Disturbance rejection control for vibration suppression of smart beams and plates under a high frequency excitation

•Complete the disturbance rejection control for vibration control of smart structures.•Vibrations excited by high frequency disturbances are suppressed.•GPI observers were developed, which perform excellent dynamic characteristics.•Lyapunov and Riccati approaches were compared for observer gain design.•Two methods were investigated for the design of control gains.

This paper aims to perfect the method of Disturbance Rejection (DR) control, based on our earlier published work (Zhang et al. 2014 [1]), for vibration suppression of smart structures under high frequency periodic disturbances. Two observation structures are discussed, namely Proportional-Integral (PI) observer which uses step functions as the fictitious model of disturbances and Generalized PI (GPI) observer which can employ any nonlinear functions. In order to stabilize the PI or GPI observer, Lyapunov and Riccati approaches are implemented and discussed. Furthermore, approximate and exact solutions are developed for obtaining control gains. These various possibilities of DR control are simulated and compared with each other, as well as those obtained by conventional control strategies, PID and LQR control.