Abstract

This paper revisits the problem of global asymptotic positioning of uncertain motion systems subject to actuator constraint and friction. A simple model-free saturated control is proposed by incorporating a relay term driven by position error into proportional-derivative (PD) methodology. Lyapunov's direct method is employed to prove global asymptotic positioning stability. The appealing advantages of the proposed approach are that it is conceived within the framework of saturated PD (SPD) control methodology with intuitive structure and absence of modeling parameter and embeds the whole control action within a single saturation function. Benefitted from these advantages, the proposed approach omits the complicated discrimination of the terms that shall be bounded in several saturation functions of the commonly used design and permits easy implementation with an improved performance. An additive feature is that the proposed control has the ability to ensure that the actuator constraint is not breached and assures global asymptotic positioning stability in the presence of unknown friction. Numerical simulations and experimental validations demonstrate the effectiveness and improved performance of the proposed approach. The proposed approach provides a model-free solution for fast transient and high-precision steady-state positioning of uncertain motion systems subject to unknown friction and actuator constraint.

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