Active vibration control for a flexible string system with input backlash

In this study, the authors are concerned with the active vibration control of a flexible string system with input backlash. For vibration suppression, active control is applied at the right boundary of the flexible string. To deal with the input backlash, a novel ‘disturbance‐like’ term is proposed in the control design. A physically motivated Lyapunov function is employed to design boundary control law to ensure the vibration suppression and guarantee the stability of the closed‐loop system. Numerical simulations illustrate the effectiveness of the proposed control method.