OBSERVER-BASED CONTROL OF A DUAL-STAGE PIEZOELECTRIC SCANNER.

Despite its proven success in a wide variety of applications, the atomic force microscope (AFM) remains limited by its slow imaging rate. One approach to overcome this challenge is to rely on algorithmic approaches that reduce the imaging time not by scanning faster but by scanning less. Such schemes are particularly useful on older instruments as they can provide significant gains despite the existing (slow) hardware. At the same time, algorithms for sub-sampling can yield even greater improvements in imaging rate when combined with advanced scanners that can be retrofitted into the system. In this work, we focus on the use of a dual-stage piezoelectric scanner coupled with a particular scanning algorithm known as Local Circular Scan (LCS). LCS drives the tip of the AFM along a circular trajectory while using feedback to center that circle on a sample edge and to move the circle along the feature, thus reducing imaging time by concentrating the samples to the region of interest. Dual-stage systems are well-suited to LCS as the algorithm is naturally described in terms of a high-frequency, short range path (the scanning circle) and a slower, long range path (the track along the sample). However, control of the scanner is not straightforward as the system is multi-input, single-output. Here we establish controllability and observability of the scanning stage, allowing us to develop individual controllers for the long-range and short-range actuators through the principle of separation. We then use an internal model controller for the short range actuator to track a sinusoidal input (to generate the circular motion) and a state-space set-point tracking controller for the long range actuator. The results are demonstrated through simulation.