We present a sampled-data adaptive harmonic control algorithm that rejects sinusoids with known frequencies that act on a completely unknown asymptotically stable linear time-invariant system. We analyze the stability and closed-loop performance for systems with at least as many controls as performance measurements. We show that the closed-loop system is uniformly Lyapunov stable and the adaptive controller asymptotically rejects the disturbances. We present numerical simulations comparing the new sampled-data adaptive controller with an existing sinusoidal disturbance rejection approach (i.e., higher harmonic control). We also present results from an active disturbance rejection experiment in an acoustic environment. These experimental results demonstrate the practical effectiveness of the adaptive harmonic controller.

中文翻译：

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自适应谐波控制，用于抑制作用于未知系统的正弦波扰动

我们提出了一种采样数据自适应谐波控制算法，该算法拒绝具有已知频率的正弦波，该正弦波作用于完全未知的渐近稳定线性时不变系统。我们分析了至少具有与性能测量结果一样多的控件的系统的稳定性和闭环性能。我们证明了闭环系统是一致的Lyapunov稳定，并且自适应控制器渐近地拒绝了扰动。我们提供了将新的采样数据自适应控制器与现有的正弦干扰抑制方法（即高次谐波控制）进行比较的数值模拟。我们还提出了在声学环境中进行主动抗扰实验的结果。这些实验结果证明了自适应谐波控制器的实际有效性。