Behavioural modelling of delayed imbalance dynamics in nature: a parametric modelling for simulation of delayed instability dynamics

Imbalance dynamics can develop very slowly, and real systems and structures may seem to be stable or balanced for long periods of time before signs of instability behaviour become apparent. This study presents two dynamic system modelling approaches for simulation of delayed instability: Firstly, fr...

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Published inInternational journal of general systems Vol. 51; no. 4; pp. 313 - 333
Main Authors Alagoz, Baris Baykant, Deniz, Furkan Nur, Koseoglu, Murat
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 19.05.2022
Taylor & Francis LLC
Subjects
Binomial expansion
Control stability
Convergence
delayed collapse
delayed imbalance
Delayed instability
Dynamic stability
dynamic system modelling
Dynamical systems
Fractional calculus
fractional order system
Frequency stability
Modelling
Operators (mathematics)
Pole placement
Series (mathematics)
Series expansion
Simulation
Voltage collapse
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Abstract Imbalance dynamics can develop very slowly, and real systems and structures may seem to be stable or balanced for long periods of time before signs of instability behaviour become apparent. This study presents two dynamic system modelling approaches for simulation of delayed instability: Firstly, frequency domain properties of the system instability are investigated, and a parametric model to represent delayed instability behaviour is formulated according to the system pole placement technique. Secondly, a new type of instability modelling approach, which is based on time-domain characteristics of fractional order derivative operators, is introduced by utilizing the finite convergence regions of the Binomial series. This special instability modelling technique essentially uses the region of convergence in the series expansion of impulse responses. Several illustrative modelling and simulation examples are illustrated for engineering problems such as slowly developing cracks in metals, the voltage collapse in power systems and the delayed instability in control systems.
AbstractList Imbalance dynamics can develop very slowly, and real systems and structures may seem to be stable or balanced for long periods of time before signs of instability behaviour become apparent. This study presents two dynamic system modelling approaches for simulation of delayed instability: Firstly, frequency domain properties of the system instability are investigated, and a parametric model to represent delayed instability behaviour is formulated according to the system pole placement technique. Secondly, a new type of instability modelling approach, which is based on time-domain characteristics of fractional order derivative operators, is introduced by utilizing the finite convergence regions of the Binomial series. This special instability modelling technique essentially uses the region of convergence in the series expansion of impulse responses. Several illustrative modelling and simulation examples are illustrated for engineering problems such as slowly developing cracks in metals, the voltage collapse in power systems and the delayed instability in control systems.
Author Alagoz, Baris Baykant
Deniz, Furkan Nur
Koseoglu, Murat
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  organization: Inonu University
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Snippet Imbalance dynamics can develop very slowly, and real systems and structures may seem to be stable or balanced for long periods of time before signs of...
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StartPage 313
SubjectTerms Binomial expansion
Control stability
Convergence
delayed collapse
delayed imbalance
Delayed instability
Dynamic stability
dynamic system modelling
Dynamical systems
Fractional calculus
fractional order system
Frequency stability
Modelling
Operators (mathematics)
Pole placement
Series (mathematics)
Series expansion
Simulation
Voltage collapse
Title Behavioural modelling of delayed imbalance dynamics in nature: a parametric modelling for simulation of delayed instability dynamics
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