An application of the fast gradient method to model predictive control of an atomic force microscope X-Y stage

Random sub-sampling imaging methods in Atomic Force Microscopy require the piezo X-Y stage to track a sequence of step inputs. Control slew-rate limits combined with linear feedback methods have been shown to limit achievable performance in this scenario. Due to its natural ability to account for actuation constraints, we consider the application of Model Predictive Control. By recasting the problem in an incremental form, the arising quadratic program takes a form that can be solved efficiently. Specifically, we solve an input constrained Model Predictive Control problem with 50 states, a control horizon of 12 samples, and a sample frequency of 25 kHz using the Fast Gradient Method. We present experimental results using the method applied to a nano-positioning stage.