{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:30:58Z","timestamp":1760059858686,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T00:00:00Z","timestamp":1752537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In recent years, pneumatic stages have attracted attention as stages for semiconductor manufacturing equipment due to their low cost and minimal maintenance requirements. However, pneumatic stages include nonlinear elements such as friction and air compressibility, making precise control challenging. To address this issue, this paper aims to achieve high-precision positioning by applying a nonlinear position control method to pneumatic stages. To achieve this, we propose a control method that combines filtered right coprime factorization and Prescribed Performance Control\u2013Sliding Mode Control (PPC-SMC). Filtered right coprime factorization not only stabilizes and simplifies the plant but also reduces noise. Furthermore, PPC-SMC enables safer and faster control by constraining the system state within a switching surface that imposes limits on the error range. Through experiments on the actual system, it was confirmed that the proposed method achieves dramatically higher precision and faster tracking compared to conventional methods.<\/jats:p>","DOI":"10.3390\/axioms14070534","type":"journal-article","created":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T11:52:58Z","timestamp":1752580378000},"page":"534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Marginal Design of a Pneumatic Stage Position Using Filtered Right Coprime Factorization and PPC-SMC"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2586-6911","authenticated-orcid":false,"given":"Tomoya","family":"Hoshina","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Computer Science, Graduate School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Tokyo 184-8588, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-7328-336X","authenticated-orcid":false,"given":"Yusaku","family":"Tanabata","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Science, Graduate School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Tokyo 184-8588, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7411-6602","authenticated-orcid":false,"given":"Mingcong","family":"Deng","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Science, Graduate School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Tokyo 184-8588, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1109\/N-SSC.2007.4785534","article-title":"A 30 year retrospective on Dennard\u2019s MOSFET scaling paper","volume":"12","author":"Bohr","year":"2009","journal-title":"IEEE Solid-State Circuits Soc. Newsl."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wang, H., Li, Q., Zhou, F., and Zhang, J. (2024). High-Precision Positioning Stage Control Based on a Modified Disturbance Observer. Sensors, 24.","DOI":"10.3390\/s24020591"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/j.precisioneng.2010.02.005","article-title":"Development of coarse\/fine dual stage using pneumatically driven bellows actuator and cylinder with air bearings","volume":"34","author":"Kawashima","year":"2010","journal-title":"Precis. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1016\/j.precisioneng.2014.03.006","article-title":"Practical and intuitive controller design method for precision positioning of a pneumatic cylinder actuator stage","volume":"38","author":"Sato","year":"2014","journal-title":"Precis. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1109\/9.376053","article-title":"A new model for control of systems with friction","volume":"40","author":"Olsson","year":"1995","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1016\/j.mechatronics.2008.02.002","article-title":"Modeling of dynamic behaviors of friction","volume":"18","author":"Yanada","year":"2008","journal-title":"Mechatronics"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.mechatronics.2011.11.009","article-title":"Modeling of dynamic friction behaviors of hydraulic cylinders","volume":"22","author":"Tran","year":"2012","journal-title":"Mechatronics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.procir.2022.05.007","article-title":"An extended LuGre model for estimating nonlinear frictions in feed drive systems of machine tools","volume":"107","author":"Xi","year":"2022","journal-title":"Procedia CIRP"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/MCS.2008.929425","article-title":"Revisiting the LuGre friction model","volume":"28","author":"Johanastrom","year":"2008","journal-title":"IEEE Control Syst. Mag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1109\/TCST.2008.2010501","article-title":"LuGre-model-based friction compensation","volume":"18","author":"Freidovich","year":"2009","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"180","DOI":"10.4236\/ica.2013.42022","article-title":"Dynamic friction behaviors of pneumatic cylinders","volume":"4","author":"Tran","year":"2013","journal-title":"Intell. Control Autom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1177\/0954406215594828","article-title":"A new mathematical model of friction for pneumatic cylinders","volume":"230","author":"Tran","year":"2016","journal-title":"Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TCST.2008.2009879","article-title":"Optimal system design of siso-servopneumatic positioning drives","volume":"18","author":"Hildebrandt","year":"2009","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"5838","DOI":"10.1109\/TIE.2015.2418319","article-title":"Active disturbance rejection position control for a magnetic rodless pneumatic cylinder","volume":"62","author":"Zhao","year":"2015","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1016\/j.precisioneng.2017.01.014","article-title":"A review on recent research trends in servo pneumatic positioning systems","volume":"49","author":"Saravanakumar","year":"2017","journal-title":"Precis. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1115\/1.1286336","article-title":"A high performance pneumatic force actuator system: Part I Nonlinear mathematical model","volume":"122","author":"Richer","year":"2000","journal-title":"J. Dyn. Sys., Meas. Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1115\/1.1286366","article-title":"A high performance pneumatic force actuator system: Part II nonlinear controller design","volume":"122","author":"Richer","year":"2000","journal-title":"J. Dyn. Sys. Meas. Control"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ishii, H., and Wakui, S. (2019, January 26\u201328). Performance improvement of PDD 2 compensator embedded in position control for pneumatic stage. Proceedings of the 2019 International Conference on Advanced Mechatronic Systems, Kusatsu, Japan.","DOI":"10.1109\/ICAMechS.2019.8861571"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ishii, H., and Wakui, S. (2019, January 18\u201320). Proposal of Speeding up Scheme for Pneumatic Stage. Proceedings of the 2019 IEEE International Conference on Mechatronics, Ilmenau, Germany.","DOI":"10.1109\/ICMECH.2019.8722939"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Aoki, S., and Deng, M. (2023, January 4\u20137). Nonlinear position control of pneumatically driven stage considering friction characteristics of pneumatic cylinder. Proceedings of the 2023 International Conference on Advanced Mechatronic Systems (ICAMechS), Melbourne, Australia.","DOI":"10.1109\/ICAMechS59878.2023.10272736"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Tanabata, Y., and Deng, M. (2024). Filtered Right Coprime Factorization and Its Application to Control a Pneumatic Cylinder. Processes, 12.","DOI":"10.3390\/pr12071475"},{"key":"ref_22","unstructured":"De Figueiredo, R.J., and Chen, G. (1993). Nonlinear Feedback Control Systems: An Operator Theory Approach, Academic Press Professional, Inc."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Deng, M. (2014). Operator-Based Nonlinear Control Systems: Design and Applications, John Wiley & Sons.","DOI":"10.1002\/9781118819814"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Bechlioulis, C.P., and Rovithakis, G.A. (2008, January 25\u201327). Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances. Proceedings of the 2008 16th Mediterranean Conference on Control and Automation, Ajaccio, France.","DOI":"10.1109\/MED.2008.4601971"},{"key":"ref_25","first-page":"1","article-title":"Prescribed performance control approaches, applications and challenges: A comprehensive survey","volume":"2020","author":"Bu","year":"2021","journal-title":"Asian J. Control"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yao, Y., Zhuang, Y., Xie, Y., Xu, P., and Wu, C. (2025). Prescribed Performance Global Non-Singular Fast Terminal Sliding Mode Control of PMSM Based on Linear Extended State Observer. Actuators, 14.","DOI":"10.3390\/act14020065"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Nguyen, V.C., and Kim, S.H. (2025). A novel fixed-time prescribed performance sliding mode control for uncertain wheeled mobile robots. Sci. Rep., 15.","DOI":"10.1038\/s41598-025-89126-6"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/534\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:09:58Z","timestamp":1760033398000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,15]]},"references-count":27,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["axioms14070534"],"URL":"https:\/\/doi.org\/10.3390\/axioms14070534","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,7,15]]}}}