Robust Performance Analysis and Nonlinearity Shaping for Closed-loop Reset Control Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918134237102080 |
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| author | Hosseini, S. Ali Kostić, Dragan HosseinNia, S. Hassan |
| author_facet | Hosseini, S. Ali Kostić, Dragan HosseinNia, S. Hassan |
| contents | Reset elements are nonlinear filters that improve control performance beyond linear time-invariant (LTI) limits but introduce higher-order harmonics that complicate design. Although frequency-domain tools like describing functions (DFs) and higher-order sinusoidal-input describing functions (HOSIDFs) analyze reset control systems (RCS), no direct method yet quantifies the impact of higher-order harmonics on the error signal without time-domain simulations. This paper introduces a robustness factor, $σ_2(ω)$, which quantifies the increase in the root-mean-square (RMS) value of the error signal due to HOSIDFs, enabling RCS to rely solely on first-order DF characteristics while accounting for nonlinear effects. By using this robustness factor, a systematic method for designing pre- and post-filters is developed to ensure a predefined bound on $σ_2(ω)$, thereby limiting the influence of higher-order harmonics without altering first-order DF behavior. The proposed framework is validated through a case study on a planar precision positioning stage, demonstrating how the robustness factor guides the reduction of nonlinearities and improves performance predictability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Performance Analysis and Nonlinearity Shaping for Closed-loop Reset Control Systems Hosseini, S. Ali Kostić, Dragan HosseinNia, S. Hassan Systems and Control Reset elements are nonlinear filters that improve control performance beyond linear time-invariant (LTI) limits but introduce higher-order harmonics that complicate design. Although frequency-domain tools like describing functions (DFs) and higher-order sinusoidal-input describing functions (HOSIDFs) analyze reset control systems (RCS), no direct method yet quantifies the impact of higher-order harmonics on the error signal without time-domain simulations. This paper introduces a robustness factor, $σ_2(ω)$, which quantifies the increase in the root-mean-square (RMS) value of the error signal due to HOSIDFs, enabling RCS to rely solely on first-order DF characteristics while accounting for nonlinear effects. By using this robustness factor, a systematic method for designing pre- and post-filters is developed to ensure a predefined bound on $σ_2(ω)$, thereby limiting the influence of higher-order harmonics without altering first-order DF behavior. The proposed framework is validated through a case study on a planar precision positioning stage, demonstrating how the robustness factor guides the reduction of nonlinearities and improves performance predictability. |
| title | Robust Performance Analysis and Nonlinearity Shaping for Closed-loop Reset Control Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2509.02143 |