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报告题目：Analysis of Synchronization of n Metronomes on a Cart via Describing Function Method

报 告 人：忻欣 教授（东南大学讲座教授）

单 位：日本Okayama Prefectural University

时 间：2017年3月29日周三上午10:00

地 点：中心楼二楼自动化学院教育部重点实验室会议室

邀请人/主持人：张侃健教授

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欢迎各位老师和研究生参加！

摘要：Synchronization means an adjustment of rhythms of oscillating objects due to their weak interaction and has attracted increasing attention from different disciplines as one of the most important concepts for investigating complex systems. A metronome, which can be modeled as a single pendulum, is a nonlinear self-sustained oscillator whose frequency is precisely tuned for practical applications, e.g., providing exact timing for musical exercise.

In this talk, we introduce our research results on the analysis of the synchronization phenomena in the system consisting of n identical metronomes placed on an elastically fixed cart by using describing function (DF) method, which deals the driving torque as a discontinuous function of the angle and angular velocity of each metronome. We present a unified DF solution of the system which shows that there exist two types of synchronization with the first harmonic of the angle of each metronome having the same amplitude. One is the out-of-phase synchronization; that is, there exist at least two of all metronomes having a nonzero phase shift. The other is the in-phase synchronization; that is, the phases of all metronomes are the same. Regarding the out-of-phase synchronization, we show that the frequency and amplitude of its first harmonic of the angle of each metronome, are independent of n and the mechanical parameters related to the cart, and are exactly the same as those of the single metronome hanging from a fixed base. We prove that the out-of-phase synchronization is stable and presents a new result of the phase shifts of n-1 metronomes with respect to a referenced metronome.

个人简介：Xin Xin received the B.S. degree in 1987 from the University of Science and Technology of China, Hefei, China, and the Ph.D. degree in 1993 from the Southeast University, Nanjing, China. From 1991 to 1993, he did his Ph.D. studies in Osaka University as a co-advised student of China and Japan with the Japanese Government Scholarship. He also received the Doctor degree in engineering in 2000 from Tokyo Institute of Technology.From 1993 to 1995, he was a postdoctoral researcher and then became an associate professor of Southeast University. From 1996 to 1997, he was with the New Energy and Industrial Technology Development, Japan as an advanced industrial technology researcher. From 1997 to 2000, he was an assistant professor of Tokyo Institute of Technology. From 2000, he has been with Okayama Prefectural University as an associate professor,where he is now a professor since 2008. He will be the Head of Department of Systems Engineering from April 2017. He has over 170 publications in journals, international conferences and book chapters.He received the division paper award of SICE 3rd Annual Conference on Control Systems in 2004. His current research interests include robotics,dynamics and control of nonlinear and complex systems.**3月29日（周三）上午10:00忻欣教授(Okayama Prefectural University)学术报告 --Analysis of Synchronization of n Metronomes on a Cart via Describing Function Method**

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++报告题目：Analysis of Synchronization of n Metronomes on a Cart via Describing Function Method

报 告 人：忻欣 教授（东南大学讲座教授）

单 位：日本Okayama Prefectural University

时 间：2017年3月29日周三上午10:00

地 点：中心楼二楼自动化学院教育部重点实验室会议室

邀请人/主持人：张侃健教授

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

欢迎各位老师和研究生参加！

摘要：Synchronization means an adjustment of rhythms of oscillating objects due to their weak interaction and has attracted increasing attention from different disciplines as one of the most important concepts for investigating complex systems. A metronome, which can be modeled as a single pendulum, is a nonlinear self-sustained oscillator whose frequency is precisely tuned for practical applications, e.g., providing exact timing for musical exercise.

In this talk, we introduce our research results on the analysis of the synchronization phenomena in the system consisting of n identical metronomes placed on an elastically fixed cart by using describing function (DF) method, which deals the driving torque as a discontinuous function of the angle and angular velocity of each metronome. We present a unified DF solution of the system which shows that there exist two types of synchronization with the first harmonic of the angle of each metronome having the same amplitude. One is the out-of-phase synchronization; that is, there exist at least two of all metronomes having a nonzero phase shift. The other is the in-phase synchronization; that is, the phases of all metronomes are the same. Regarding the out-of-phase synchronization, we show that the frequency and amplitude of its first harmonic of the angle of each metronome, are independent of n and the mechanical parameters related to the cart, and are exactly the same as those of the single metronome hanging from a fixed base. We prove that the out-of-phase synchronization is stable and presents a new result of the phase shifts of n-1 metronomes with respect to a referenced metronome.

个人简介：Xin Xin received the B.S. degree in 1987 from the University of Science and Technology of China, Hefei, China, and the Ph.D. degree in 1993 from the Southeast University, Nanjing, China. From 1991 to 1993, he did his Ph.D. studies in Osaka University as a co-advised student of China and Japan with the Japanese Government Scholarship. He also received the Doctor degree in engineering in 2000 from Tokyo Institute of Technology.From 1993 to 1995, he was a postdoctoral researcher and then became an associate professor of Southeast University. From 1996 to 1997, he was with the New Energy and Industrial Technology Development, Japan as an advanced industrial technology researcher. From 1997 to 2000, he was an assistant professor of Tokyo Institute of Technology. From 2000, he has been with Okayama Prefectural University as an associate professor,where he is now a professor since 2008. He will be the Head of Department of Systems Engineering from April 2017. He has over 170 publications in journals, international conferences and book chapters.He received the division paper award of SICE 3rd Annual Conference on Control Systems in 2004. His current research interests include robotics,dynamics and control of nonlinear and complex systems.

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