Sampled-Data Control using Hermite-Obreschkoff Methods with an IDA-PBC Example
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908339331399680 |
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| author | Zhang, Le Kotyczka, Paul |
| author_facet | Zhang, Le Kotyczka, Paul |
| contents | The motivation for this paper is the implementation of nonlinear state feedback control, designed based on the continuous-time plant model, in a sampled control loop under relatively slow sampling. In previous work we have shown that using one-step predictions of the target dynamics with higher order integration schemes, together with possibly higher order input shaping, is a simple and effective way to increase the feasible sampling times until performance degradation and instability occur. In this contribution we present a unifying derivation for arbitrary orders of the previously used Lobatto IIIA collocation and Hermite interpolation schemes through the Hermite-Obreschkoff formula. We derive, moreover, an IDA-PBC controller for a magnetic levitation system, which requires a non-constant target interconnection matrix, and show experimental results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sampled-Data Control using Hermite-Obreschkoff Methods with an IDA-PBC Example Zhang, Le Kotyczka, Paul Systems and Control The motivation for this paper is the implementation of nonlinear state feedback control, designed based on the continuous-time plant model, in a sampled control loop under relatively slow sampling. In previous work we have shown that using one-step predictions of the target dynamics with higher order integration schemes, together with possibly higher order input shaping, is a simple and effective way to increase the feasible sampling times until performance degradation and instability occur. In this contribution we present a unifying derivation for arbitrary orders of the previously used Lobatto IIIA collocation and Hermite interpolation schemes through the Hermite-Obreschkoff formula. We derive, moreover, an IDA-PBC controller for a magnetic levitation system, which requires a non-constant target interconnection matrix, and show experimental results. |
| title | Sampled-Data Control using Hermite-Obreschkoff Methods with an IDA-PBC Example |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2501.11495 |