{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:30:34Z","timestamp":1760236234531,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T00:00:00Z","timestamp":1635811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the National Natural Science Foundation of China","award":["U1810119","51774161","51804151"],"award-info":[{"award-number":["U1810119","51774161","51804151"]}]},{"name":"the Taishan scholar funding scheme","award":["tsqn201909113"],"award-info":[{"award-number":["tsqn201909113"]}]},{"name":"the Key projects of applied basic research program in Shanxi Province","award":["201901D111007(ZD)"],"award-info":[{"award-number":["201901D111007(ZD)"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents a robust nonlinear control scheme with time-varying output constraint for the electro-hydraulic force control system (EHFCS). Two typical double-rod symmetrical hydraulic cylinders are employed to simulate force environments in the EHFCS. Therefore, in order to improve the performance of the EHFCS, firstly, the model of the EHFCS is established with taking external disturbances, parameter uncertainties as well as structural vibrations into consideration. Secondly, in order to estimate external disturbances, parameter uncertainties and structural vibrations in the EHFCS and compensate them in the following robust controller design, two disturbance observers (DOs) are designed according to the nonlinear system model. Thirdly, with two estimation values from two DOs, a time-varying constraint-based robust controller (TVCRC) is presented in detail. Moreover, the stability of the proposed controller is analyzed by defining a proper Lyapunov functions. Finally, in order to validate the performance of the proposed controller, a series of simulation studies are conducted using the MATLAB\/Simulink software. These simulation results give a fine proof of the efficiency of the proposed controller. What\u2019s more, an experimental setup of the EHFCS is established to further validate the performance. Comparative experimental results show that the proposed controller exhibits better performance than the TVCRC without two DOs and a conventional proportional integral (PI) controller.<\/jats:p>","DOI":"10.3390\/sym13112074","type":"journal-article","created":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T22:14:52Z","timestamp":1635891292000},"page":"2074","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Robust Nonlinear Control Scheme for Electro-Hydraulic Force Tracking Control with Time-Varying Output Constraint"],"prefix":"10.3390","volume":"13","author":[{"given":"Wanshun","family":"Zang","sequence":"first","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0122-8771","authenticated-orcid":false,"given":"Jinpeng","family":"Su","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao 266590, China"},{"name":"State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Long","family":"Feng","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electronic Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1109\/TCST.2017.2699166","article-title":"Nonlinear adaptive control of hydraulic system with observing and compensating mismatching uncertainties","volume":"26","author":"Wang","year":"2017","journal-title":"IEEE Trans. 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