Analysis of Duffing oscillator with time-delayed fractional-order PID controller |
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| Affiliation: | 1. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, China;2. School of Information Science and Technology, Shijiazhuang Tiedao University, Shijiazhuang, China;1. Department of Mechanical Engineering, National Cheng-Kung University, Tainan 701, Taiwan, ROC;2. Department of Mechanical Engineering, Southern Taiwan University of Science and Technology, Tainan 710, Taiwan, ROC |
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| Abstract: | The free vibration of Duffing oscillator with time-delayed fractional-order Proportional-Integral-Derivative (FOPID) controller based on displacement feedback is studied. The second-order approximate analytical solution is obtained by KBM asymptotic method. The effects of the parameters in FOPID controller on the dynamical properties are characterized by some equivalent parameters. The correctness of the approximate analytical results is verified by the numerical results. The effects of the time-delayed FOPID controller with displacement feedback on control performances of Duffing oscillator are analyzed in detail by time response, and the stability conditions of zero solution and periodic motions are also presented. Finally, the control performances on Duffing oscillator with large damping are further analyzed. And the results show that one could take the advantage of time delay, when the parameters of time-delayed FOPID controller are chosen reasonably. |
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| Keywords: | Approximate analytical solution Fractional-order PID control System stability Time delay KBM method |
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