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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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。

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	侯静玉1
	杨绍普2
	李强1
	刘永强2
	3

关键词 ：齿轮, 分数阶PID控制器, 增量谐波平衡法, 速度反馈, 齿侧间隙

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.

Key words： gear fractional-order PID controller incremental harmonic balance method velocity feedback backlash

收稿日期: 2020-12-14 出版日期: 2021-12-15

引用本文:

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. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(23): 175-181.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I23/175

[1] CHANG W. PID control for chaotic synchronization using particle swarm optimization [J]. Chaos Solitons & Fractals, 2009, 39(2): 910-917.
[2] CHANG H C, CHEN L H. Bifurcation characteristics of nonlinear systems under conventional PID control [J]. Chemical Engineering Science, 1984, 39(7-8): 1127-1142.
[3] POUNDS P E I, BERSAK D R, DOLLAR A M. Stability of small-scale UAV helicopters and quadrotors with added payload mass under PID control [J]. Autonomous Robots, 2012, 33(1-2): 129-142.
[4] TSAVNIN A, EFIMOV S, ZAMYATIN S. Overshoot elimination for control systems with parametric uncertainty via a PID controller [J]. Journal of Mathematics, 2020, 12: 1092.
[5] MENDONCA T, LAGO P. PID control strategies for the automatic control of neuromuscular blockade [J]. Control Engineering Practice, 1998, 6(10): 1225-1231.
[6] LI Q, SHI G B, WEI J, LIN Y. Yaw stability control of active front steering with fractional-order PID controller [C]// 2009 International Conference on Information Engineering and Computer Science, IEEE, 2009.
[7] VAHAB H H, MONJE CONCEPCION A. Fractional-order PID control of a MIMO distillation column process using improved bat algorithm [J]. Soft Computing, 2019, 23(18): 8887-8906.
[8] WANG Y M, LIU Y J, ZHU R, et al. Fractional-order PID controller of a heating-furnace system [J]. Advanced Materials Research, 2012, 490-495: 1145-1149.
[9] 牛江川,申永军,杨绍普,等.位移反馈分数阶PID控制对单自由度线性振子的影响[J]. 控制理论与应用, 2016, 33(09): 1265-1271.
NIU Jiangchuan, SHEN Yongjun, YANG Shaopu, et al. Effect of fractional-order PID controller on the dynamical response of linear single degree-of-freedom oscillator with displacement feedback [J]. Control Theory & Application, 2016, 33(09): 1265-1271.
[10] 牛江川,申永军,杨绍普,等.基于速度反馈分数阶PID控制的达芬振子的主共振[J]. 力学学报, 2016, 48(002): 422-429.
NIU Jiangchuan, SHEN Yongjun, YANG Shaopu, et al. Primary resonance of duffing oscillator with fractional-order PID controller based on velocity feedback [J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(002): 422-429.
[11] LIU L, NIU J C, LI X H. Dynamic analysis of gear system under fractional-order PID control with the feedback of meshing error change rate [J]. Acta Mechanica, 2018, 229(9): 3833-3851.
[12] XIAO M, TAO B B, ZHENG W X, et al. Fractional-order PID controller synthesis for bifurcation of fractional-order small-world networks [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019(99): 1-13.
[13] RAWAT A, JHA S K, KUMAR B, et al. Nonlinear fractional order PID controller for tracking maximum power in photo-voltaic system [J]. Journal of Intelligent and Fuzzy Systems, 2020(10): 1-11.
[14] SHEN Y J, YANG S P, LIU X D. Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method [J]. International Journal of Mechanical Sciences, 2006, 48(11): 1256-1263.
[15] HUANG G H, XU S S, ZHANG W H, et al. Super-harmonic resonance of gear transmission system under stick-slip vibration in high-speed train [J]. Journal of Central South University, 2017, 24(3): 726-735.
[16] KAHRAMAN A, SINGH R. Non-linear dynamics of a spur gear pair [J]. Journal of Sound and Vibration, 1990, 142(1): 49-75.
[17] XIA Y, WAN Y, LIU Z Q. Bifurcation and chaos analysis for a spur gear pair system with friction [J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2018, 40(11): 529.
[18] 王立华,李润方,林腾蛟,等.齿轮系统时变刚度和间隙非线性振动特性研究[J]. 中国机械工程, 2003(13).
WANG Lihua, LI Ruifang, LIN Tengjiao, et al. Research on nonlinear vibration characteristics due to time-varying mesh stiffness and gear backlash in gear system [J]. China Mechanical Engineering, 2003(13): 69-72+5.
[19] 张思进,王紧业,文桂林.含间隙齿轮碰振系统的全局动力学分析[J].动力学与控制学报, 2018, 16(02): 129-135.
ZHANG Sijin, WANG Jinye, WEN Guilin. Global dynamic analysis of gear vibration system with clearance [J]. Journal of Dynamic and Control, 2018, 16(02): 129-135.
[20] LI X H, HOU J Y. Bursting phenomenon in a piecewise mechanical system with parameter perturbation in stiffness [J]. International Journal of Non-Linear Mechanics, 2016: 165-176.
[21] PODLUBNY I. Fractional-order systems and -controllers [J]. IEEE Transactions on Automatic Control, 1999, 44(1): 208-214.
[22] HOU J Y, YANG S P, LI Q, et al. Nonlinear dynamic analysis of spur gear system based on fractional-order calculus [J]. Modern Physics Letters B, 2020(3): 2050420.
[23] NIU J C, HOU J, SHEN Y J, et al. Dynamic analysis and vibration control of nonlinear boring bar with fractional-order model of magnetorheological fluid [J]. International Journal of Non-Linear Mechanics, 2020, 121: 103459.