Experimental validation of the simultaneous damping and tracking controller design strategy for high‐bandwidth nanopositioning – a PAVPF approach

Abstract

For scanning applications, damping and tracking controllers are employed in a dual‐loop fashion. Whilst these damping and tracking controllers are designed sequentially in literature (damping first, tracking later), it has been found that the tracking controller (typically integral or proportional–integral) influences the ‘desired’ pole locations (and thereby its damping performance) achieved by the positive acceleration, velocity and position feedback (PAVPF) damping controller. This work starts by first highlighting this unwanted effect that results in low positioning bandwidth. To address this drawback, this work presents the design, analysis and experimental validation of the simultaneous design method for the PAVPF control‐based combined damping and tracking scheme, aimed at achieving accurate, high‐bandwidth nanopositioning. It also details a recursive analytical method to simultaneously optimise the damping and tracking controller parameters resulting in almost a three‐fold increase in closed‐loop bandwidth when compared with the traditional sequential method. To further confirm the advantages of the proposed simultaneous design method, comparative experimental results conducted on one axis of a piezo‐actuated nanopositioner are presented. Significant improvements in the steady‐state positioning as well as transient response are noted. These improvements combined, result in significant gains in the raster scanning performance of nanopositioning stages.

How Far Should Poles Be Placed? Selecting Positive Feedback Controllers for Damping and Tracking Applications: A Complete Characterisation

“…where γ 1 , ω 1 and ζ 1 are the first resonant mode numerator constant, resonant frequency, damping ratio, respectively, and d f is the feed-through term, which accounts for truncation effects. In order to dampen the dominant resonant mode of such systems, a family of positive feedback controllers have been developed, namely PPF (Positive Position Feedback) [27], PVPF (Positive Velocity Position Feedback) [22], PAVPF (Positive Acceleration Velocity Position Feedback) [16] and IRC (Integral Resonant Control) [23]. In this work, the primary focus is the positive feedback controller consisting of PPF through to PAVPF.…”

“…Once these are found, they can be substituted into Equation ( 25), which will yield the correction optimisation problem for K and, hence, the correct choice of K. This will be shown in detail for each controller type in this paper. Moreover, in the following section, the open-loop system is generated from experimentally sourced frequency response data based on the nanopositioner system at the University of Aberdeen [16].…”

“…A detailed model of the nanopositioner axis is established from experimental frequency response data (FRD) from the University of Aberdeen's nanopositioner [15,16]. The model consists of the combination of four-second-order resonance models for each significant mode in the experimental system, one first-order low pass filter for the amplifier in the experimental setup, another first-order low pass filter for the sensor measuring the experimental setup, a second-order Padé model to account for the small time delay in the system and lastly, a Bouc-Wen hysteresis model.…”

“…Another family of second-order damping controllers that are typically implemented in a positive feedback configuration are also equally popular. This group consists of the Positive Position Feedback (PPF), the Positive Velocity Position Feedback (PVPF) and Positive Acceleration Velocity Position Feedback (PAVPF) [13][14][15][16]. Successful application of these Positive Feedback Controllers (PFCs) is well-documented throughout relevant literature.…”

Research on Active Repetitive Control for Tracking Lissajous Scan Trajectories with Voice Coil Motors Actuated Fast Steering Mirror

“…The nonlinearity of piezoelectric actuator has been identified online and compensated for using singularity-free neural networks. A. K. Babarinde et al [30] proposed the design, analysis, and experimental validation of the simultaneous method for a positive acceleration, velocity, and position feedback control-based combined damping and tracking scheme. C. Chang [31] proposed a four-degree-of-freedom (DOF) actuator for FSM compensation systems to compensate for 4-DOF laser errors.…”