Adaptive backstepping control of gear transmission systems with elastic deadzone

This paper deals with the tracking control problem of uncertain transmission systems in the presence of elastic deadzone. Due to the derivative term in the elastic deadzone model, it is not straightforward to apply the backstepping control for the elastic system which is not in strict feedback form. To overcome this limitation, the system is first transformed into two cascaded subsystems and an adaptive backstepping controller is proposed based on the transformed cascaded system. The stability analysis is carried out within the framework of Lyapunov functions and shows that all the states of the closed-loop system are bounded and the tracking error is uniformly ultimately bounded. Finally, simulations are presented to demonstrate the performance of the controlled system.