{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T18:37:03Z","timestamp":1785004623927,"version":"3.55.0"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,9,5]],"date-time":"2022-09-05T00:00:00Z","timestamp":1662336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873016"],"award-info":[{"award-number":["61873016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61633002"],"award-info":[{"award-number":["61633002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62173019"],"award-info":[{"award-number":["62173019"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Symmetry is presented in the frame structure, modeling, and disturbance analysis of the three-axis inertially stabilized platform (ISP), which affects the control performance of the ISP. To realize high-performance control for the ISP, a nonlinear dynamic model based on the geographic coordinates and a compound control method based on the adaptive extended state observer (ESO) and adaptive back-stepping integral sliding mode control (SMC) are proposed. The nonlinear dynamic model based on geographic coordinates could avoid the degradation of measurement and control performance due to complex coordinate transformations. An adaptive ESO (AESO) has been developed to estimate the unknown disturbances of ISP. With the information from the ISP system, the adaptive bandwidth of AESO can deal with the peaking phenomenon without introducing excessive noise. Furthermore, based on the integral sliding mode, the adaptation laws of parameter uncertainty and disturbance estimation compensation have been developed for the back-stepping integral SMC method, which can reduce the estimation burden and improve the disturbance estimation accuracy of AESO. The asymptotic stability of the compound control method has been proven by the Lyapunov stability theory. Through a series of simulations and experiments, the effectiveness of the compound method is validated.<\/jats:p>","DOI":"10.3390\/sym14091848","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T09:51:09Z","timestamp":1662630669000},"page":"1848","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A High-Performance Compound Control Method for a Three-Axis Inertially Stabilized Platform under Multiple Disturbances"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8186-0245","authenticated-orcid":false,"given":"Xusheng","family":"Lei","sequence":"first","affiliation":[{"name":"The School of Instrument Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4899-1224","authenticated-orcid":false,"given":"Fa","family":"Fu","sequence":"additional","affiliation":[{"name":"The School of Instrument Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5277-5885","authenticated-orcid":false,"given":"Rui","family":"Wang","sequence":"additional","affiliation":[{"name":"The School of Instrument Science and Opto-Electronics Engineering, Beihang University, Beijing 100191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/MCS.2007.910201","article-title":"Inertially stabilized platforms for optical imaging systems","volume":"28","author":"Masten","year":"2008","journal-title":"IEEE Control Syst. 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