ResearchFields

Signal Transformation Approach to Nanopositioning

Use of feedback control is necessary for robust and desired performance of many nanopositioning applications such as high-density data-storage-devices. In linear feedback control systems, accurate positioning demands a high closed-loop bandwidth. However, structural uncertainties, resonance or unstable modes, non-minimum-phase characteristics, and measurement noise limit the achievable control bandwidth. Standard sensors used for nano-positioning typically have a noise density of 20pm/Hz0.5. The precision of positioning can be reduced 0.2nm, just due to sensor noise, for each hundredfold increase in closed-loop bandwidth. The aforementioned restriction on positioning precision due to sensor noise is a fundamental limitation of linear control systems.

Signal Transformation is a novel and promising approach to the foregoing limitation. In this method, appropriate mappings are incorporated in the control system such that the compensator just needs to follow a smooth ramp signal, while the reference signal is a non-smooth triangular trajectory (Fig. 1). These mappings take the burden of providing non-smooth actuation signals, which requires a high bandwidth in ordinary feedback systems, off the compensator transfer function. In this way, for a specified tracking performance, the control system with signal transformation can be designed with much less bandwidth than that of the ordinary feedback system. Thus, the part of sensor noise reflected into the real displacement by feedback (projected noise) is much less with signal transformation compared to the ordinary control system. Hence, using signal transformation, the positioning precision is increased beyond the linear control limits.

Fig. 1
Signal Transformation Method

In the original work on signal transformation, capability of the method for tracking of fast triangular waveforms was demonstrated with a considerably low bandwidth. We have also done a thorough analysis of the method, which gives necessary and sufficient stability conditions as well as sufficient conditions for performance improvement. The method was successfully implemented for Scanning Probe Microscopy, where a methodology was offered to incorporate robustness against plant uncertainties and disturbances (Fig. 2). We also managed to extend the method for tracking of reference signals with arbitrary profiles (not necessarily triangular), where nonlinear system theory becomes a must for analysis.

Fig. 2
Images of a calibration grating obtained by a scanning probe microscope. The bandwidths of fast axis controllers are adjusted to have projected noises with similar standard deviation of 0.11nm and use (a) Signal Transformation, and (b) Ordinary Feedback, respectively. The image distortion in figure (b), which is due to poor tracking of the ordinary low bandwidth feedback loop, is improved by signal transformation method (see figure (a)).

Signal transformation as a novel method has a number of problems, such as word-length limitation, transient, and unknown reference, which are solvable without compromising its noise rejection benefit. Our objective in this project is to solve these problems while applying the method to achieve better performances in applications such as probe-based microscopy and data-storage devices.