Two degree of freedom control for nanopositioning systems: Fundamental limitations, control design, and related trade-offs

This paper studies and analyzes fundamental trade-offs between positioning resolution, tracking bandwidth and robustness to modeling uncertainties in two-degree-offreedom (2DOF) control designs for nanopositioning systems. The analysis of these systems is done in optimal control setting with various architectural constraints imposed on the 2DOF framework. In terms of these trade-offs, our analysis shows that the primary role of feedback is providing robustness to the closed-loop device whereas the feedforward component is mainly effective in overcoming fundamental algebraic constraints that limit the feedback-only designs. This paper presents (1) an optimal prefilter model matching design for a system with an existing feedback controller and (2) a simultaneous feedforward and feedback control design in an optimal H _∞ mixed sensitivity framework. The experimental results on applying these controllers show a significant improvement, as high as 330% increase in bandwidth for similar robustness and resolution level over optimal feedback-only designs. Other performance objectives are similarly improved.We demonstrate that the 2DOF freedom design achieves performance specifications that are analytically impossible for the feedback-only design.