A fast transient tracking differentiator for high-precision motion systems

High-quality velocity signal plays an important role in fast and precise motion systems, but most commercially available motion systems are not commonly equipped with velocity sensors; hence, full access to the system states is impossible. A fast transient tracking differentiator is proposed in this article for obtaining the noise-less time derivative from a noisy measurement. The fast transient tracking differentiator is conceived within the framework of tracking differentiator methodology and is accomplished by integrating a power-like function with a smooth hyperbolic sine function. Tracking differentiator theory and Lyapunov direct method are employed to show the global asymptotic convergence. Advantages of the proposed fast transient tracking differentiator include the easy implementation with intuitive structure and high computational efficiency and faster transient and higher noise attenuation for both small and large initial estimation errors. The proposed fast transient tracking differentiator can be applied to a large class of motion systems by cascading to a robust output feedback proportional-derivative control for fast and high-precision positioning with position measurement only. Numerical simulation and real-time experimental comparisons demonstrate that the proposed approach provides an easygoing model-free output feedback solution for fast and accurate velocity reconstruction and high-performance positioning of uncertain motion systems with position measurement only.