Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912020330184704 |
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| author | Shi, Kanghong Petersen, Ian R. |
| author_facet | Shi, Kanghong Petersen, Ian R. |
| contents | We introduce a hybrid control system called a hybrid integrator-gain system (HIGS) based integral resonant controller (IRC) to stabilize negative imaginary (NI) systems. A HIGS-based IRC has a similar structure to an IRC, with the integrator replaced by a HIGS. We show that a HIGS-based IRC is an NI system. Also, for a SISO NI system with a minimal realization, we show there exists a HIGS-based IRC such that their closed-loop interconnection is asymptotically stable. Also, we propose a proportional-integral-double-integral resonant controller and a HIGS-based proportional-integral-double-integral resonant controller, and we show that both of them can be applied to asymptotically stabilize an NI system. An example is provided to illustrate the proposed results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems Shi, Kanghong Petersen, Ian R. Systems and Control Optimization and Control We introduce a hybrid control system called a hybrid integrator-gain system (HIGS) based integral resonant controller (IRC) to stabilize negative imaginary (NI) systems. A HIGS-based IRC has a similar structure to an IRC, with the integrator replaced by a HIGS. We show that a HIGS-based IRC is an NI system. Also, for a SISO NI system with a minimal realization, we show there exists a HIGS-based IRC such that their closed-loop interconnection is asymptotically stable. Also, we propose a proportional-integral-double-integral resonant controller and a HIGS-based proportional-integral-double-integral resonant controller, and we show that both of them can be applied to asymptotically stabilize an NI system. An example is provided to illustrate the proposed results. |
| title | Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2403.15140 |