标题： Q滤波器带宽在扰动观测器中的确定，以在测量噪声下保证瞬态和稳态性能 显示英文标题

标题： Determination of Bandwidth of Q-filter in Disturbance Observers to Guarantee Transient and Steady State Performance under Measurement Noise

摘要： 基于Q滤波器的扰动观测器（DOB）由于其设计简单，是应用最广泛的鲁棒控制器之一。 这种简单性源于减少低通滤波器的时间常数，不仅确保了鲁棒稳定性，还增强了名义性能恢复能力——即恢复名义闭环系统的轨迹的能力。 然而，与无噪声环境相比，在存在测量噪声的情况下，过小的时间常数反而会损害名义性能恢复。 也就是说，最小化时间常数不再能立即保证名义性能恢复。 受此观察的启发，本文专注于确定时间常数以确保瞬态和稳态性能。 该分析基于坐标变换的Lyapunov方法，受奇异摄动理论的启发。 结果，我们提出了一个可接受的噪声水平和一个开区间，用于时间常数，以保证所需的性能。 该分析还可以导致理论证明，即仅在无噪声情况下，过度减小时间常数才能保证达到目标性能。 显示英文摘要

摘要： Q-filter-based disturbance observer (DOB) is one of the most widely used robust controller due to its design simplicity. Such simplicity arises from that reducing the time constant of low pass filters, not only ensures robust stability but also enhances nominal performance recovery -- ability to recover the trajectory of nominal closed-loop system. However, in contrast to noise-free environment, excessively small time constant can rather damage the nominal performance recovery under measurement noise. That is, minimizing time constant is no longer immediately guaranteeing nominal performance recovery. Motivated by this observation, this paper concentrates on determination of time constant to ensure transient and steady state performance. This analysis uses Lyapunov method based on the coordinate change inspired by the singular perturbation theory. As a result, we present an affordable noise level and open interval for the time constant that guarantees both the required performances. The analysis can also lead to theoretical demonstration on that excessively reducing time constant is assured to achieve target performance only for noise-free case.