Efficient stability chart computation for general delayed linear time periodic systems

Daniel Bachrathy, G. Stépán

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

2 Citations (Scopus)

Abstract

The determination of the stability of systems with time delay is of high importance in many industrial and research applications, like cutting processes, wheel shimmy, traffic jams and even in neural systems, human balancing. A user friendly numerical method was implemented to analyse the general form of delayed linear time periodic systems with time periodic coefficients. The goal is to create a freeware Matlab package which is able to determine automatically the so-called stability chart, which illustrates the parameter range for which the given linear system is stable. The user has to define the governing equation by the time periodic coefficient matrices, the corresponding time delays, the orders of time derivatives of the general coordinate vector, as well as the range of the parameters and the resolution of the stability chart. The method is optimized for 2 parameters, which is a typical case in engineering applications, but 1 and 3 parameter stability charts are also supported and tested. The stability is analysed in frequency domain based on the N rth order approximation of Hill's infinite determinant. The parameter points where the number of unstable Floquet multipliers changes are computed by the Multi Dimensional Bisection Method. From these parameter points, another algorithm selects the stability boundary lines. The algorithm is tested by means of numerous examples.

Original languageEnglish
Title of host publication9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers
Volume7 B
ISBN (Print)9780791855973
DOIs
Publication statusPublished - 2013
EventASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States
Duration: Aug 4 2013Aug 7 2013

Other

OtherASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013
CountryUnited States
CityPortland, OR
Period8/4/138/7/13

Fingerprint

Time varying systems
Periodic Systems
Chart
Linear Time
Periodic Coefficients
Time Delay
Time delay
Floquet multipliers
Bisection Method
Traffic Jam
Order of Approximation
Engineering Application
Balancing
Wheel
Range of data
MATLAB
Frequency Domain
Linear systems
Governing equation
Numerical methods

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation

Cite this

Bachrathy, D., & Stépán, G. (2013). Efficient stability chart computation for general delayed linear time periodic systems. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 7 B). [V07BT10A070] American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2013-13660

Efficient stability chart computation for general delayed linear time periodic systems. / Bachrathy, Daniel; Stépán, G.

9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B American Society of Mechanical Engineers, 2013. V07BT10A070.

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

Bachrathy, D & Stépán, G 2013, Efficient stability chart computation for general delayed linear time periodic systems. in 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. vol. 7 B, V07BT10A070, American Society of Mechanical Engineers, ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013, Portland, OR, United States, 8/4/13. https://doi.org/10.1115/DETC2013-13660
Bachrathy D, Stépán G. Efficient stability chart computation for general delayed linear time periodic systems. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B. American Society of Mechanical Engineers. 2013. V07BT10A070 https://doi.org/10.1115/DETC2013-13660
Bachrathy, Daniel ; Stépán, G. / Efficient stability chart computation for general delayed linear time periodic systems. 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B American Society of Mechanical Engineers, 2013.
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