Abstract
Long-stroke compliant parallel mechanisms (CPMs) are widely used in precision applications. However, stress stiffening and sensitivity to external disturbances in CPMs present challenges in the design of controller. In this paper, the nonlinear stiffness model of the stage is established which is incorporated into the dynamic model. In particular, the method of adaptive nonsingular fast terminal sliding mode control (ANFTSMC) is developed based on the dynamic model. This method addresses the problems of the system parameter uncertainty and the slow convergence of traditional sliding mode control (SMC) at the equilibrium point. The stability of the presented ANFTSMC strategy has been proved based on the Lyapunov analysis. Finally, the proposed control architecture is implemented on the designed 4-prismatic-prismatic-revolute (4-PPR) CPM. The results demonstrate that the developed method exhibits excellent tracking accuracy and robustness compared to the traditional linear sliding mode control (LSMC) and proportional-integral-derivative (PID) control.
Similar content being viewed by others
Data availability
All data included in this study are available upon request by contacting with the corresponding author.
References
Al-Jodah, A., Shirinzadeh, B., Ghafarian, M., Das, T.K., Tian, Y., Zhang, D., Wang, F.: Development and control of a large range XY\(\theta\) micropositioning stage. Mechatronics 669, 102343 (2020). https://doi.org/10.1016/j.mechatronics.2020.102343
Al-Jodah, A., Shirinzadeh, B., Ghafarian, M., Das, T.K., Pinskier, J.: Design, modeling, and control of a large range 3-DOF micropositioning stage. Mech. Mach. Theory 156, 104159 (2021). https://doi.org/10.1016/j.mechmachtheory.2020.104159
Awtar, S., Parmar, G.: Design of a large range XY nanopositioning system. Precis. Eng. 48, 323–330 (2017). https://doi.org/10.1016/j.precisioneng.2017.01.002
Awtar, S., Slocum, A.H., Sevincer, E.: Characteristics of beam-based flexure modules. J. Mech. Des. 129, 625–639 (2007). https://doi.org/10.1115/1.2717231
Cecil, J., Kumar, M.B.B.R., Lu, Y., Basallali, V.: A review of micro-devices assembly techniques and technology. Int. J. Adv. Manuf. Technol. 83, 1569–1581 (2015). https://doi.org/10.1007/s00170-015-7698-6
Dai, G., Pohlenz, F., Danzebrink, H.-U., Xu, M., Hasche, K., Wilkening, G.: Metrological large range scanning probe microscope. Rev. Sci. Instrum. 75, 962–969 (2017). https://doi.org/10.1063/1.1651638
Gan, M., Qiao, Z., Li, Y.: Sliding mode control with perturbation estimation and hysteresis compensator based on bouc-wen model in tackling fast-varying sinusoidal position control of a piezoelectric actuator. J. Syst. Sci. Complex. 29, 367–381 (2016). https://doi.org/10.1007/s11424-016-5127-z
Guo, Z., Tian, Y., Liu, C., Wang, F., Liu, X., Shirinzadeh, B., Zhang, D.: Design and control methodology of a 3-DOF flexure-based mechanism for micro/nano-positioning. IEEE Trans. Rob. 28, 478–491 (2012). https://doi.org/10.1016/j.rcim.2014.10.003
Habibullah, Pota, H.R., Petersen, I.R., Rana, M.S.: Creep, hysteresis, and cross-coupling reduction in the high-precision positioning of the piezoelectric scanner stage of an atomic force microscope. IEEE Trans. Nanotechnol. 12, 1125–1134 (2013). https://doi.org/10.1109/tnano.2013.2280793
Hao, G., Yu, J., Liu, Y.: Compliance synthesis of a class of planar compliant parallelogram mechanisms using the position space concept. In: Proc. 4th IEEE/IFToMM Int. Conf. Reconfigurable Mechanisms Robots Delft, Netherland, pp. 1–10 (2018)
Howell, L.L. (ed.): Handbook of Compliant Mechanism. Wiley, New York (2013)
Lee, C., Stepanick, C.K., Lee, S.-K., Tarbutton, J.A.: Cross-coupling effect of large range XY nanopositioning stage fabricated by stereolithography process. Precis. Eng. 46, 81–87 (2016). https://doi.org/10.1016/j.precisioneng.2016.04.001
Ling, M., Wang, J., Wu, M., Cao, L., Fu, B.: Design and modeling of an improved bridge-type compliant mechanism with its application for hydraulic piezo-valves. Sens. Actuators A 324, 112687 (2021). https://doi.org/10.1016/j.sna.2021.112687
Ling, J., Feng, Z., Chen, L., Zhu, Y.: Neural network-based iterative learning control of a piezo-driven nanopositioning stage. Precis. Eng. 81, 112–123 (2023). https://doi.org/10.1016/j.precisioneng.2023.02.006
Lu, S., Tian, C., Yan, P.: Adaptive extended state observer-based synergetic control for a long-stroke compliant microstage with stress stiffening. IEEE/ASME Trans. Mechatron. 25, 259–270 (2019). https://doi.org/10.1109/tmech.2019.2960513
Qin, Y., Shirinzadeh, B., Zhang, D., Tian, Y.: Design and kinematics modeling of a novel 3-DOF monolithic manipulator featuring improved scott-russell mechanisms. J. Mech. Des. 135, 101–104 (2013). https://doi.org/10.1115/1.4024979
Roy, N.K., Cullinan, M.A.: Fast trajectory tracking of a flexure-based, multi-axis nanopositioner with 50 mm travel. IEEE/ASME Trans. Mechatron. 23, 2805–2813 (2018). https://doi.org/10.1109/tmech.2018.2871162
Tang, H., Li, J., Jia, Y., Gao, J., Li, Y.: Development and testing of a large-stroke nanopositioning stage with linear active disturbance rejection controller. IEEE Trans. Autom. Sci. Eng. 19, 2461–2470 (2021). https://doi.org/10.1109/tase.2021.3085481
Wang, Z., Xu, R., Wang, L., Tian, D.: Finite-time adaptive sliding mode control for high-precision tracking of piezo-actuated stages. ISA Trans. 129, 436–445 (2022). https://doi.org/10.1016/j.isatra.2021.12.001
Wang, G., Zhou, Y., Ni, L., Aphale, S.S.: Global fast non-singular terminal sliding-mode control for high-speed nanopositioning. ISA Trans. 136, 560–570 (2023). https://doi.org/10.1016/j.isatra.2022.10.028
Wu, H., Lai, L., Zhang, L., Zhu, L.: A novel compliant xy micro-positioning stage using bridge-type displacement amplifier embedded with scott-russell mechanism. Precis. Eng. 73, 284–295 (2021). https://doi.org/10.1016/j.precisioneng.2021.09.014
Xu, Q.: New flexure parallel-kinematic micropositioning system with large workspace. IEEE Trans. Rob. 28, 478–491 (2012). https://doi.org/10.1109/tro.2011.2173853
Xu, Q.: Design and development of a compact flexure-based XY precision positioning system with centimeter range. IEEE Trans. Ind. Electron. 61, 893–903 (2014). https://doi.org/10.1109/tie.2013.2257139
Xu, Q.: Adaptive integral terminal third-order finite-time sliding-mode strategy for robust nanopositioning control. IEEE Trans. Ind. Electron. 68, 6161–6170 (2021). https://doi.org/10.1109/tie.2020.2998751
Yang, M., Du, Z., Chen, F., Dong, W., Zhang, D.: Kinetostatic modelling of a 3-PRR planar compliant parallel manipulator with flexure pivots. Precis. Eng. 48, 323–330 (2017). https://doi.org/10.1016/j.precisioneng.2017.01.002
Yang, M., Sun, M., Wu, Z., Li, J., Long, Y.: Design of a redundant actuated 4-PPR planar 3-DOF compliant nanopositioning stage. Precis. Eng. 82, 68–79 (2023). https://doi.org/10.1016/j.precisioneng.2023.03.001
Yu, Y., Zhang, N.: Dynamic modeling and performance of compliant mechanisms with inflection beams. Mech. Mach. Theory 134, 455–475 (2019). https://doi.org/10.1016/j.mechmachtheory.2019.01.010
Zhang, Y., Tan, K.K., Huang, S.: Vision-servo system for automated cell injection. IEEE Trans. Ind. Electron. 56, 231–238 (2009). https://doi.org/10.1109/tie.2008.925771
Zhang, C., Yu, H., Yang, M., Chen, S., Yang, G.: Nonlinear kinetostatic modeling and analysis of a large range 3-PPR planar compliant parallel mechanism. Precis. Eng. 74, 264–277 (2021). https://doi.org/10.1109/tro.2011.2173853
Zhu, H., Pang, C.K., Teo, T.J.: A flexure-based parallel actuation dual-stage system for large-stroke nanopositioning. IEEE Trans. Ind. Electron. 64, 5553–5563 (2017). https://doi.org/10.1109/TIE.2017.2677306
Zhu, W., Yang, F., Rui, X.: Robust independent modal space control of a coupled nano-positioning piezo-stage. Mech. Syst. Sig. Process. 106, 466–479 (2018). https://doi.org/10.1016/j.ymssp.2018.01.016
Acknowledgements
This research was funded by the NSFC Zhejiang Joint Fund for the Integration of Industrialization and Informatization (U1609206), the Ningbo Natural Science Foundation (2023J406, 2022J315), and the National Natural Science Foundation of China (51905523, 52305041).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there are no conflict of interests.
Contest to publication
This paper is submitted for possible publication in the focused section on New Trends on Intelligent Automation by Industrial Robots.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ren, J., Zhang, C., Yang, M. et al. Modeling and control for a long-stroke 4-PPR compliant parallel mechanism. Int J Intell Robot Appl 8, 96–110 (2024). https://doi.org/10.1007/s41315-023-00313-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41315-023-00313-y