Abstract
Advances in miniaturization of micromachines are receiving considerable industrial attention, with a crucial aspect of research being on precision positioning and manipulation at the micro-nanoscale. Nanopositioners are precision mechatronic systems designed to deal with objects at extremely precise resolution wherein piezoelectric actuators have a high potential to impact emerging markets. However, the major bottleneck in harvesting the advantages of piezoelectric actuator for nanopositioning is the presence of inherent nonlinearity, mostly hysteresis, along with the presence of external dynamical disturbance, and traditional feedback controller cannot handle. Dithering has been used in the parlance of piezoelectric actuation as a surprisingly simple yet powerful means of enhancing system performance. This research presents the design framework of an adaptive voltage dither control logic based on spectral analysis of the system output using normalized harmonic ratio. The proposed controller adaptively tunes the intensity of dither amplitude depending on the system response to an optimum value that yields satisfactory results. A commercially available piezo-actuator has been used to model the system along with hysteresis using Dahl model, and system parameters have been identified experimentally. Performance of the proposed controller has been investigated by subjecting the plant model to several real-time perturbations like plant parameter variation, sinusoidal motion tracking, multi-amplitude multi-frequency input signal, external disturbances like Gaussian and impulse, step response, etc., and with the results showing better control performance and disturbance rejection capability as compared to traditional feedback control.
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An, D., Li, H., Xu, Y., & Zhang, L. (2018). Compensation of hysteresis on piezoelectric actuators based on tripartite PI model. Micromachines, 9, 44.
Basso, M., Dahleh, M., Mezic, I., & Salapaka, M. V. (1999) Stochastic resonance in AFM’s. In Proceedings of the American control conference (ACC’99) (Vol. 6, pp. 3774–3778).
Benzi, R., Parisi, G., Sutera, A., & Vulpiani, A. (1982). Stochastic resonance in climatic change. Hamburg: Tellus.
Bilinskis, J., & Mikelsons, A. (1992). Randomized signal processing. Englewood Cliffs, NJ: Prentice-Hall.
Cahyadi, A. I., & Yamamoto, Y. (2006) Modeling a micro manipulation system with flexure hinge. In Proceedings of the IEEE international conference on robotics, automation and mechatronics (pp. 1–5).
Carbone, P., & Petri, D. (1994). Effect of additive dither on the resolution of ideal quantizers. IEEE Transactions on Instrumentation and Measurement, 43, 389–396.
Chen, Y. Y., Chen, Y. H., & Huang, C. Y. (2017a). Nano-scale positioning design with piezoelectric materials. Micromachines, 8, 360.
Chen, T., Wang, Y., Yang, Z., Liu, H., Liu, J., & Sun, L. (2017b). A PZT actuated triple-finger gripper for multi-target micromanipulation. Micromachines, 8, 33.
Chen, W., Zhang, X., & Fatikow, S. (2016). A novel microgripper hybrid driven by a piezoelectric stack actuator and piezoelectric cantilever actuators. Review of Scientific Instruments, 87(11), 115003.
Das, A. N., Murthy, R., Popa, D. O., & Stephanou, H. E. (2012). A multiscale assembly and packaging system for manufacturing of complex micro-nano devices. IEEE Transactions on Automation Science and Engineering, 9(1), 160–170.
Devasia, S., Eleftheriou, E., & Reza Moheimani, S. O. (2007). A survey of control issues in nano-positioning. IEEE Transactions on Control Systems Technology, 15(5), 802–823.
Ding, B., & Li, Y. (2018). Hysteresis compensation and sliding mode control with perturbation estimation for piezoelectric actuators. Micromachines, 9, 241.
Gammaitoni, L. (1995). Stochastic resonance in multi-threshold systems. Physics Letters, 208(4–6), 315–322.
Gammaitoni, L., Hänggi, P., Jung, P., & Marchesoni, F. (1998). Stochastic resonance. Reviews of Modern Physics, 70(1), 223–287.
Gammaitoni, L., Hänggi, P., Jung, P., & Marchesoni, F. (2009). Stochastic Resonance: A remarkable idea that changed our perception of noise. European Physical Journal B, 69, 1–3.
Goldfarb, M., & Celanovic, N. (1997). Modeling piezoelectric stack actuators for control of micromanipulation. IEEE Transactions on Control Systems Technology, 17(3), 69–79.
Habineza, D., Rakotondrabe, M., & Gorrec, Y. (2015). Bouc–Wen modeling and feedforward control of multivariable hysteresis in piezoelectric systems application to a 3-DOF piezotube scanner. IEEE Transactions on Control Systems Technology, 23(5), 1797–1806.
Hassani, V., & Tjahjowidodo, T. (2017). A hysteresis model for a stacked-type piezoelectric actuator. Mechanics of Advanced Materials and Structures, 24(1), 73–87.
Hong, T., & Chang, T. N. (1995). Control of nonlinear piezoelectric stack using adaptive dither. In Proceedings of the American control conference (pp. 76–80).
Hu, Y., Kang, W., Fang, Y., Xie, L., Qiu, L., & Jin, T. (2018). Piezoelectric poly (vinylidene fluoride) (PVDF) polymer-based sensor for wrist motion signal detection. Applied Sciences, 8, 836.
Jiang, G., Luo, M., Bai, K., & Chen, S. (2017). A precise positioning method for a puncture robot based on a PSO-optimized BP neural network algorithm. Applied Sciences, 7, 969.
Kim, B., & Yoon, J.-Y. (2018). Modified LMS strategies using internal model control for active noise and vibration control systems. Applied Sciences, 8, 1007.
Kuhnen, K. (2006). Modeling, identification and compensation of complex hysteretic nonlinearities: A modified Prandtl–Ishlinskii approach. European Journal of Control, 9(4), 407–418.
Long, Z., Wang, R., Fang, J., Dai, X., & Li, Z. (2017). Hysteresis compensation of the Prandtl–Ishlinskii model for piezoelectric actuators using modified particleswarm optimization with chaotic map. Review of Scientific Instruments, 88(7), 075003.
Priplata, A. A., Patritti, B. L., Niemi, J. B., et al. (2006). Noise-enhanced balance control in patients with diabetes and patients with stroke. Annals of Neurology, 59, 4–12.
Qin, Y., Zhao, X., & Zhou, L. (2017). Modeling and identification of the rate-dependent hysteresis of piezoelectric actuator using a modified Prandtl–Ishlinskii model. Micromachines, 8, 114.
Schrock, J., Meurer, T., & Kugi, A. (2013). Motion planning for piezo-actuated flexible structures: modeling, design, and experiment. IEEE Transactions on Control Systems Technology, 21(3), 807–819.
Shome, S. K., Pradhan, S., Mukherjee, A., & Datta, U. (2013). Dither based precise position control of piezo actuated micro-nano manipulator. In Proceedings of the 39th annual conference of the IEEE industrial electronics society (IECON ‘13) (pp. 3486–3491).
Stepanenko, Y., & Su, C. Y. (1998). Intelligent control of piezoelectric actuators. In Proceedings of the international conference on decision and control (pp. 4234–4239).
Tang, H., & Li, Y. (2013). Design, analysis and test of a novel 2-DOF nanopositioning system driven by dual-mode. IEEE Transactions on Robotics, 29, 650–662.
Tang, H., Li, Y., & Huang, J. (2012). Design and analysis of a parallel XY micromanipulator for micro/nano manipulation driven by dual-mode. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 226(12), 3043–3057.
Wang, F. J., Liang, C. M., Tian, Y. L., Zhao, X. Y., & Zhang, D. W. (2016). Design and control of a compliant microgripper with a large amplification ratio for high-speed micro manipulation. IEEE/ASME Transactions on Mechatronics, 21(3), 1262–1271.
Wiesenfeld, K., & Moss, F. (1995). Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature, 373, 33–36.
Xu, Q., & Li, Y. (2010). Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation. Journal of Dynamic Systems, Measurement and Control, 132(4), 041011. https://doi.org/10.1115/1.4001712.
Yang, Y., Wei, Y., Lou, J., Fu, L., Fang, S., & Chen, T. (2018). Dynamic modeling and adaptive vibration suppression of a high-speed macro-micro manipulator. Journal of Sound and Vibration, 422, 318–342.
Yang, Y. L., Wei, Y. D., Lou, J. Q., Xie, F. R., & Fu, L. (2016). Development and precision position/force control of a new flexure-based micro gripper. Journal of Micromechanics and Microengineering, 26(1), 015005.
Yao, J., Xiao, C., Wan, Z., Zhang, S., & Zhang, X. (2018). Acceleration harmonics identification for an electro-hydraulic servo shaking table based on a nonlinear adaptive algorithm. Applied Sciences, 8, 1332.
Zhang, T., Li, H. G., Zhong, Z. Y., & Cai, G. P. (2015). Hysteresis model and adaptive vibration suppression for a smart beam with time delay. Journal of Sound and Vibration, 358, 35–47.
Zhao, Y., & Jayasuriya, S. (1995). Feedforward controllers and tracking accuracy in the presence of plant uncertainties. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, 117(4), 490–495.
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The authors gratefully acknowledge the funding received from Indo French Center for the Promotion of Advanced Research (IFCPAR/CEFIPRA) for carrying out the project work.
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Shome, S.K., Jana, S., Mukherjee, A. et al. Design of Adaptive Voltage Dither Control Framework Based on Spectral Analysis for Nonlinear Piezoelectric Actuator. J Control Autom Electr Syst 30, 954–969 (2019). https://doi.org/10.1007/s40313-019-00506-6
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DOI: https://doi.org/10.1007/s40313-019-00506-6