<i>H</i> _∞ Filter and Extended State Observer-Based Disturbance Rejection Control for Systems With Uncertainty and Noise

The extended state observer (ESO) is widely used in disturbance rejection methods for its ability to achieve rapid convergence through high-gain design. However, this high-gain ESO often leads to significant noise amplification and increased sensitivity to disturbances, which adversely affects performance. To address this issue, we propose a novel method that integrates an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter into the ESO framework. Unlike conventional methods, this approach does not assume Gaussian noise or require prior knowledge of noise statistics. Instead, it only assumes bounded noise, making it applicable to a broader range of scenarios. The method employs the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filter to attenuate noise within a predefined bound, after which the filtered signal is passed to the ESO for state and disturbance estimation. This significantly reduces the sensitivity of the high-gain ESO to noise. Finally, the proposed method is applied to the speed control of a permanent magnet synchronous motor servo system to verify its effectiveness. The results demonstrate that the method successfully suppresses noise, enhances control performance, and provides a parameter adjustment steps and recommendations its application.