Across the industrial sector, precision engineering represents a set of technologies that are the key to successful international competitive development. Ultra precision machine tools demand to control the point of contact of tool and workpiece within the range 100 nm to 0.1 nm. This work presents the novel Adjustable Accuracy (AA) approximation of a DT function based on user-defined previous steps values. Three control and observation problems are addressed with this novel AA Disturbance Estimation that allows to achieve an adjustable accuracy boundary layer of order O(T^β) of the corresponding sliding manifold of the closed loop system in the presence of disturbances while avoiding the undesired chattering phenomenon with an ultimate bound that decay exponentially w.r.t. the used number of previous steps for the disturbance approximation. The corresponding simulations show the effectiveness of each scheme.

在整个工业领域，精密工程代表了一组技术，这些技术是成功实现国际竞争发展的关键。超精密机床要求将刀具与工件的接触点控制在100 nm至0.1 nm的范围内。这项工作提出了基于用户定义的先前步骤值的DT函数的新颖的可调精度（AA）近似值。三个控制和观察的问题与这种新颖的AA扰动估计，允许实现顺序的一个可调节的准确性边界层寻址ø（Ť ^β）在存在扰动的情况下闭环系统的相应滑动歧管），同时避免了不希望有的震颤现象，其最终极限会以指数形式衰减扰动近似的先前步骤的使用次数。相应的仿真显示了每种方案的有效性。