In this paper,we propose a novel fractionalorder fast terminal sliding mode control method,based on an integer-order scheme,to stabilize the chaotic motion of two typical microcomponents.We apply the fractional Lyapun...In this paper,we propose a novel fractionalorder fast terminal sliding mode control method,based on an integer-order scheme,to stabilize the chaotic motion of two typical microcomponents.We apply the fractional Lyapunov stability theorem to analytically guarantee the asymptotic stability of a system characterized by uncertainties and external disturbances.To reduce chattering,we design a fuzzy logic algorithm to replace the traditional signum function in the switching law.Lastly,we perform numerical simulations with both the fractional-order and integer-order control laws.Results show that the proposed control law is effective in suppressing chaos.展开更多
The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam ...The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior.The first primary resonance of the vertical beam,owing to modal coupling,exhibits an abrupt amplitude increase,namely the Hopf bifurcation.The frequency comb phenomenon induced by modal coupling is measured experimentally.A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon.The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.展开更多
基金supported by the National Natural Science Foundation of China(No.11372210 and No.51405343)the Research Fund for the Doctoral Program of Higher Education of China(No.20120032110010)Tianjin Research Program of Application Foundation and Advanced Technology(No.12JCZDJC28000 and No.15JCQNJC05000)
文摘In this paper,we propose a novel fractionalorder fast terminal sliding mode control method,based on an integer-order scheme,to stabilize the chaotic motion of two typical microcomponents.We apply the fractional Lyapunov stability theorem to analytically guarantee the asymptotic stability of a system characterized by uncertainties and external disturbances.To reduce chattering,we design a fuzzy logic algorithm to replace the traditional signum function in the switching law.Lastly,we perform numerical simulations with both the fractional-order and integer-order control laws.Results show that the proposed control law is effective in suppressing chaos.
基金supported by the National Natural Science Foundation of China(No.11902182)the Program of Shanghai Academic/Technology Research Leader of China(No.19XD1421600)+2 种基金the China Postdoctoral Science Foundation(No.2019M651485)the Natural Science Foundation of Shandong Province of China(No.ZR2019BA001)the Natural Science Foundation of Tianjin of China(No.20JCQNJC01070)。
文摘The nonlinear modal coupling in a T-shaped piezoelectric resonator,when the former two natural frequencies are away from 1:2,is studied.Experimentally sweeping up the exciting frequency shows that the horizontal beam exhibits a nonlinear hardening behavior.The first primary resonance of the vertical beam,owing to modal coupling,exhibits an abrupt amplitude increase,namely the Hopf bifurcation.The frequency comb phenomenon induced by modal coupling is measured experimentally.A Duffing-Mathieu coupled model is theoretically introduced to derive the conditions of the modal coupling and frequency comb phenomenon.The results demonstrate that the modal coupling results from nonlinear stiffness hardening and is strictly dependent on the loading range and sweeping form of the driving voltage and the frequency of the piezoelectric patches.
