High Precision Over Long Range: A Macro–Micro Approach to Quantized Positioning Systems

This article proposes a macro-micro approach to deal with sensor quantization in positioning systems. First, a control strategy able to asymptotically drive the quantized (macro) actuator toward an oscillatory motion around the desired reference is presented. A microactuator is, then, added to compensate for these oscillations so that the reference is asymptotically tracked. Besides theoretical guarantees, the proposed strategy is validated in an experimental setup and proved able to achieve a steady-state tracking error within
$\pm 0.2~\mu \text{m}$
when subject to a sensor quantization level of
$5~\mu \text{m}$
. Perfect knowledge of the system parameters is not necessary to design and implement the proposed control strategy, which relies on the internal model principle and makes use of traditional frequency domain tools.