Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension
Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension
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DOI：
10.1016/s0022-460x(03)00519-4
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发表时间：
2004-06
影响因子：
4.7
通讯作者：
Kyung-Jinn Yang;K. Hong;F. Matsuno
中科院分区：
文献类型：
--
作者：
Kyung-Jinn Yang;K. Hong;F. Matsuno
本文研究了轴向运动弦线在时空变化张力和未知边界扰动下的振动抑制方案。张力变化的下限被假定为充分大于张力的导数。轴向移动管柱系统被分成两个跨度，即，一个受控跨度和一个非受控跨度，通过位于钻柱中间部分的液压接触辊致动器。采用液压触辊作动器控制琴弦受控跨距部分的横向振动，并将作动器的位置视为受控跨距部分的右边界。利用汉密尔顿原理，推导了由描述运动弦动力学的双曲型偏微分方程和描述驱动器动力学的常微分方程组成的系统数学模型。采用李亚普诺夫方法设计了鲁棒边界控制律和自适应律，以保证受控跨度部分的振动衰减。利用半群理论证明了闭环系统在鲁棒自适应边界控制方案下的渐近稳定性。仿真结果验证了所提出的鲁棒自适应边界控制器的有效性。
In this paper, a vibration suppression scheme for an axially moving string under a spatiotemporally varying tension and an unknown boundary disturbance is investigated. The lower bound of the tension variation is assumed to be sufficiently larger than the derivatives of the tension. The axially moving string system is divided into two spans, i.e., a controlled span and an uncontrolled span, by a hydraulic touch-roll actuator which is located in the middle section of the string. The transverse vibration of the controlled span part of the string is controlled by the hydraulic touch-roll actuator, and the position of the actuator is considered as the right boundary of the controlled span part. The mathematical model of the system, which consists of a hyperbolic partial differential equation describing the dynamics of the moving string and an ordinary differential equation describing the actuator dynamics, is derived by using the Hamilton's principle. The Lyapunov method is employed to design a robust boundary control law and adaptation laws for ensuring the vibration reduction of the controlled span part. The asymptotic stability of the closed loop system under the robust adaptive boundary control scheme is proved through the use of semigroup theory. Simulation results verify the effectiveness of the robust adaptive boundary controller proposed.