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首页> 外文期刊>International Journal of Adaptive Control and Signal Processing >Adaptive robust boundary control of shaft vibrations under perturbations with unknown upper bounds
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Adaptive robust boundary control of shaft vibrations under perturbations with unknown upper bounds

机译：上限未知的扰动下轴振动的自适应鲁棒边界控制

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This paper presents robust and adaptive boundary control designs to stabilize the two-dimensional vibration of hybrid shaft model. The hybrid shaft is mathematically represented by a set of partial differential equations, governing the shaft vibrations, coupled to ordinary differential equations, describing rigid body spinning and dynamic boundary conditions. The control objective is to stabilize the transverse vibrations of the perturbed shaft while regulating the spinning rate. To achieve this, the paper first establishes robust boundary control laws that fulfil the control objective in the presence of modeling uncertainties and external disturbances operating over the shaft domain and boundary. Lyapunov-based analyses show that the proposed robust control exponentially stabilizes the shaft with vanishing distributive perturbations, while assuring ultimately bounded vibrations in the case of nonvanishing perturbations. Then, adaptive control philosophy is utilized to achieve redesigned robust controllers that only use online adaptation of control gains without acquiring the knowledge of bounds on perturbations, as well as dynamic parameters. An advantage of this design is avoiding an overconservative robust control law, which may induce poor stability and chattering in tackling system perturbations with unknown upper bounds. Simulations through finite element method illustrate the results. Copyright (c) 2014 John Wiley & Sons, Ltd.
机译：本文提出了鲁棒的自适应边界控制设计，以稳定混合轴模型的二维振动。混合轴在数学上由一组控制轴振动的偏微分方程组表示，与普通的微分方程耦合，描述了刚体旋转和动态边界条件。控制目标是在调节旋转速度的同时稳定受扰轴的横向振动。为了实现这一目标，本文首先建立了鲁棒的边界控制律，该律在存在建模不确定性和在轴域和边界上运行的外部干扰的情况下实现了控制目标。基于李雅普诺夫的分析表明，所提出的鲁棒控制以消失的分布扰动指数地稳定了轴，同时确保了在不消失的扰动情况下最终的极限振动。然后，利用自适应控制原理来实现重新设计的鲁棒控制器，该控制器仅使用控制增益的在线自适应，而无需了解扰动的界线以及动态参数。这种设计的优点是避免了过于保守的鲁棒控制定律，该定律可能会导致稳定性变差，并在解决具有未知上限的系统扰动时产生颤动。通过有限元方法进行的仿真说明了结果。版权所有（c）2014 John Wiley＆Sons，Ltd.

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