Identification, control and hysteresis compensation of a 3 DOF metrological AFM

Abstract

Atomic Force Microscopes (AFMs) are widely used for the investigation of samples at the nanometer scale. The metrological AFM used in this work uses a 3 degrees-of-freedom (DOFs) stage, driven by piezo-stack actuators, for sample manipulation in combination with a fixed cantilever. The piezostack actuators suffer from hysteresis, which acts as a nonlinear disturbance on the system and/or can change the system dynamics. The contributions of this paper are the application of feedback control to all 3 DOFs of the metrological AFM and the design and application of a hysteresis feedforward for the asymmetric hysteresis present in the system. The amount of coupling between the DOFs is assessed by a non-parametric multiple-input-multipleoutput (MIMO) identification. Since the dynamics appear to be decoupled in the frequency range of interest, feedback controllers are designed for each DOF separately. For the modeling of the asymmetric hysteresis an extended Coleman-Hodgdon model is proposed. This model is used for feedforward compensation of the hysteresis. The combination of feedback control for all DOFs and the asymmetric hysteresis feedforward enables the AFM to track scanning profiles within the sensor bound of 5 nm. Real-time imaging of the sample is possible with an accuracy of 2 nm.

A Survey of Modeling and Control of Piezoelectric Actuators

“…Recent researches adopting this scheme can be found, e.g. in [136] a hysteresis compensator based on the inverse Preisach hysteresis model was used as the feedforward controller to compensate for hysteresis whist a PID feedback controller was used to account for other effects, in [137] a inverse nonlinear differential equation hysteresis model was used as the feedforward controller and a PI controller was used as a feedback controller, and in [16] a inverse extended Coleman-Hodgdon model was used as the feedforward controller and a feedback controller designed via loop shaping techniques was employed.…”

“…The multi-DOF PEA-driven positioning systems reported in the literature can be divided in to two categories: series mechanisms and parallel mechanisms. Among which, multi-DOF PEA-driven series mechanisms [16] and the xyz-type parallel mechanisms (translations along x-, y-and z-axis) such as those in [16,[158][159][160] can usually be treated as a series of individual 1-DOF PEAdriven mechanisms without significant coupling between the moving axes, as such their modeling and control can be well address with the techniques applied to the single-DOF systems.…”

“…For the first kind of workflows, a kinematic model is firstly constructed based on the geometric structure of the mechanism, and then either a phenomenological [114] or physical [160] dynamic model can be established based on the kinematic model. The second kind of workflows involves direct identification of the dynamic model of the mechanism without establishing the kinematic model [16].…”

“…PEA-driven positioning systems have also been developed with various configurations, for example, 1-degree-of-freedom (1-DOF) positioning systems with flexure hinge mechanisms [11,12], stick-slip actuators [13], multiple PEAs-driven inchworms [14], or walking actuators [15]; multi-DOF positioning systems with series mechanism [16], parallel mechanism [17], or stick-and-clamping actuators [18]. In all positioning control applications, the hysteresis and creep effects of PEAs have shown to be able to significantly degrade the system performance and even system stability [19].…”

Self-tuning of a switching controller for scanning motion systems

“…This is because one controller is used for both operating conditions and thus performance is compromised. Other examples of nonlinear control in the given context include optical storage [10] and hard disk drives [16], or hysteresis feedforward control in atomic force microscopes [17].…”