Robust Stability of Discrete-time Disturbance Observers: Understanding Interplay of Sampling, Model Uncertainty and Discrete-time Designs
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866917874586615808 |
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| author | Park, Gyunghoon Lee, Chanhwa Joo, Youngjun Shim, Hyungbo |
| author_facet | Park, Gyunghoon Lee, Chanhwa Joo, Youngjun Shim, Hyungbo |
| contents | In this paper, we address the problem of robust stability for uncertain sampled-data systems controlled by a discrete-time disturbance observer (DT-DOB). Unlike most of previous works that rely on the small-gain theorem, our approach is to investigate the location of the roots of the characteristic polynomial when the sampling is performed sufficiently fast. This approach provides a generalized framework for the stability analysis in the sense that (i) many popular discretization methods are taken into account; (ii) under fast sampling, the obtained robust stability condition is necessary and sufficient except in a degenerative case; and (iii) systems of arbitrary order and of large uncertainty can be dealt with. The relation between sampling zeros---discrete-time zeros that newly appear due to the sampling---and robust stability is highlighted, and it is explicitly revealed that the sampling zeros can hamper stability of the overall system when the Q-filter and/or the nominal model are carelessly selected in discrete time. Finally, a design guideline for the Q-filter and the nominal model in the discrete-time domain is proposed for robust stabilization under the sampling against the arbitrarily large (but bounded) parametric uncertainty of the plant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_08722 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Robust Stability of Discrete-time Disturbance Observers: Understanding Interplay of Sampling, Model Uncertainty and Discrete-time Designs Park, Gyunghoon Lee, Chanhwa Joo, Youngjun Shim, Hyungbo Systems and Control In this paper, we address the problem of robust stability for uncertain sampled-data systems controlled by a discrete-time disturbance observer (DT-DOB). Unlike most of previous works that rely on the small-gain theorem, our approach is to investigate the location of the roots of the characteristic polynomial when the sampling is performed sufficiently fast. This approach provides a generalized framework for the stability analysis in the sense that (i) many popular discretization methods are taken into account; (ii) under fast sampling, the obtained robust stability condition is necessary and sufficient except in a degenerative case; and (iii) systems of arbitrary order and of large uncertainty can be dealt with. The relation between sampling zeros---discrete-time zeros that newly appear due to the sampling---and robust stability is highlighted, and it is explicitly revealed that the sampling zeros can hamper stability of the overall system when the Q-filter and/or the nominal model are carelessly selected in discrete time. Finally, a design guideline for the Q-filter and the nominal model in the discrete-time domain is proposed for robust stabilization under the sampling against the arbitrarily large (but bounded) parametric uncertainty of the plant. |
| title | Robust Stability of Discrete-time Disturbance Observers: Understanding Interplay of Sampling, Model Uncertainty and Discrete-time Designs |
| topic | Systems and Control |
| url | https://arxiv.org/abs/1901.08722 |