{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T15:30:43Z","timestamp":1774452643630,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,11]],"date-time":"2017-04-11T00:00:00Z","timestamp":1491868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>To improve the phase-shifting accuracy, this paper presents a novel integrated framework for design, control and experimental validation of the piezoelectric actuated phase shifter with a trade-off between accuracy and cost. The piezoelectric actuators with built-in sensors are adopted to drive the double parallel four-bar linkage flexure hinge-based mechanisms. Three mechanisms form the tripod structure of the assembled phase shifter. Then, a semi-closed loop controller with inner feedback and outer feedforward loops via the external laser interferometer is developed for accurate positioning of the phase shifter. Finally, experiments related with travel range, step response, linearity and repeatability are carried out. The linearity error is 0.21% and the repeatability error of 10    \u03bc   m displacement is 3 nm. The results clearly demonstrate the good performance of the developed phase shifter and the feasibility of the proposed integrated framework.<\/jats:p>","DOI":"10.3390\/s17040838","type":"journal-article","created":{"date-parts":[[2017,4,11]],"date-time":"2017-04-11T11:41:42Z","timestamp":1491910902000},"page":"838","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Piezoelectric Actuated Phase Shifter Based on External Laser Interferometer: Design, Control and Experimental Validation"],"prefix":"10.3390","volume":"17","author":[{"given":"Peng-Zhi","family":"Li","sequence":"first","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Xiao-Dong","family":"Wang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}]},{"given":"Yong-Xin","family":"Sui","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}]},{"given":"De-Fu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}]},{"given":"Dong-Fang","family":"Wang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}]},{"given":"Li-Jian","family":"Dong","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}]},{"given":"Ming-Yang","family":"Ni","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3049","DOI":"10.1364\/AO.24.003049","article-title":"Phase shifter calibration in phase-shifting interferometry","volume":"24","author":"Cheng","year":"1985","journal-title":"App. Opt."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8863","DOI":"10.1364\/AO.45.008863","article-title":"Phase-step calibration technique based on a two-run-times-two-frame phase-shift method","volume":"45","author":"Zhong","year":"2006","journal-title":"Appl. Opt."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"16861","DOI":"10.1364\/OE.17.016861","article-title":"Phase-shifts n\/2 calibration method for phase-stepping interferometry","volume":"17","author":"Bai","year":"2009","journal-title":"Opt. Express"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.optcom.2016.06.001","article-title":"Phase-shifting of correlation fringes created by image processing as an alternative to improve digital shearography","volume":"380","author":"Braga","year":"2016","journal-title":"Opt. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Leach, R. (2011). Optical Measurement of Surface Topography (Chapter 8: Phase Shifting Interferometry), Springer.","DOI":"10.1007\/978-3-642-12012-1"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chen, T., Wang, Y., Liu, H., Yang, Z., Wang, P., and Sun, L. (2017). Topologically optimized nano-positioning stage integrating with a capacitive comb sensor. Sensors, 17.","DOI":"10.3390\/s17020257"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1246","DOI":"10.1109\/TFUZZ.2015.2502282","article-title":"Adaptive fuzzy hysteresis internal model tracking control of piezoelectric actuators with nanoscale application","volume":"24","author":"Li","year":"2016","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/j.ymssp.2012.10.004","article-title":"A simple fuzzy system for modelling of both rate-independent and rate-dependent hysteresis in piezoelectric actuators","volume":"36","author":"Li","year":"2013","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1459","DOI":"10.1109\/TMECH.2012.2203315","article-title":"Motion control of piezoelectric positioning stages: modeling, controller design, and experimental evaluation","volume":"18","author":"Gu","year":"2013","journal-title":"IEEE\/ASME Trans. Mech."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2675","DOI":"10.3390\/s100402675","article-title":"Development of X-Y servo pneumatic-piezoelectric hybrid actuators for position control with high response, large stroke and nanometer accuracy","volume":"10","author":"Chiang","year":"2010","journal-title":"Sensors"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5826","DOI":"10.3390\/s130505826","article-title":"Development of a micro-gripper using piezoelectric bimorphs","volume":"13","author":"Hamzaid","year":"2013","journal-title":"Sensors"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"14671","DOI":"10.3390\/s121114671","article-title":"Modelling and analysis of a new piezoelectric dynamic balance regulator","volume":"12","author":"Du","year":"2012","journal-title":"Sensors"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3409","DOI":"10.3390\/s150203409","article-title":"Improving atomic force microscopy imaging by a direct inverse asymmetric PI hysteresis model","volume":"15","author":"Wang","year":"2015","journal-title":"Sensors"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10673","DOI":"10.3390\/s101210673","article-title":"A compact vertical scanner for atomic force microscopes","volume":"10","author":"Park","year":"2010","journal-title":"Sensors"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhang, X., Wang, C., Gao, R.X., Yan, R., Chen, X., and Wang, S. (2016). A novel hybrid error criterion-based active control method for on-line milling vibration suppression with piezoelectric actuators and sensors. Sensors, 16.","DOI":"10.3390\/s16010068"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e16158","DOI":"10.1038\/lsa.2016.158","article-title":"Optical disassembly of cellular clusters by tunable \u2019tug-of-war\u2019 tweezers","volume":"5","author":"Bezryadina","year":"2016","journal-title":"Light Sci. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"e16190","DOI":"10.1038\/lsa.2016.190","article-title":"High-finesse Fabry-Perot cavities with bidimensional Si3N4 photonic-crystal slabs","volume":"6","author":"Chen","year":"2016","journal-title":"Light Sci. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"e16019","DOI":"10.1038\/lsa.2016.19","article-title":"Orbital angular momentum photonic quantum interface","volume":"5","author":"Zhou","year":"2016","journal-title":"Light Sci. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/j.mechatronics.2009.01.004","article-title":"Design and modeling of a novel 3-DOF precision micro-stage","volume":"19","author":"Kim","year":"2009","journal-title":"Mechatronics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1016\/j.ijmecsci.2006.07.006","article-title":"Investigation of a 3-DOF micro-positioning table for surface grinding","volume":"48","author":"Zhang","year":"2006","journal-title":"Int. J. Mech. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"121101","DOI":"10.1063\/1.4765048","article-title":"High-speed flexure-guided nanopositioning: mechanical design and control issues","volume":"83","author":"Yong","year":"2012","journal-title":"Rev. Sci. Instrum."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.precisioneng.2007.05.002","article-title":"Review of circular flexure hinge design equations and derivation of empirical formulations","volume":"32","author":"Yong","year":"2008","journal-title":"Precis. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3601","DOI":"10.1109\/TIE.2010.2084972","article-title":"A novel piezoactuated XY stage with parallel, decoupled, and stacked flexure structure for micro-\/nanopositioning","volume":"58","author":"Li","year":"2011","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/j.compstruct.2003.12.008","article-title":"Dynamic and static modelling of piezoelectric composite structures using a thermal analogy with MSC\/NASTRAN","volume":"65","author":"Cote","year":"2004","journal-title":"Compos. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"692","DOI":"10.1016\/j.mechrescom.2005.01.004","article-title":"A new technique for large deflection analysis of non-prismatic cantilever beams","volume":"32","author":"Dado","year":"2005","journal-title":"Mech. Res. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1109\/TCST.2005.847331","article-title":"PID control system analysis, design, and technology","volume":"13","author":"Ang","year":"2005","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/j.measurement.2016.02.041","article-title":"Repeatability and reproducibility techniques for the analysis of measurement systems","volume":"86","author":"Zanobini","year":"2016","journal-title":"Measurement"},{"key":"ref_28","unstructured":"(2017, March 29). Physik Instrumente Products: S315.10. Available online: https:\/\/www.physikinstrumente.com\/en\/products\/z-tip-tilt-platforms\/piezo-platforms\/s-310-s-316-piezo-z-tip-tilt-scanner-300600."},{"key":"ref_29","unstructured":"(2017, March 29). Queensgate Products: NPS-Z-15H. Available online: http:\/\/www.nanopositioning.com\/products\/nanomechanisms\/nps-z-15h."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/838\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:32:24Z","timestamp":1760207544000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/838"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,11]]},"references-count":29,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,4]]}},"alternative-id":["s17040838"],"URL":"https:\/\/doi.org\/10.3390\/s17040838","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,11]]}}}