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.
Keywords
Robust control, Multi model-Hinfinity synthesis, LMI, quasi-LPV modeling, Multi-observers, state feedback