Robust adaptive fuzzy sliding mode control of nonlinear uncertain MIMO fluttering FGP plate based on feedback linearization

Abstract

In this study using an adaptive fuzzy sliding mode control (AFSMC) scheme, the robust stabilization of multi-input–multi-output (MIMO) nonlinear aero-elastic fluttering of the Functionally Graded Piezoelectric (FGP) plate in the presence of mismatched time-varying uncertainties have been investigated. It is assumed that the aerodynamic load is modeled by the first order piston theory and the piezoelectric patches are assumed to be bonded to the top and bottom surfaces of the plate in order to produce the controlling bending moment excitations. Using the airy stress function and applying the Hamilton's principle the governing coupled partial differential equations of motion are derived. Then considering the immovable simply supported edges boundary conditions and employing the aero-elastic multi-mode interactions and applying the Galerkin's method, the nonlinear coupled partial differential equations of motion are reduced to nonlinear ordinary differential equations in time. Then using the full state input-output feedback linearization technique, the nonlinear dynamics of the model is linearized and transformed into the multiple decupled single input-single output uncertain subsystems. In order to overcome the chattering phenomenon arises due to the sliding mode control (SMC) discontinuous inputs, a hybrid adaptive fuzzy sliding mode control technique is utilized to approximate the discontinuous synthetic control inputs. It is showed that considering the physical input limitations, the designed AFSMC control system, effectively suppress the fluttering motions in presence of the bounded external inaccuracies and it prevents the unwanted chattering of the subsystems inputs.