This paper studies the active damping of the oscillations of lightly damped linear systems whose parameters are indeterminate or may change through time. Systems with an arbitrary number of vibration modes are considered. Systems described by partial differential equations, that yield an infinite number of vibration modes, can also be included. In the case of collocated feedback, i.e. the sensor is placed at the same location of the actuator, a simple fractional order differentiation or integration of the measured signal is proposed that provides an effective control: (1) it guarantees a minimum phase margin or damping of the closed-loop system at all vibration modes, (2) this feature is robustly achieved, i.e., it is attained for very large variations or uncertainties of the oscillation frequencies of the system and (3) it is robust to spillover effects, i.e., to the unstabilizing effects of the vibration modes neglected in the controller design (especially important in infinite dimensional systems). Moreover, the sensitivity of the gain crossover frequency to such variations is assessed. Finally, these results are applied to the position control of a single link flexible robot. Simulated results are provided.

本文研究了参数不确定或可能随时间变化的轻阻尼线性系统的振动主动阻尼。考虑具有任意数量的振动模式的系统。也可以包括由偏微分方程描述的产生无限多个振动模式的系统。在并置反馈的情况下，即传感器放置在执行器的同一位置，建议对测量信号进行简单的分数阶微分或积分，以提供有效的控制：（1）确保最小的相位裕度或阻尼闭环系统在所有振动模式下的特性，（2）可以稳健地实现此功能，即 它是针对系统振荡频率的很大变化或不确定性而获得的，并且（3）对于溢出效应具有鲁棒性，即对于控制器设计中忽略的振动模式的不稳定效应（在无穷维系统中尤其重要） 。而且，评估了增益交叉频率对这种变化的敏感性。最后，这些结果被应用于单链接柔性机器人的位置控制。提供了模拟结果。