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

• Published in: International journal of general systems Vol. 51; no. 4; pp. 313 - 333
• Main Authors: Alagoz, Baris Baykant, Deniz, Furkan Nur, Koseoglu, Murat
• Format: Journal Article
• Language: English
• 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
• ISSN: 0308-1079; 1563-5104
• DOI: 10.1080/03081079.2022.2025795

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.