating a state feedback design control by reducing the DPS in lumped model. In this case, it is important to note that input/output exact linearization control technique is the most attractive approach for its distinctive simplicity. However, for several choices of output variables, tracking control cannot be achieved. Such limits are generally fully understood to non experts with non linear control theory. In this work, two state feedback control laws would be studied to avoid tracking problems for non linear spatio-temporal systems having unstable zero dynamics. It is shown that, for large scale systems, synthesis of state feedback control using linear matrix inequalities (LMI) tools can provide more systematic procedure than exact linearizing approach. A simulated example is providing to show comparison between exact and numerical linearizing control techniques.