速度反馈分数阶PID控制对齿轮系统振动特性的影响

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (23) : 175-181.

论文

侯静玉1，杨绍普2，李强1，刘永强2,3

作者信息 +

Effects of speed feedback fractional order PID control on vibration characteristics of gear system

HOU Jingyu1, YANG Shaopu2, LI Qiang1, LIU Yongqiang2, 3

Author information +

文章历史 +

摘要

为了控制齿轮工作过程中产生的振动，将分数阶比例-积分-微分（简称PID）控制器引入，建立了基于速度反馈分数阶PID控制的齿轮传动系统动力学模型。利用增量谐波平衡法求得了该模型的五阶近似解析解，并利用幂级数展开法验证了该解析方法的正确性。通过幅频响应曲线详细地分析了速度反馈分数阶PID控制器各环节的系数和分数阶阶次对齿轮传动系统振动特性的影响。最后对在分数阶PID控制器、整数阶PID控制器及无PID控制器作用下的系统响应进行了比较，并讨论了分数阶PID控制器对于啮合刚度系数和激励幅值的鲁棒性。

Abstract

A fractional-order proportion-integration-differentiation (PID) controller is introduced for controlling the vibration produced when the gear is in operation, and the dynamic model of gear transmission system with fractional-order PID controller based on velocity feedback is modeled. The fifth-order approximation solution of the system by using the incremental harmonic balance method (IHBM) is obtained, and it is verified by power series expansion method. The effect of the coefficient and order of each link of fractional-order PID controller with velocity feedback on the vibration characteristics of gear system is analyzed in detail by using the amplitude-frequency response curve. Finally, the response of the system with fractional-order PID controller is compared with that of integer-order PID controller and without PID controller, and the robustness of fractional-order PID controller for mesh stiffness coefficient and excitation amplitude is discussed.

导出引用

侯静玉1，杨绍普2，李强1，刘永强2,3. 速度反馈分数阶PID控制对齿轮系统振动特性的影响[J]. 振动与冲击, 2021, 40(23): 175-181

HOU Jingyu1, YANG Shaopu2, LI Qiang1, LIU Yongqiang2, 3. Effects of speed feedback fractional order PID control on vibration characteristics of gear system[J]. Journal of Vibration and Shock, 2021, 40(23): 175-181

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