Stationary Set Analysis for PD Controlled Mechanical Systems
Stationary Set Analysis for PD Controlled Mechanical Systems
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DOI：
10.1109/tcst.2010.2070067
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发表时间：
2011-09
影响因子：
4.8
通讯作者：
Kai Zheng;T. Shen;Yu Yao
中科院分区：
文献类型：
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作者：
Kai Zheng;T. Shen;Yu Yao
本简介提出了一种利用比例微分 (PD) 控制来分析高维机械系统平稳集的综合方法。系统行为采用 Filippov 微分包含来表征，其中主要由静摩擦引起的不连续扰动通过相对于速度的凸集值图进行建模。通过计算Filippov意义上的静解，得到闭环系统的平稳集。平稳集也被证明是渐近稳定的，而比例积分微分（PID）控制系统则无法获得渐近稳定性。最后，在三轴旋转台上进行实验来说明我们的分析结果。
This brief presents a comprehensive method to analyze the stationary set of the high-dimensional mechanical systems with proportional-derivative (PD) control. The system behavior is characterized by Filippov's differential inclusion, in which the discontinuous disturbance mainly caused by static friction is modeled by a convex set-valued map with respect to the velocity. The stationary set of the closed-loop system is obtained by calculating the static solution in the sense of Filippov. The stationary set is also proved to be asymptotically stable, while the asymptotic stability cannot be obtained for proportional-integral-derivative (PID) controlled systems. Finally, the experiments on a three-axis rotation table are carried out to illustrate our analysis results.