Enhanced robust nanopositioning control for an X-Y piezoelectric stage with sensor delays: An infinite dimensional [formula omitted] optimization approach

Abstract

In nanopositioning systems with capacitive displacement sensors, the analog-to-digital (A/D) conversion time is not negligible, particularly for the sub-nano resolution cases with 16 (or more) digital bits. The sensor induced delay will complicate modeling and control of such systems, due to the infinite dimensionality of the delay block. In this paper, we analyze the piezoelectric nanopositioner with a Hammerstein-like model incorporating uncertainties and a measurement delay. An infinite dimensional H∞ control approach is proposed for robust and nanopositioning control of the piezoelectric stage. To eliminate the fragility problem of the H∞ controller on its implementation, an equivalent structure including a Finite Impulse Response (FIR) filter is derived, and the matrix-function-based rational approximation (MFRA) for the FIR filter is presented. Real time experiments with the proposed control method are conducted where the positioning performance, robustness, and hysteresis compensation capability are comprehensively evaluated. Comparative studies demonstrate significant improvements over conventional methods such as Proportional–Integral–Derivative (PID) control and the finite dimensional robust control.