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.

No abstract

No abstract

This paper presents a method to extend the eigenstructure assignment based design of the Positive Position Feedback (PPF) damping controller to the family of well-known second-order Positive Feedback Controllers (PFC) namely: (i) the Positive Velocity and Position Feedback (PVPF) and (ii) the Positive Acceleration Velocity and Position Feedback (PAVPF) using appropriate eigenstructure assignment. This design problem entails solving a set of linear equations in the controller parameters using Linear Matrix Inequalities (LMI) to specify a convex design constraint. These damping controllers are popularly used in tandem with a tracking controller (typically an integrator) to deliver high-bandwidth nanopositioning performance. Consequently, the closed-loop performance of all three controllers (PPF, PVPF and PAVPF) employed in tandem with suitably gained integral tracking loops is thoroughly quantified via relevant performance metrics, using measured frequency response data from one axis of a piezo-stack actuated x-y nanopositioner.