---
_id: '22206'
abstract:
- lang: eng
  text: <jats:title>Abstract</jats:title><jats:p>We consider tracking control for
    multibody systems which are modeled using holonomic and non-holonomic constraints.
    Furthermore, the systems may be underactuated and contain kinematic loops and
    are thus described by a set of differential-algebraic equations that cannot be
    reformulated as ordinary differential equations in general. We propose a control
    strategy which combines a feedforward controller based on the servo-constraints
    approach with a feedback controller based on a recent funnel control design. As
    an important tool for both approaches, we present a new procedure to derive the
    internal dynamics of a multibody system. Furthermore, we present a feasible set
    of coordinates for the internal dynamics avoiding the effort involved with the
    computation of the Byrnes–Isidori form. The control design is demonstrated by
    a simulation for a nonlinear non-minimum phase multi-input, multi-output robotic
    manipulator with kinematic loop.</jats:p>
author:
- first_name: Thomas
  full_name: Berger, Thomas
  last_name: Berger
- first_name: Svenja
  full_name: Drücker, Svenja
  last_name: Drücker
- first_name: Lukas Johannes
  full_name: Lanza, Lukas Johannes
  id: '78640'
  last_name: Lanza
- first_name: Timo
  full_name: Reis, Timo
  last_name: Reis
- first_name: Robert
  full_name: Seifried, Robert
  last_name: Seifried
citation:
  ama: Berger T, Drücker S, Lanza LJ, Reis T, Seifried R. Tracking control for underactuated
    non-minimum phase multibody systems. <i>Nonlinear Dynamics</i>. 2021. doi:<a href="https://doi.org/10.1007/s11071-021-06458-4">10.1007/s11071-021-06458-4</a>
  apa: Berger, T., Drücker, S., Lanza, L. J., Reis, T., &#38; Seifried, R. (2021).
    Tracking control for underactuated non-minimum phase multibody systems. <i>Nonlinear
    Dynamics</i>. <a href="https://doi.org/10.1007/s11071-021-06458-4">https://doi.org/10.1007/s11071-021-06458-4</a>
  bibtex: '@article{Berger_Drücker_Lanza_Reis_Seifried_2021, title={Tracking control
    for underactuated non-minimum phase multibody systems}, DOI={<a href="https://doi.org/10.1007/s11071-021-06458-4">10.1007/s11071-021-06458-4</a>},
    journal={Nonlinear Dynamics}, author={Berger, Thomas and Drücker, Svenja and Lanza,
    Lukas Johannes and Reis, Timo and Seifried, Robert}, year={2021} }'
  chicago: Berger, Thomas, Svenja Drücker, Lukas Johannes Lanza, Timo Reis, and Robert
    Seifried. “Tracking Control for Underactuated Non-Minimum Phase Multibody Systems.”
    <i>Nonlinear Dynamics</i>, 2021. <a href="https://doi.org/10.1007/s11071-021-06458-4">https://doi.org/10.1007/s11071-021-06458-4</a>.
  ieee: T. Berger, S. Drücker, L. J. Lanza, T. Reis, and R. Seifried, “Tracking control
    for underactuated non-minimum phase multibody systems,” <i>Nonlinear Dynamics</i>,
    2021.
  mla: Berger, Thomas, et al. “Tracking Control for Underactuated Non-Minimum Phase
    Multibody Systems.” <i>Nonlinear Dynamics</i>, 2021, doi:<a href="https://doi.org/10.1007/s11071-021-06458-4">10.1007/s11071-021-06458-4</a>.
  short: T. Berger, S. Drücker, L.J. Lanza, T. Reis, R. Seifried, Nonlinear Dynamics
    (2021).
date_created: 2021-05-17T05:24:00Z
date_updated: 2022-01-06T06:55:29Z
doi: 10.1007/s11071-021-06458-4
language:
- iso: eng
publication: Nonlinear Dynamics
publication_identifier:
  issn:
  - 0924-090X
  - 1573-269X
publication_status: published
status: public
title: Tracking control for underactuated non-minimum phase multibody systems
type: journal_article
user_id: '78640'
year: '2021'
...
---
_id: '16709'
author:
- first_name: Tuhin
  full_name: Sahai, Tuhin
  last_name: Sahai
- first_name: Adrian
  full_name: Ziessler, Adrian
  last_name: Ziessler
- first_name: Stefan
  full_name: Klus, Stefan
  last_name: Klus
- first_name: Michael
  full_name: Dellnitz, Michael
  last_name: Dellnitz
citation:
  ama: Sahai T, Ziessler A, Klus S, Dellnitz M. Continuous relaxations for the traveling
    salesman problem. <i>Nonlinear Dynamics</i>. 2019. doi:<a href="https://doi.org/10.1007/s11071-019-05092-5">10.1007/s11071-019-05092-5</a>
  apa: Sahai, T., Ziessler, A., Klus, S., &#38; Dellnitz, M. (2019). Continuous relaxations
    for the traveling salesman problem. <i>Nonlinear Dynamics</i>. <a href="https://doi.org/10.1007/s11071-019-05092-5">https://doi.org/10.1007/s11071-019-05092-5</a>
  bibtex: '@article{Sahai_Ziessler_Klus_Dellnitz_2019, title={Continuous relaxations
    for the traveling salesman problem}, DOI={<a href="https://doi.org/10.1007/s11071-019-05092-5">10.1007/s11071-019-05092-5</a>},
    journal={Nonlinear Dynamics}, author={Sahai, Tuhin and Ziessler, Adrian and Klus,
    Stefan and Dellnitz, Michael}, year={2019} }'
  chicago: Sahai, Tuhin, Adrian Ziessler, Stefan Klus, and Michael Dellnitz. “Continuous
    Relaxations for the Traveling Salesman Problem.” <i>Nonlinear Dynamics</i>, 2019.
    <a href="https://doi.org/10.1007/s11071-019-05092-5">https://doi.org/10.1007/s11071-019-05092-5</a>.
  ieee: T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for
    the traveling salesman problem,” <i>Nonlinear Dynamics</i>, 2019.
  mla: Sahai, Tuhin, et al. “Continuous Relaxations for the Traveling Salesman Problem.”
    <i>Nonlinear Dynamics</i>, 2019, doi:<a href="https://doi.org/10.1007/s11071-019-05092-5">10.1007/s11071-019-05092-5</a>.
  short: T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).
date_created: 2020-04-16T14:05:04Z
date_updated: 2022-01-06T06:52:55Z
department:
- _id: '101'
doi: 10.1007/s11071-019-05092-5
language:
- iso: eng
publication: Nonlinear Dynamics
publication_identifier:
  issn:
  - 0924-090X
  - 1573-269X
publication_status: published
status: public
title: Continuous relaxations for the traveling salesman problem
type: journal_article
user_id: '47427'
year: '2019'
...
---
_id: '8924'
abstract:
- lang: eng
  text: In forced systems with cyclic symmetry localization can occur due toparameter
    uncertainties. Often, Monte-Carlo simulations are used to findregions, where the
    system response is sensitive to parameteruncertainties. These simulations require
    a large computation time.Therefore, an approximate method to calculate the envelopes
    of thefrequency response functions is developed in this paper. An example of anonlinear
    system with cyclic symmetry is a bladed disk assembly withfriction dampers. Friction
    dampers can be installed underneath the bladeplatforms of turbine blades. Due
    to dry friction and the relative motionbetween blades and dampers, energy is dissipated,
    which results in areduction of blade vibration amplitudes. By optimizing the mass
    of thefriction dampers, the best damping effects are obtained, which lead toan
    increase in the reliability of the turbine. In this paper, thecalculated response
    of a mistuned bladed disk assembly with frictiondampers is discussed. An approximate
    method is developed to calculatethe envelopes of the corresponding frequency response
    function forstatistically varying eigenfrequencies of the blades. Regions wherelocalization
    can occur with a high probability, are calculated by thismethod.
author:
- first_name: Walter
  full_name: Sextro, Walter
  id: '21220'
  last_name: Sextro
- first_name: Karl
  full_name: Popp, Karl
  last_name: Popp
- first_name: Tomasz
  full_name: Krzyzynski, Tomasz
  last_name: Krzyzynski
citation:
  ama: Sextro W, Popp K, Krzyzynski T. Localization in Nonlinear Mistuned Systems
    with Cyclic Symmetry. <i>Nonlinear Dynamics</i>. 2001;25(1-3):207-220. doi:<a
    href="https://doi.org/10.1023/A:1012915002568">10.1023/A:1012915002568</a>
  apa: Sextro, W., Popp, K., &#38; Krzyzynski, T. (2001). Localization in Nonlinear
    Mistuned Systems with Cyclic Symmetry. <i>Nonlinear Dynamics</i>, <i>25</i>(1–3),
    207–220. <a href="https://doi.org/10.1023/A:1012915002568">https://doi.org/10.1023/A:1012915002568</a>
  bibtex: '@article{Sextro_Popp_Krzyzynski_2001, title={Localization in Nonlinear
    Mistuned Systems with Cyclic Symmetry}, volume={25}, DOI={<a href="https://doi.org/10.1023/A:1012915002568">10.1023/A:1012915002568</a>},
    number={1–3}, journal={Nonlinear Dynamics}, publisher={Kluwer Academic Publishers},
    author={Sextro, Walter and Popp, Karl and Krzyzynski, Tomasz}, year={2001}, pages={207–220}
    }'
  chicago: 'Sextro, Walter, Karl Popp, and Tomasz Krzyzynski. “Localization in Nonlinear
    Mistuned Systems with Cyclic Symmetry.” <i>Nonlinear Dynamics</i> 25, no. 1–3
    (2001): 207–20. <a href="https://doi.org/10.1023/A:1012915002568">https://doi.org/10.1023/A:1012915002568</a>.'
  ieee: W. Sextro, K. Popp, and T. Krzyzynski, “Localization in Nonlinear Mistuned
    Systems with Cyclic Symmetry,” <i>Nonlinear Dynamics</i>, vol. 25, no. 1–3, pp.
    207–220, 2001.
  mla: Sextro, Walter, et al. “Localization in Nonlinear Mistuned Systems with Cyclic
    Symmetry.” <i>Nonlinear Dynamics</i>, vol. 25, no. 1–3, Kluwer Academic Publishers,
    2001, pp. 207–20, doi:<a href="https://doi.org/10.1023/A:1012915002568">10.1023/A:1012915002568</a>.
  short: W. Sextro, K. Popp, T. Krzyzynski, Nonlinear Dynamics 25 (2001) 207–220.
date_created: 2019-04-15T10:14:18Z
date_updated: 2022-01-06T07:04:05Z
department:
- _id: '151'
doi: 10.1023/A:1012915002568
intvolume: '        25'
issue: 1-3
keyword:
- bladed disk assembly
- mistuning
- sensitivity
- localization
language:
- iso: eng
page: 207-220
publication: Nonlinear Dynamics
publication_identifier:
  issn:
  - 0924-090X
publisher: Kluwer Academic Publishers
status: public
title: Localization in Nonlinear Mistuned Systems with Cyclic Symmetry
type: journal_article
user_id: '55222'
volume: 25
year: '2001'
...