Robust adaptive vibration control of a nonlinear functionally graded micro-beam based on couple stress theory

This paper investigates the problem of controllingvibrations of nonlinear size-dependent functionally gradedmaterial micro beam tip. The modified couple stress theoryis used to derive the equations of motion. The system’spartial equations are converted to a set of ordinarydifferential equations using Galerkin method. The systemparameters are assumed to be unknown an the system issubjected to bounded disturbances. The purpose of thecontrol algorithm is to establish an output tracking controlbased on the dynamic model of the micro beam system. Thesupply voltage of two in-plane electrodes are considered asthe control input. Also a penalty signal is introduced toavoid high gain inputs. The stability of the controlledsystem, while the external disturbance is being rejected, isproved using Lyapunov function method. The response ofthe controlled system is simulated and presented for 5modes of the Galerking method approximation.