Keywords

Introduction

Controlling motion of an actuator to within a single atom, known as nanopositioning, may seem as an impossible task. Yet, it has become a key requirement in many systems to emerge in recent years. In scanning probe microscopy nanopositioning is needed to scan a probe over a sample surface for imaging and to control the interaction between the probe and the surface during interrogation and manipulation (Meyer et al. 2004). Nanopositioning is the enabling technology for mask-less lithography tools under development to replace optical lithography systems (Vettiger et al. 2002). Novel nanopositioning tools are required for positioning of wafers and for mask alignment in the semiconductor industry (Verma et al. 2005). Nanopositioning systems are vital in molecular biology for imaging, alignment, and nanomanipulation in applications such as DNA analysis (Meldrum et al. 2001) and nanoassembly (Whitesides and Christopher Love 2001). Nanopositioning is an important technology in optical alignment systems (Krogmann 1999). In data storage systems, nanometer-scale precision is needed for emerging probe-storage devices, for dual-stage hard-disk drives, and for next generation tape drives (Cherubini et al. 2012).

The Need for High-Speed Nanopositioning

In all applications of nanopositioning, there is a significant and growing demand for high speeds. The ability to operate a nanopositioner at a bandwidth of tens of kHz, as opposed to today’s hundreds of Hz, is the key to unlocking countless technological possibilities in the future (Gao et al. 2000; Pantazi et al. 2008; Salapaka 2003; Sebastian et al. 2008b; Yong et al. 2012). The atomic force microscope (AFM) is an example of such technologies. A typical commercial atomic force microscope is a slow device, taking up to a minute or longer to generate an image. Such imaging speeds are too slow to investigate phenomena with fast dynamics. For example, rapid biological processes that occur in seconds, such as rapid movement of cells or fast dehydration and denaturation of collagen, are too fast to be observed by a typical commercial AFM (Zou et al. 2004). A key obstacle in realizing high-speed and video-rate atomic force microscopy is the limited speed of nanopositioners.

The Vital Role of Feedback Control in High-Speed Nanopositioning

The systems described above depend on a precision mechatronic device, known as a nanopositioner, or a scanner for their operation. A high-speed scanner is shown in Fig. 1. In all applications where nanopositioning is a necessity, the key objective is to make the scanner follow, or track, a given reference trajectory (Devasia et al. 2007). A large number of control design methods have been proposed for this purpose, including feedforward control (Clayton et al. 2009), feedback control (Salapaka 2003), and combinations of those (Yong et al. 2009). These control techniques are required in order to compensate for the mechanical resonances of the scanner as well as for various nonlinearities and uncertainties in the dynamics of the nanopositioner. At low speeds, feedforward techniques are usually sufficient to address many of the arising challenges. However, over a wide bandwidth, model uncertainties, sensor noise, and mechanical cross-couplings become significant, and hence feedback control becomes essential to achieve the requisite nanoscale accuracy and precision at high speeds (Devasia et al. 2007; Salapaka 2003).

Control for High-Speed Nanopositioning, Fig. 1
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A 3DoF flexure-guided high-speed nanopositioner (Yong et al. 2013). The three axes are actuated independently using piezoelectric stack actuators. Movement of lateral axes is measured using capacitive sensors

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Control Design Challenges

A feedback loop typically encountered in nanopositioning is illustrated in Fig. 2. The purpose of the feedback controller is to control the position of the scanner such that it follows a given reference trajectory based on the measurement provided by a displacement sensor. The resulting tracking error contains both deterministic and stochastic components. Deterministic errors are typically due to insufficient closed-loop bandwidth. They may also arise from excitation of mechanical resonant modes of the scanner or actuator nonlinearities such as piezoelectric hysteresis and creep (Croft et al. 2001). The factors that limit the achievable closed-loop bandwidth include phase delays and non-minimum phase zeros associated with the actuator and scanner dynamics (Devasia et al. 2007). The dynamics of the nanopositioner, the controller, and the reference trajectory selected for scanning play a key role in minimizing the deterministic component of the tracking error.

Control for High-Speed Nanopositioning, Fig. 2
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A feedback loop typically encountered in nanopositioning. Purpose of the controller is to control the position of the scanner such that it follows the intended reference trajectory based on the position measurement obtained from a position sensor

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Tracking errors of a stochastic nature mostly arise from external noise and vibrations and from position measurement noise. External noise and vibrations can be significantly reduced by operating the nanopositioner in a controlled environment. However, dealing with the measurement noise is a significant challenge (Sebastian et al. 2008a). The feedback loop allows the sensing noise to generate a random positioning error that deteriorates the positioning precision. Increasing the closed-loop bandwidth (to decrease the deterministic errors) tends to worsen this effect. Low sensitivity to measurement noise is, therefore, a key requirement in feedback control design for high-speed nanopositioning and a very hard problem to address.

Summary and Future Directions

While high-precision nanoscale positioning systems have been demonstrated at low speeds, despite an intensive international race spanning several years, the longstanding challenge remains to achieve high-speed motion and positioning with Ångstrom-level accuracy. Overcoming this barrier is believed to be the necessary catalyst for emergence of ground breaking innovations across a wide range of scientific and technological fields. Control is a critical technology to facilitate the emergence of such systems.