Resonant control of an atomic force microscope micro-cantilever for active Q control

Abstract

Active Q control may be used to modify the effective quality (Q) factor of an atomic force microscope (AFM) micro-cantilever when operating in tapping mode. The control system uses velocity feedback to obtain an effective cantilever Q factor to achieve optimal scan speed and image resolution for the imaging environment and sample type. Time delay of the cantilever displacement signal is the most common method of cantilever velocity estimation. Spill-over effects from unmodeled dynamics may degrade the closed loop system performance, possibly resulting in system instability, when time delay velocity estimation is used. A resonant controller is proposed in this work as an alternate method of velocity estimation. This new controller has guaranteed closed loop stability, is easy to tune, and may be fitted into existing commercial AFMs with minimal modification. Images of a calibration grating are obtained using this controller to demonstrate its effectiveness.

Sensorless Implementation of a PPF Controller for Active <inline-formula> <tex-math notation="TeX">$Q$ </tex-math></inline-formula> Control of an AFM Microcantilever

“…By representing the piezoelectric shunt control system in block diagram form, as shown in Fig. 3, the transfer function from the applied voltage v s to tip displacement d is determined to be [11] …”

“…Tapping mode AFM has a relatively slow scan speed compared with alternative imaging modes. The maximum obtainable scan speed is limited by the bandwidth of the z-axis feedback loop, which is inversely proportional to the quality (Q) factor of the sensing cantilever [8]- [10]. Significant increases in scan speed have been demonstrated with the use of active Q control to reduce the cantilever Q factor [8]- [11].…”

“…The time delay controller may have a spill-over effect [12] on higher order resonance modes of the cantilever, which may lead to a reduction in scan speed rather than an increase, and in some cases result in instability of the cantilever [10], [13]. For this reason, researchers have developed other control techniques to modify the cantilever Q factor such as observer-based control [14], resonant control [10], and piezoelectric shunt control [11], [15].…”

“…For this reason, researchers have developed other control techniques to modify the cantilever Q factor such as observer-based control [14], resonant control [10], and piezoelectric shunt control [11], [15]. Passive piezoelectric shunt control has an advantage over both observer-based control and resonant control in that the optical sensor [16], typically used to measure cantilever deflection, is removed from the active Q control feedback loop.…”

“…Therefore, elimination of this sensor from the feedback loop is an advantage. In [11], we demonstrated the advantages of using passive piezoelectric shunt control to decrease the cantilever Q factor for increased scan speeds when imaging in air. There is a limitation to how far the cantilever Q factor may be reduced using this technique due to the passive nature of the shunt impedance used.…”