Model-based feedback controller design for dual actuated atomic force microscopy

In atomic force microscopy (AFM) the imaging speed is strongly limited by the bandwidth of the feedback loop that controls the interaction force between the measurement tip and the sample. A significant increase in closed-loop bandwidth without sacrificing positioning range can be achieved by combining a long-range, low-bandwidth actuator with a short-range, high-bandwidth actuator, forming a dual actuated system. This contribution discusses the design of a model-based feedback controller that controls the tip-sample force in dual actuated AFM. Special emphasis is given on guaranteeing robust stability of the feedback loop under influence of variations in the dynamical behavior of the system, and to prevent strong destructive interference between both actuators. To prevent instability of the feedback loop due to saturation of the short-range actuator, an anti-windup controller is presented that robustly stabilizes the system under all imaging conditions. The designed feedback controller is implemented on a prototype dual actuated AFM system, and demonstrates a disturbance rejection bandwidth of 20 kHz, which is about 20 times faster than the model-based controlled single actuated system. AFM images are obtained verifying a significant reduction of force variations between the tip and the sample while imaging. The faster control of the tip-sample force reduces the residual tracking error and, thus, reduces the chance of damage or wear of the tip and the sample, and allows for faster imaging.