Two dimensional input shaping for one dimensional continua

Amir Lotfi-Gaskarimahalle, Christopher D. Rahn

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper extends input shaping control to one dimensional continua. Unlike discrete systems where the input is shaped only in the temporal domain, temporal and spatial in-put shaping can produce zero residual vibration in setpoint position control of distributed strings and beams. For collocated and noncollocated boundary control of strings and domain control of strings and pinned beams, the response to step in-puts is solved in closed form using delays. For a clamped beam model, a closed form infinite modal series is used. The boundary controlled string can be setpoint regulated using two-pulse Zero Vibration (ZV) and three-pulse Zero Vibration and Derivative (ZVD) shapers but ZVD is not more robust to parameter variations than ZV Noncolocated ZV and ZVD boundary control enables rigid body translation of a string with zero residual vibration. Domain controlled strings and pinned beams with spatial input distributions that satisfy certain orthogonality conditions (e.g. midspan point load or uniformly distributed load) can be setpoint regulated with shaped inputs. For the cantilevered beam, modal shaping of the input distribution and ZV or ZVD temporal shaping drives the tip to the desired position with zero residual vibration.

Original languageEnglish (US)
Title of host publicationProceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Dynamic Systems and Control Division
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Print)0791837904, 9780791837900
DOIs
StatePublished - Jan 1 2006
Event2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Chicago, IL, United States
Duration: Nov 5 2006Nov 10 2006

Publication series

NameAmerican Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC
ISSN (Print)1071-6947

Other

Other2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006
CountryUnited States
CityChicago, IL
Period11/5/0611/10/06

    Fingerprint

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Software

Cite this

Lotfi-Gaskarimahalle, A., & Rahn, C. D. (2006). Two dimensional input shaping for one dimensional continua. In Proceedings of 2006 ASME International Mechanical Engineering Congress and Exposition, IMECE2006 - Dynamic Systems and Control Division (American Society of Mechanical Engineers, Dynamic Systems and Control Division (Publication) DSC). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2006-14611