Linear Matrix Inequality approach to designing damping and tracking control for nanopositioning application

Adedayo Kayode Babarinde; Sumeet S. Aphale

doi:10.3390/vibration5040050

Linear Matrix Inequality approach to designing damping and tracking control for nanopositioning application

Adedayo Kayode Babarinde, Sumeet S. Aphale^* (Corresponding Author)

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	846-859
Number of pages	14
Journal	Vibration
Volume	5
Issue number	4
DOIs	https://doi.org/10.3390/vibration5040050
Publication status	Published - 29 Nov 2022

Bibliographical note

This article belongs to the Topic Advances in Piezoelectric/Ultrasonic Sensors and Actuators

Funding Information:
RW reports lecture fees from NovoNordisk and travel grants from Eli Lilly. He served on the advisory board of Akcea Therapeutics. In addition to his current work, ALB reports lecture fees from Astra Zeneca, Boehringer Ingelheim, and NovoNordisk. He served on the advisory boards of Astra Zeneca, Boehringer Ingelheim, and NovoNordisk. Besides his current work, AF reports lecture fees and advisory board membership from Sanofi, Novo Nordisk, Eli Lilly, and AstraZeneca. In addition to his current work, MH reports research grants from Boehringer Ingelheim and Sanofi (both to the University Hospital of Tübingen) and lecture fees from Amryt, Lilly, Novo Nordisk, Sanofi, and Boehringer Ingelheim. He also served on an advisory board for Boehringer Ingelheim. None of the other authors report conflicts of interest directly related to the contents of this work.

Publisher Copyright:
© 2022 by the authors.

Keywords

damping
eigen-vector assignment
linear matrix inequality
nanopositioning

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10.3390/vibration5040050

Cite this

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title = "Linear Matrix Inequality approach to designing damping and tracking control for nanopositioning application",

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.",

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author = "Babarinde, {Adedayo Kayode} and Aphale, {Sumeet S.}",

note = "This article belongs to the Topic Advances in Piezoelectric/Ultrasonic Sensors and Actuators Funding Information: RW reports lecture fees from NovoNordisk and travel grants from Eli Lilly. He served on the advisory board of Akcea Therapeutics. In addition to his current work, ALB reports lecture fees from Astra Zeneca, Boehringer Ingelheim, and NovoNordisk. He served on the advisory boards of Astra Zeneca, Boehringer Ingelheim, and NovoNordisk. Besides his current work, AF reports lecture fees and advisory board membership from Sanofi, Novo Nordisk, Eli Lilly, and AstraZeneca. In addition to his current work, MH reports research grants from Boehringer Ingelheim and Sanofi (both to the University Hospital of T{\"u}bingen) and lecture fees from Amryt, Lilly, Novo Nordisk, Sanofi, and Boehringer Ingelheim. He also served on an advisory board for Boehringer Ingelheim. None of the other authors report conflicts of interest directly related to the contents of this work. Publisher Copyright: {\textcopyright} 2022 by the authors.",

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N2 - 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.

AB - 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.

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KW - linear matrix inequality

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JF - Vibration

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ER -

Linear Matrix Inequality approach to designing damping and tracking control for nanopositioning application

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