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However, for FHAUV control, there is a lack of research on phenomena or problems caused by large changes in the air\/water transition. In addition, the effects of wind, wave, other factors and conditions on motion control are not investigated. This paper presents the first control study on the above issues. The motion model of FHAUV is developed, with the effects of wind and wave disturbances. Then, this paper improves a cascade gain scheduling (CGS) PID for different media environments (air and water) and proposes a cascade state feedback (CSF) control strategy to address the convergence problem of FHAUV control caused by large speed change in the air\/water transition. In the comparisons of the two control schemes in various tracking cases including trajectory slopes, reference speeds, wind and wave disturbances, CSF has a better control effect, convergence rate and robustness; the key factors and conditions of the air\/water transition are investigated, the critical relations and feasible domains of the trajectory slopes and reference speeds that the FHAUV must meet to successfully exit the water and enter the air are obtained, the critical slope decreases as the reference speed increases, and the feasible domain of CSF is larger than that of CGS, revealing that CSF is superior than CGS for exiting the water.<\/jats:p>","DOI":"10.1007\/s10846-024-02099-y","type":"journal-article","created":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T09:01:48Z","timestamp":1718874108000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Trajectory Tracking Control of Fixed-Wing Hybrid Aerial Underwater Vehicle Subject to Wind and Wave Disturbances"],"prefix":"10.1007","volume":"110","author":[{"given":"Junping","family":"Li","sequence":"first","affiliation":[]},{"given":"Yufei","family":"Jin","sequence":"additional","affiliation":[]},{"given":"Rui","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Yulin","family":"Bai","sequence":"additional","affiliation":[]},{"given":"Di","family":"Lu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7026-1386","authenticated-orcid":false,"given":"Zheng","family":"Zeng","sequence":"additional","affiliation":[]},{"given":"Lian","family":"Lian","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,20]]},"reference":[{"key":"2099_CR1","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.paerosci.2014.12.005","volume":"74","author":"X Yang","year":"2015","unstructured":"Yang, X., Wang, T., Liang, J., et al.: Survey on the novel hybrid aquatic\u2013aerial amphibious aircraft: aquatic unmanned aerial vehicle (AquaUAV)[J]. 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