伺服系统受摩擦扰动产生极限环的原因及稳定性分析  

Reasoning and stability of limit cycle generated by friction in servo system

作　　者：宋彦[1,2] 高慧斌[1] 田彦涛[3] 张淑梅[1] 

机构地区：[1]中国科学院长春光学精密机械与物理研究所,长春130033 [2]中国科学院研究生院,北京100039 [3]吉林大学控制理论与智能系统研究室长春130022

出　　处：《吉林大学学报（工学版）》2011年第1期214-220,共7页Journal of Jilin University:Engineering and Technology Edition

基　　金：“863”国家高技术研究发展计划项目(2008AA0047)

摘　　要：讨论了低速工况下,由摩擦造成极限环现象。首先,采用分段线性化的方法,将Stri-beck摩擦模型转换为线性的摩擦模型,获得了系统的状态方程;随后,应用系统平衡点性质分析和Poincare-Bendixson定理,证明了极限环的存在,确定了存在区域;最后,通过对Poincare映射的分析,判断了极限环的稳定性。仿真与实验结果均表明,在低速状态下,受摩擦扰动的伺服系统存在稳定的极限环;原因是运动过程中平衡点的稳定性反复发生变化。对系统根轨迹的分析表明:避免极限环出现的方法在于系统受摩擦扰动时,保证闭环系统的鲁棒稳定性。The phenomenon of limit cycle was observed in low-velocity servo system. With the help of nonlinear analysis tools, this paper analyzes the kinetics of limit cycle and finds out the reasons that induce this phenomenon. First, the Stribeck model was converted to piecewise linearized friction model and the state space model was also obtained. Then, by analyzing the feature of the system balance point and using Poincare-Bendixson theorem, the existence of the limit cycle was proved. The region where the limit cycle occurs was also found. Finally, the stability of the limit cycle was analyzed based on the Poincare map. Simulation and experiment results show that, under low-velocity state, stable limit cycle occurs in the servo system that is disturbed by friction. The reason is that the stability of the equilibrium changes repeatedly. Through the analysis of the system root locus, the measure to eliminate the limit cycle is found.

关 键 词：自动控制技术 摩擦扰动 非线性动力学 极限环 速度平稳性 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]