This article presents the design, identification, and control of a nano-positioning device suited to image biological samples as part of an atomic force microscope. The device is actuated by a piezoelectric stack and its motion is sensed by a linear variable differential transformer. It is demonstrated that the conventional proportional-integral control architecture does not meet the bandwidth requirements for positioning. The design and implementation of an H∞ controller demonstrates substantial improvements in the positioning speed and precision, while eliminating the undesirable nonlinear effects of the actuator. The characterization of the resulting device in terms of bandwidth, resolution, and repeatability provided illustrates the effectiveness of the modern robust control paradigm.

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Scale formation presents an enormous cost to the global economy. Classical nucleation theory dictates that to reduce the heterogeneous nucleation of scale, the surface should have low surface energy and be as smooth as possible. Past approaches have focused on lowering surface energy via the use of hydrophobic coatings and have created atomically smooth interfaces to eliminate nucleation sites, or both, via the infusion of lowsurface-energy lubricants into rough superhydrophobic substrates. Although lubricant-based surfaces are promising candidates for antiscaling, lubricant drainage inhibits their utilization. Here, we develop methodologies to deposit slippery omniphobic covalently attached liquids (SOCAL) on arbitrary substrates. Similar to lubricant-based surfaces, SOCAL has ultralow roughness and surface energy, enabling low nucleation rates and eliminating the need to replenish the lubricant. To enable SOCAL coating on metals, we investigated the surface chemistry required to ensure high-quality functionalization as measured by ultralow contact angle hysteresis (<3°). Using a multilayer deposition approach, we first electrophoretically deposit (EPD) silicon dioxide (SiO 2 ) as an intermediate layer between the metallic substrate and SOCAL. The necessity of EPD SiO 2 is to smooth (<10 nm roughness) as well as to enable the proper surface chemistry for SOCAL bonding. To characterize antiscaling performance, we utilized calcium sulfate (CaSO 4 ) scale tests, showing a 20× reduction in scale deposition rate than untreated metallic substrates. Descaling tests revealed that SOCAL dramatically decreases scale adhesion, resulting in rapid removal of scale buildup. Our work not only demonstrates a robust methodology for depositing antiscaling SOCAL coatings on metals but also develops design guidelines for the creation of antifouling coatings for alternate applications such as biofouling and high-temperature coking.

This paper studies and analyses fundamental trade-offs between positioning resolution, tracking bandwidth, and robustness to modeling uncertainties in two-degree-of-freedom (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, (2) a simultaneous feedforward and feedback control design in an optimal mixed sensitivity framework, and (3) a 2DOF optimal robust model matching design. The experimental results on applying these controllers show a significant improvement, as high as 330% increase in bandwidth for similar robustness and resolution over optimal feedback-only designs. Other performance objectives can be improved similarly. We demonstrate that the 2DOF freedom design achieves performance specifications that are analytically impossible for feedback-only designs.

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