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arXiv · 2403.15140

Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems

Kanghong Shi·Ian R. Petersen
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Abstract

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.

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Kanghong Shi, Ian R. Petersen. 2024-03-22. Hybrid integrator-gain system based integral resonant controllers for negative imaginary systems. https://arxiv.org/abs/2403.15140

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