PD-like Regulation of Mechanical Systems with Prescribed Bounds of Exponential Stability

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PD-like Regulation of Mechanical Systems with Prescribed Bounds of Exponential Stability

the Point-to-Point Case

Journal Article (2021)

Author(s)

Davide Calzolari (Technische Universität München, Deutsches Zentrum für Luft- und Raumfahrt (DLR))

Cosimo Della Santina (Deutsches Zentrum für Luft- und Raumfahrt (DLR), TU Delft - Learning & Autonomous Control, Technische Universität München)

Alin Albu-Schaffer (Deutsches Zentrum für Luft- und Raumfahrt (DLR), Technische Universität München)

Research Group

Learning & Autonomous Control

PID control Measurement Robotics Convergence Lyapunov methods PD control Tensors Manifolds Mechanical systems Lyapunov methods.

DOI related publication

https://doi.org/10.1109/LCSYS.2020.3046538 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:300b1e53-b55d-44fe-83a4-f9c30f93a507

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Publication Year

2021

Language

English

Research Group

Learning & Autonomous Control

Bibliographical Note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Journal title

IEEE Control Systems Letters

Issue number

6

Volume number

5

Pages (from-to)

2102-2107

Downloads counter

159

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Institutional Repository

Abstract

This letter discusses an extension of the famous PD regulator implementing point to point motions with prescribed exponential rates of convergence. This is achieved by deriving a novel global exponential stability result, dealing with mechanical systems evolving on uni-dimensional invariant manifolds of the configuration space. The construction of closed loop controllers enforcing the existence of such manifolds is then discussed. Explicit upper and lower bounds of convergence are provided, and connected to the gains of the closed loop controller. Simulations are carried out, assessing the effectiveness of the controller and the tightness of the exponential bounds.