Multi-model based robust LPV-Hinfinity control and observation design of non linear multivariable three tank system

Abstract

• This paper deals with a design a robust multi-variable control technique based on a multi-model (MM)  Linear Parameter  Varying (LPV)  approach  coupled with  «H? »  synthesis.  The  developed  technique is applied to a three-tanknon linear  system  (NL).  The first part concerns  the modeling of the three-tank  system by  using  two  approaches (MMbased on linearization (MM-L) around several equilibrium points and MM quasi Linear Parameters Varying (MM-qLPV)polytopic  approach.  The second part is  devoted to the design of two control  laws:  a  multivariable  polytopic  state feedback  control and  a  robust multivariable  MM-Hinfinity  control by dynamic output  feedback  (using  MM  polytopic formulation  and Linear Matrix Inequalities (LMI)).  Indeed, these control laws are based on the development of several local controllers (one controller per local model).  Then, with a convex polytopic  formulation,  the  MM approachcombines  these controllers to form a global controller that stabilizes the complete  non linear  system.  Besides, a  multi-observer  (MM based observer) is used to estimate the  immeasurable states.  Finally, the two synthesized global controllers are applied to the water level regulation of the  previously modelled three-tank  system.  Furthermore, a comparison between the robust performances of these two controllers is made in nominal and disturbed modes.