Adaptive Backstepping Control of Uncertain Gear Transmission Servosystems with Asymmetric Dead-Zone Nonlinearity

In this paper, an adaptive backstepping control scheme is presented to solve the position control problem for a gear transmission servosystem with unknown asymmetric sandwiched dead-zone nonlinearity. All the parameters involved in both the system and dead-zone models are allowed to be totally unknown. In contrast to the previous results where the effects of symmetric dead zone can be treated as additive disturbances in a transformed system, most of the unknown parameters of the transformed system are now time varying and dependent on the real-time value of relative displacement between the driving and driven gears. To deal with the above issue, new compensating terms in the quadratic form are introduced in the design of the virtual control signal for each recursive step. With the adaptive laws modified correspondingly, we can still show that all the closed-loop signals are ensured to be bounded and the output regulation error will converge to a compact set. Simulation results are provided to show the effectiveness of the proposed adaptive control scheme.