Simultaneous Design of Positive Acceleration Velocity and Position Feedback Based Combined Damping and Tracking Control Scheme for Nanopositioners

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

“…To this end, the denominator coefficients seen in Table 1 are rewritten in terms of a system of matrix equations. The method is based on nonlinear optimisation, in which a sophisticated objective function, as seen in Equation ( 16), is comprised of Equations ( 14) and (15). It should be noted that the objective function originates from matrixial representation (12) of the characteristic polynomial in a closed-loop system.…”

“…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.…”

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

“…To ensure the broadest possible positioning bandwidth – the key goal of any control scheme aimed at nanopositioning applications, this paper reports a simultaneous design of the PAVPF‐based damping and tracking control scheme. The paper builds on the preliminary results presented in [36] by: (1) Presenting the full theoretical design of the employed simultaneous PAVPF damping and integral tracking control scheme. (2) Optimising the controller parameters of both the PAVPF damping and integral tracking controllers using a recursive analytical method. (3) Showcasing extensive experimental results validating the practically achieved frequency and time‐domain positioning performance of the proposed control scheme, thereby demonstrating the superiority of the proposed scheme over the traditional sequential design. …”