Modulated–demodulated control: Q control of an AFM microcantilever

We outline the application of modulated–demodulated control to the quality (Q) factor control of an atomic force microscope microcantilever. We review the modulated–demodulated control technique, emphasize its linear time invariant nature and develop state space representations of the controller for design and analysis. The modulated–demodulated controller can be configured as both positive position feedback (PPF) and resonant controllers, which are effective in the control of negative imaginary systems. Negative imaginary systems theory has important application in the control of collocated mechanical systems and we briefly summarize the key relevant results. A high-frequency, tunable modulated–demodulated controller, designed specifically for MHz operation, was developed for experimental validation. The modulated–demodulated controller enables the use of a low-bandwidth baseband controller in the configuration of a high-bandwidth controller, thus simplifying the implementation of high-bandwidth controllers. We outline the controller characterization and demonstrate closed-loop control of a Bruker DMASP microcantilever. We also present AFM images highlighting the improvements in scan speed and image quality achieved as a result of Q control. Modulated–demodulated control appears well suited to the control of high-frequency resonant dynamics. In addition to high-speed atomic force microscopy, we believe this control technique may find applications in high-frequency microelectromechanical systems (MEMS).