Adaptive Control for a Flexible Manipulator with Backlash

In this paper, we consider a flexible manipulator system with unknown backlash nonlinearity. By introducing a smooth backlash inverse function, the control input is divided into an expected input and a compensation error, and then a symbolic function is proposed to deal with this error. Subsequently, the direct Lyapunov method is utilized to prove the system's bounded stability. Finally, simulation results illuminate the effectiveness of the derived control.