A study on the effectiveness of proportional-integral-derivative control in multi-actuated atomic force microscopy

Improving the speed of atomic force microscopes (AFM) enables the study of dynamic nano-scale processes and unlocks novel scientific discoveries. At the heart of AFM, performance of the sample scanner plays a crucial role in achieving this goal. Multi-actuated AFM scanners have been recently shown to achieve high scan speed, while maintaining a large scan range. Given the stringent requirements of high-speed AFM, control of these multi-component scanners can be quite challenging. The substantially variant dynamics of AFMs in different imaging conditions necessitates a flexible/robust control scheme which can maintain satisfactory tracking performance at high imaging speed. Due to their simplicity and easy adaptation to dynamics variations, PID controllers continue to be the control method of choice for state-of-the-art AFMs. To extend their application to multi-actuated AFMs, in this work we aim to understand the conditions under which a PID controller suffices to meet the requirements of high-speed/large-range atomic force microscopy. For this purpose, the desired characteristics of controllers obtained through H_∞-optimal design are investigated. It is then concluded that a PID controller combined with auxiliary compensators shares these characteristics and indeed meets the requirements of high-speed/large-range imaging. A simple data-based compensator design scheme is then presented. The proposed methodology is implemented on a multi-component AFM scanner.