This research is motivated by the problem of regenerative chatter vibration, which is an extremely harmful phenomenon in machining in general, and in internal turning in particular. In addition to limiting the production rate and accelerating the tool wear, regenerative chatter deteriorates the surface finish, which is especially undesired in the context of precision machining. This paper presents an active control design method for slender bars with delayed excitation which can be applied to the problem of active control of regenerative chatter in internal turning. The presented control method is based on the delay-dependent output feedback controller synthesis. The contribution of the presented design approach stems from incorporating into the design procedure the delayed dynamics of the regenerative chatter, the flexible bar model uncertainty, and the hardware limitations. Furthermore, the delay dynamics is taken explicitly in the synthesis of an $H_{\infty }$ output feedback controller by linear matrix inequalities. The resulting controller is tested by simulations and experiments using a testbed imitating the dynamics of the internal turning process. The results demonstrate the effectiveness of the presented controller synthesis method in comparison to the commonly used approaches.

这项研究是基于再生颤振的问题，该问题通常在机械加工中，特别是在内部车削中是极为有害的现象。除了限制生产率和加速工具磨损之外，再生颤动还会使表面光洁度恶化，这在精密加工的情况下尤其不希望如此。提出了一种具有延迟激励的细长杆主动控制设计方法，该方法可应用于内转中再生颤振的主动控制问题。所提出的控制方法基于与延迟有关的输出反馈控制器综合。提出的设计方法的贡献源于将再生颤振的延迟动态，灵活的条形模型不确定性，和硬件限制。此外，延迟动态是在综合$H_{\infty }$线性矩阵不等式的输出反馈控制器。使用模拟内部车削过程动力学的试验台，通过仿真和实验对所得的控制器进行测试。结果证明了与常用方法相比，所提出的控制器综合方法的有效性。