Tracking control of a nanopositioner using complementary sensors

Piezoelectric tube actuators are widely used in atomic force and scanning tunneling microscopy (STM) for nanoscale positioning. There has been a consistent effort to increase the scan speed of these actuators using feedback control techniques. A feedback controller requires a measurement of the scanner's deflection, which is often provided by a capacitive sensor. Such measurements are corrupted by sensor noise, typically in the order of 20 pm/√Hz rms. Over a bandwidth of 10 kHz, this translates into an rms noise of 2 nm, clearly inadequate for applications that require subnanometer positioning accuracy, e.g., STM. In this paper, we illustrate how the strain voltage induced in a free electrode of the scanner can be used as an additional displacement signal. The noise level corresponding to the strain signal is about three orders of magnitude less than that of a capacitive sensor, making it an ideal choice for nanopositioning applications. However, it cannot be used for dc and low-frequency measurements. A two-sensor-based controller is designed to use the capacitive sensor signal at low frequencies, and the strain displacement signal at high frequencies. By limiting the capacitive sensor feedback loop bandwidth to less than 100 Hz, the rms value of the noise is reduced to well below 1 nm. For almost the same noise level, the two-sensor-based control structure achieves a closed-loop bandwidth of more than three times that of the single-sensor-based controller.