Vibration control of a Timoshenko beam system with input backlash

In this study, a novel boundary control algorithm is designed for a class of Timoshenko beams with unknown external disturbance and uncertain input backlash non-linearity. The Timoshenko beam is described by partial differential equations as governing equations and ordinary differential equations as boundary conditions. The representation of input backlash is modified as a desired control input associated with input non-linear error, which will be transformed into the external disturbance. The unknown `disturbance-like´ item is defined based on input error and disturbance, and the boundary of this unknown `disturbance-like´ item will be estimated by a disturbance observer. The unknown backlash can be handled and the ultimately uniform stability of the closed-loop system is ensured. Numerical simulations are provided to verify the performance of the author´s proposed control.