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

This paper investigates the problem of controlling vibrations of nonlinear size-dependent functionally graded material micro beam tip. The modified couple stress theory is used to derive the equations of motion. The system’s partial equations are converted to a set of ordinary differential equations using Galerkin method. The system parameters are assumed to be unknown an the system is subjected to bounded disturbances. The purpose of the control algorithm is to establish an output tracking control based on the dynamic model of the micro beam system. The supply voltage of two in-plane electrodes are considered as the control input. Also a penalty signal is introduced to avoid high gain inputs. The stability of the controlled system, while the external disturbance is being rejected, is proved using Lyapunov function method. The response of the controlled system is simulated and presented for 5 modes of the Galerking method approximation.