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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (5): 845-850.doi: 10.3969/j.issn.1005-3085.2022.05.013

• • 上一篇    

具有分数阶形状记忆合金系统的时滞反馈控制与稳定性分析

王进斌1,2,   马立峰1   

  1. 1. 太原科技大学机械工程学院，太原 030024；2. 太原科技大学应用科学学院，太原 030024
  • 出版日期:2022-10-15 发布日期:2022-12-15
  • 基金资助:
    山西省科技重大专项 (201603D111004; 20181102016).

Bifurcation and Stability Analysis of a Fractional-order Shape Memory Alloy Oscillator with Delayed Feedback

WANG Jinbin1,2,   MA Lifeng1   

  1. 1. College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024
    2. School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024
  • Online:2022-10-15 Published:2022-12-15
  • Supported by:
    The Key Research and Development Program of Shanxi Province (201603D111004; 20181102016).

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摘要：

将分数阶引入到形状记忆合金振子模型中，针对分数阶对其系统动力学的影响进行了研究。首先基于分数阶微分方程理论，构建了分数阶形状记忆合金系统，并给出了该系统的稳定性和 Hopf 分岔存在性条件。其次，设计了时滞反馈控制器，用来控制分数阶形状记忆合金系统的稳定性。研究结果表明，形状记忆合金系统中的时滞和分数阶对系统的动力学性质有着重要的调控作用。

关键词: 分数阶, 稳定性, Hopf 分支, 时滞

Abstract:

The fractional order is introduced into the shape memory alloy oscillator model, and the effect of fractional order on the system dynamics is discussed. Firstly, based on the fractional differential equation theory, the fractional shape memory alloy system (FSMA) is constructed, and the stability of the system and the existence conditions of Hopf bifurcation are presented. Then, a time-delay feedback controller is designed to control the stability of the FSMA system. Finally, the numerical results indicate that the time delay and fractional order play important roles in regulating the dynamic properties of the shape memory alloy system.

Key words: fractional order, stability, Hopf bifurcation, time delay

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