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<p>The disturbance observer (DOB)-based control is a powerful robust control technique characterized by external disturbance rejection and nominal performance recovery. However, the conventional DOB encounters numerical challenges in implementation when the plant has a high relative degree. This is due to its high-gain observer structure inside which requires gains that scale with the reciprocal of the time constant, and the gain is further powered up to the relative degree, leading to a potential numerical instability. To address this issue, we propose a modified DOB whose gains are limited to at most the second order of the high-gain parameter, regardless of how large the relative degree is. The key idea is replacing the original high-gain observer with the so-called ‘low-power” high-gain observer. The proposed “low-power” DOB not only preserves the original capability of DOB that allows the outer-loop controller to be designed without consideration about robustness, but also provides estimated state of the plant for the outer-loop controller without numerical issues. A robust stability condition is analyzed via singular perturbation theory, and a systematic design methodology for the design coefficients is developed based on Kharitonov theorem and root locus techniques. The numerical simulation results are provided to validate the theoretical results.</p>

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Low-Power Disturbance Observer for Linear Systems of High Relative Degree with Robust Stability Condition

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Donghyeon Song,
  • Hyuntae Kim,
  • Hyungbo Shim

摘要

The disturbance observer (DOB)-based control is a powerful robust control technique characterized by external disturbance rejection and nominal performance recovery. However, the conventional DOB encounters numerical challenges in implementation when the plant has a high relative degree. This is due to its high-gain observer structure inside which requires gains that scale with the reciprocal of the time constant, and the gain is further powered up to the relative degree, leading to a potential numerical instability. To address this issue, we propose a modified DOB whose gains are limited to at most the second order of the high-gain parameter, regardless of how large the relative degree is. The key idea is replacing the original high-gain observer with the so-called ‘low-power” high-gain observer. The proposed “low-power” DOB not only preserves the original capability of DOB that allows the outer-loop controller to be designed without consideration about robustness, but also provides estimated state of the plant for the outer-loop controller without numerical issues. A robust stability condition is analyzed via singular perturbation theory, and a systematic design methodology for the design coefficients is developed based on Kharitonov theorem and root locus techniques. The numerical simulation results are provided to validate the theoretical results.