Observability, controllability and stability of a nonlinear RLC circuit in form of a Duffing oscillator by means of theoretical mechanical approach
Yükleniyor...
Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Slovak University of Technology in Bratislava
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this research article, observability, controllability and stability of a nonlinear RLC circuit with a nonlinear capacitor is investigated as a Duffing oscillator beginning with the dissipative equations of generalized motion using Lagrange-dissipative model ({L, D}-model briefly). The force related to the potential energy, equilibria, and their well known stability properties are given using state space approach. Prerequisite that the condition for a Legendre transform is fulfilled, for the same system, also Hamiltonian of the system is found. Using Hamiltonian and dissipation function, dissipative canonical equations are obtained. These equations are written in state space form. Then the equality to the same results obtained using the dissipative equations of generalized motion related equilibria and their stability was shown. Thus a Lyapunov function as residual energy function (REF) is justified in terms of stability of the overall system. As last step, different electrical and mechanical (physical) realization possibilities are discussed.
Açıklama
Anahtar Kelimeler
Duffing Denklemi, Duffing Oszillator, Duffing Oscillator
Kaynak
Journal of Electrical Engineering-Elektrotechnicky Casopis
WoS Q Değeri
Q4
Scopus Q Değeri
N/A
Cilt
73
Sayı
2
Künye
In this research article, observability, controllability and stability of a nonlinear RLC circuit with a nonlinear capacitor is investigated as a Duffing oscillator beginning with the dissipative equations of generalized motion using Lagrange-dissipative model ({L, D}-model briefly). The force related to the potential energy, equilibria, and their well known stability properties are given using state space approach. Prerequisite that the condition for a Legendre transform is fulfilled, for the same system, also Hamiltonian of the system is found. Using Hamiltonian and dissipation function, dissipative canonical equations are obtained. These equations are written in state space form. Then the equality to the same results obtained using the dissipative equations of generalized motion related equilibria and their stability was shown. Thus a Lyapunov function as residual energy function (REF) is justified in terms of stability of the overall system. As last step, different electrical and mechanical (physical) realization possibilities are discussed.
