Nonlinear vibration analysis in precision motion stage with PID and time-delayed feedback controls
Nonlinear vibration analysis in precision motion stage with PID and time-delayed feedback controls
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DOI：
10.1007/s11071-020-05779-0
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发表时间：
2020-07
影响因子：
5.6
通讯作者：
S. K. Gupta;Jiamin Wang;O. Barry
中科院分区：
文献类型：
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作者：
S. K. Gupta;Jiamin Wang;O. Barry
研究了在LuGre摩擦动力学作用下精密运动平台摩擦振动的控制问题。我们考虑一个集总参数模型的精密运动平台与PID和线性时滞状态反馈控制作用在运动的平台的方向。线性稳定性分析揭示了积分增益在稳定性中的临界性，并相应地给出了系统参数选择时存在多个稳定叶和余维2的Hopf点.分岔的性质是由分析研究确定的方法，使用多尺度和谐波平衡。我们观察到存在的亚临界和超临界系统中的Hopf分岔，取决于控制参数的选择。因此，由于动态摩擦模型的非线性既可以是稳定的或不稳定的性质，因此，粘滑非线性是必不可少的捕捉系统动力学的全局行为。通过数值分岔分析，揭示了系统在Hopf点附近存在倍周期分岔。我们观察到复杂的解决方案，如周期4，准周期，大振幅粘滑极限环沿着与混沌吸引子的系统。
We investigate the control of friction-induced vibration in a precision motion stage under the effect of the LuGre friction dynamics. We consider a lumped parameter model of the precision motion stage with PID and linear time-delayed state feedback control acting in the direction of the motion of the stage. Linear stability analysis reveals the criticality of integral gain in the stability and, accordingly, the existence of multiple stability lobes and codimension-2 Hopf points for a given choice of system parameters. The nature of the bifurcation is determined by an analytical study using the method of multiple scales and harmonic balance. We observe the existence of both subcritical and supercritical Hopf bifurcations in the system, depending on the choice of control parameters. Hence, the nonlinearity due to dynamic friction model could both be stabilizing or destabilizing in nature, and therefore, stick-slip nonlinearity is essential to capture the global behavior of the system dynamics. Furthermore, numerical bifurcation analysis of the system reveals the existence of period-doubling bifurcation near the Hopf points. We observe complicated solutions such as period-4, quasi-periodic, large-amplitude stick-slip limit cycles along with chaotic attractor in the system.