Sensor Fusion for Improved Control of Piezoelectric Tube Scanners

In nanopositioning applications, capacitive or inductive sensors are used to measure displacement and provide feedback to eliminate actuator nonlinearity, dynamics, cross-coupling between axes, and thermal drift. Due to their noise density, typically 20 pm/root Hz for 100-mu m range transducers, feedback loops are restricted to a few tens of Hertz if nanometer precision is required. In this study, a capacitive displacement sensor is used with a piezoelectric strain voltage measurement to reduce sensor noise at frequencies above 1 Hz. The piezoelectric strain voltage is derived from an open-circuit electrode on a four-quadrant piezoelectric tube actuator and requires no additional hardware. The noise density of the piezoelectric strain voltage is measured to be three orders of magnitude lower than the capacitive sensor. This allows a large increase in closed-loop bandwidth with no penalty on sensor-induced noise. The advantageous properties of the capacitive sensor and piezoelectric strain voltage are discussed and utilized to design a Kalman filter that combines the two signals in a statistically optimal way. A receding horizon control strategy is then introduced as a technique for controlling the tube scanner. A wide-bandwidth controller is implemented that provides reference tracking and damping of the actuator resonance, with root-mean-square displacement noise below 0.4 nm.