A Robust Disturbance Rejection Method for Uncertain Flexible Mechanical Vibrating Systems Under Persistent Excitation

This paper presents a robust disturbance rejection method for a class of flexible mechanical vibrating systems with time-varying parameter perturbations subject to persistent excitation. The control input is split into two parts as a common strategy: one is obtained from the regulator design that is responsible for primary stabilization; the other is assigned to cancel the effect of the persistent excitation. The states of controlled dynamics and excitation dynamics are estimated by a Kalman filter. Then, taking into account plant variations, a robust stability condition is proposed to ensure the stability of the resulting closed system. It is shown that, using the proposed stability condition, the designed controller can effectively suppress the persistent excitation and keep the flexible mechanical system from the possibility of instability caused by spillover and time-varying parameter perturbations. Finally, two examples are given to demonstrate the use of the design method.