Fast setpoint tracking of an Atomic Force Microscope X−Y stage via optimal trajectory tracking

Acquiring Atomic Force Microscope images using compressed sensing requires the piezo X-Y stage to track a sequence of step commands. To achieve fast tracking of such commands requires a precise system model. We show that once such a model is obtained, standard linear feedback can be used to achieve excellent tracking of step inputs. The system under consideration has a significant amount of time delay, and we develop a computationally efficient state estimator for this scenario. We demonstrate that beyond a certain step size threshold, the control law attempts to violate actuator slew-rate limits, resulting in a severely deteriorated response. We then show how this can be overcome by tracking an optimal trajectory obtained by solving a constrained, finite horizon Linear Quadratic Regulator problem and demonstrate the feasibility of this approach experimentally.