Input-to-state stability analysis of linear motor motion systems
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摘要: 直线电机是一种典型的直接驱动系统，具有高速度、高精度和大推力的优点，适用于各种高端装备中的精密直线运动场合。然而，直线电机运动系统的“零传动”特性，使得负载变化、非线性摩擦力、推力波动等扰动因素直接作用于系统，进而严重影响系统的性能和运动精度。为了分析扰动对系统状态的影响，针对直线电机运动系统进行建模并研究系统的输入到状态稳定性分析问题，提出一种基于李雅普诺夫方法的直线电机运动系统输入到状态稳定性分析方法，建立控制器增益与系统输入到状态稳定性之间的关系，为控制器增益的选取提供理论支持。Abstract: Linear motor is a typical direct drive system with high speed, high precision, and large thrust, which can be applied to high precision linear motor occasions in sophisticated equipment. However, the “zero transmission” property of linear motor motion system makes the disturbance factors including load variation and nonlinear friction force and so on, can act on the motion systems. It implies that disturbances can affect the performance and kinematic accuracy of systems. In this paper, the mode of linear motor motion systems with closed loop controllers is given and input-to-state stability analysis of the mode is considered. Based on the Lyapunov function method, an input-to-state stability criterion of linear motor motion systems can be obtained. The relationship between the controller gains and input-to-state stability is provided, which can provide auxiliary support for the selection of controller gains.
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Key words:
- linear motor motion systems /
- disturbances /
- input-to-state stability
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表 1 保证系统输入到状态稳定的${K_{\rm{P}}}$最小值
${K_{\rm{P}}}$ ${K_{\rm{I}}}$ 0.01 0.1 1 10 $\alpha $ 0.01 0.826 9 0.827 1 0.829 4 0.852 6 0.05 – 4.133 6 4.135 9 4.159 0 0.1 – – 8.268 0 8.291 3 0.15 – – 12.399 1 12.422 4 0.2 – – 16.529 1 16.552 4 
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