Alternative Proofs of Four Stability Properties of Rigid Link Manipulators under PID Position Control
Alternative Proofs of Four Stability Properties of Rigid Link Manipulators under PID Position Control
复制标题
PID位置控制下刚性连杆机械臂四种稳定性特性的替代证明
DOI：
10.1017/s0263574712000136
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发表时间：
2012
期刊：
影响因子：
2.7
通讯作者：
Ryo Kikuuwe
中科院分区：
文献类型：
--
作者：
Takanori Ikeda;Yuichiro Kawabata;Hidenori Hamada;Kazuo Yamada;Ryo Kikuuwe
本文给出了比例-积分-微分（PID）位置控制下刚性连杆机械臂的四个稳定性性质（半严格无源性、半渐近稳定性、半输入-状态稳定性和半一致最终有界性及任意可约最终有界性）的新证明。证明采用了严格的李雅普诺夫函数和一种新的参数化提供了四个不等式条件的稳定性。在这些不等式中，如果关节都是转动的或都是棱柱的，则对物理量的算术运算是物理上一致的。提出了一种增益选择方法，通过该方法可以独立地设计速度误差、位置误差及其积分的极限。
This paper presents new proofs of four stability properties (semiglobal strict passivity, semiglobal asymptotic stability, semiglobal input-to-state stability, and semiglobal uniform ultimate boundedness with an arbitrarily reducible ultimate bound) of a rigid-link manipulator under proportional-integral-derivative (PID) position control. The proofs employ a strict Lyapunov function and a novel parameterization to provide four inequality conditions for the stability properties. In those inequalities, arithmetic operations on physical quantities are physically consistent if the joints are all revolute or all prismatic. A gain selection procedure is presented by which the ultimate bounds of velocity error, position error, and its integral can be independently designed.