Model Predictive Control of a Piezoelectric Vortex-Induced Vibrations Energy Harvester
Publication: Journal of Energy Engineering
Volume 146, Issue 5
Abstract
In this paper, an optimal control method is proposed for a piezoelectric vortex-induced vibrations (VIV) energy harvester. The harvester comprises a blunt cylinder attached to the tip of a flexible beam. The beam is a composite cantilever that is partially covered by piezoelectric plates. A nonlinear model is derived for the VIV of the harvester by using the Euler–Lagrange principle with the unsteady aerodynamic force due to vortex shedding. To achieve the maximum energy production, an optimal controller is designed using the model predictive control (MPC) method. The MPC design problem turned out to be a linear quadratic optimization problem that is solved by efficient numerical methods. The closed-loop response of the MPC scheme is studied through extensive numerical simulation for several working conditions. The results showed that, compared with the conventional methods, the MPC scheme significantly increases the output electrical power of the VIV harvester.
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Data Availability Statement
The MATLAB codes of the reduced-order dynamic model, MPC controller design, and closed-loop simulations developed during this study are available from the corresponding author by request.
References
Abdelkefi, A., and M. Ghommem. 2013. “Piezoelectric energy harvesting from morphing wing motions for micro air vehicles.” Theor. Appl. Mech. Lett. 3 (5): 052004. https://doi.org/10.1063/2.1305204.
Abdelkefi, A., M. R. Hajj, and A. H. Nayfeh. 2012a. “Power harvesting from transverse galloping of square cylinder.” Nonlinear Dyn. 70 (2): 1355–1363. https://doi.org/10.1007/s11071-012-0538-4.
Abdelkefi, A., M. R. Hajj, and A. H. Nayfeh. 2013. “Piezoelectric energy harvesting from transverse galloping of bluff bodies.” Smart Mater. Struct. 22 (1): 015014. https://doi.org/10.1088/0964-1726/22/1/015014.
Abdelkefi, A., A. H. Nayfeh, and M. R. Hajj. 2012b. “Design of piezoaeroelastic energy harvesters.” Nonlinear Dyn. 68 (4): 519–530. https://doi.org/10.1007/s11071-011-0233-x.
Abdelkefi, A., A. H. Nayfeh, and M. R. Hajj. 2012c. “Modeling and analysis of piezoaeroelastic energy harvesters.” Nonlinear Dyn. 67 (2): 925–939. https://doi.org/10.1007/s11071-011-0035-1.
Akaydin, H. D., N. Elvin, and Y. Andreopoulos. 2012. “The performance of a self-excited fluidic energy harvester.” Smart Mater. Struct. 21 (2): 025007. https://doi.org/10.1088/0964-1726/21/2/025007.
Amin Karami, M., and D. J. Inman. 2012. “Powering pacemakers from heartbeat vibrations using linear and nonlinear energy harvesters.” Appl. Phys. Lett. 100 (4): 042901. https://doi.org/10.1063/1.3679102.
Azadi Yazdi, E. 2018. “Nonlinear model predictive control of a vortex-induced vibrations bladeless wind turbine.” Smart Mater. Struct. 27 (7): 075005. https://doi.org/10.1088/1361-665X/aac0b6.
Azadi Yazdi, E. 2019. “Optimal control of a broadband vortex-induced vibration energy harvester.” J. Intell. Mater. Syst. Struct. 31 (1): 137–151. https://doi.org/10.1177/1045389X19888711.
Bianchi, F. D., R. J. Mantz, and H. De Battista. 2007. “Wind turbine control systems: Advances in Industrial.” In Control. London: Springer.
Bishop, R. E. D., and A. Y. Hassan. 1964. “The lift and drag forces on a circular cylinder in a flowing fluid.” Proc. R. Soc. A: Math. Phys. Eng. Sci. 277 (1368): 32–50. https://doi.org/10.1098/rspa.1964.0004.
Chizfahm, A., E. Azadi Yazdi, and M. Eghtesad. 2018. “Dynamic modeling of vortex induced vibration wind turbines.” Renewable Energy 121 (Jun): 632–643. https://doi.org/10.1016/j.renene.2018.01.038.
Cordonnier, J., F. Gorintin, A. De Cagny, A. H. Clément, and A. Babarit. 2015. “SEAREV: Case study of the development of a wave energy converter.” Renewable Energy 80 (Aug): 40–52. https://doi.org/10.1016/j.renene.2015.01.061.
Dai, H. L., A. Abdelkefi, and L. Wang. 2014a. “Piezoelectric energy harvesting from concurrent vortex-induced vibrations and base excitations.” Nonlinear Dyn. 77 (3): 967–981. https://doi.org/10.1007/s11071-014-1355-8.
Dai, H. L., A. Abdelkefi, and L. Wang. 2014b. “Theoretical modeling and nonlinear analysis of piezoelectric energy harvesting from vortex-induced vibrations.” J. Intell. Mater. Syst. Struct. 25 (14): 1861–1874. https://doi.org/10.1177/1045389X14538329.
Dang, D. Q., S. Wu, Y. Wang, and W. Cai. 2010. “Model predictive control for maximum power capture of variable speed wind turbines.” In Proc., 2010 9th Int. Power and Energy Conf., IPEC 2010, 274–279. New York: IEEE.
Facchinetti, M. L., E. de Langre, and F. Biolley. 2004. “Coupling of structure and wake oscillators in vortex-induced vibrations.” J. Fluids Struct. 19 (2): 123–140. https://doi.org/10.1016/j.jfluidstructs.2003.12.004.
Faedo, N., S. Olaya, and J. V. Ringwood. 2017. “Optimal control, MPC and MPC-like algorithms for wave energy systems: An overview.” IFAC J. Syst. Control 1 (Sep): 37–56. https://doi.org/10.1016/j.ifacsc.2017.07.001.
Ferreau, H. J., H. G. Bock, and M. Diehl. 2008. “An online active set strategy to overcome the limitations of explicit MPC.” Int. J. Robust Nonlinear Control 18 (8): 816–830. https://doi.org/10.1002/rnc.1251.
Harne, R. L., and K. W. Wang. 2013. “A review of the recent research on vibration energy harvesting via bistable systems.” Smart Mater. Struct. 22 (2): 023001. https://doi.org/10.1088/0964-1726/22/2/023001.
Hasheminejad, S. M., A. H. Rabiee, and M. Jarrahi. 2017. “Semi-active vortex induced vibration control of an elastic elliptical cylinder with energy regeneration capability.” Int. J. Struct. Stab. Dyn. 17 (9): 1750107. https://doi.org/10.1142/S0219455417501073.
Hasheminejad, S. M., A. H. Rabiee, M. Jarrahi, and A. H. D. Markazi. 2014. “Active vortex-induced vibration control of a circular cylinder at low Reynolds numbers using an adaptive fuzzy sliding mode controller.” J. Fluids Struct. 50 (Oct): 49–65. https://doi.org/10.1016/j.jfluidstructs.2014.06.011.
Homer, J. R., and R. Nagamune. 2018. “Physics-based 3-D control-oriented modeling of floating wind turbines.” IEEE Trans. Control Syst. Technol. 26 (1): 14–26. https://doi.org/10.1109/TCST.2017.2654420.
Hong, Y., R. Waters, C. Boström, M. Eriksson, J. Engström, and M. Leijon. 2014. “Review on electrical control strategies for wave energy converting systems.” Renewable Sustainable Energy Rev. 31 (Mar): 329–342. https://doi.org/10.1016/j.rser.2013.11.053.
Jiao, P., W. Borchani, H. Hasni, and N. Lajnef. 2017. “Enhancement of quasi-static strain energy harvesters using non-uniform cross-section post-buckled beams.” Smart Mater. Struct. 26 (8): 085045. https://doi.org/10.1088/1361-665X/aa746e.
Kazantzis, N., K. T. Chong, J. H. Park, and A. G. Parlos. 2003. “Control-relevant discretization of nonlinear systems with time-delay using taylor-lie series.” In Proc., American Control Conf. (ACC), 149–154. New York: IEEE. https://doi.org/10.1109/ACC.2003.1238929.
Kramer, M. M., L. Marquis, P. Frigaard, and P. Allé. 2011. “Performance evaluation of the wavestar prototype.” In Proc., 9th European Wave and Tidal Energy Conf. Southampton, UK: EWTEC.
Kumar, A., V. V. Bhanu Prasad, K. C. James Raju, and A. R. James. 2015. “Poling electric field dependent domain switching and piezoelectric properties of mechanically activated ceramics.” J. Mater. Sci. - Mater. Electron. 26 (6): 3757–3765. https://doi.org/10.1007/s10854-015-2899-1.
Lefeuvre, E., A. Badel, C. Richard, and D. Guyomar. 2005. “Piezoelectric energy harvesting device optimization by synchronous electric charge extraction.” J. Intell. Mater. Syst. Struct. 16 (10): 865–876. https://doi.org/10.1177/1045389X05056859.
Lei, M., L. Shiyan, J. Chuanwen, L. Hongling, and Z. Yan. 2009. “A review on the forecasting of wind speed and generated power.” Renewable Sustainable Energy Rev. 13 (4): 915–920. https://doi.org/10.1016/j.rser.2008.02.002.
Ma, F., C. Fu, J. Yang, and Q. Yang. 2020. “Control strategy for adaptive active energy harvesting in sediment microbial fuel cells.” J. Energy Eng. 146 (1): 04019034 https://doi.org/10.1061/(ASCE)EY.1943-7897.0000640.
Maolikul, S., S. Kiatgamolchai, and T. Chavarnakul. 2017. “Low-power energy harvesting of thermoelectric battery charger with step-up DC-DC converter: Applicable case study for personal electronic gadgets.” J. Energy Eng. 143 (4): 05017001 https://doi.org/10.1061/(ASCE)EY.1943-7897.0000432.
Mehmood, A., A. Abdelkefi, M. R. Hajj, A. H. Nayfeh, I. Akhtar, and A. O. Nuhait. 2013. “Piezoelectric energy harvesting from vortex-induced vibrations of circular cylinder.” J. Sound Vib. 332 (19): 4656–4667. https://doi.org/10.1016/j.jsv.2013.03.033.
Meliga, P., J. M. Chomaz, and F. Gallaire. 2011. “Extracting energy from a flow: An asymptotic approach using vortex-induced vibrations and feedback control.” J. Fluids Struct. 27 (5–6): 861–874. https://doi.org/10.1016/j.jfluidstructs.2011.03.005.
Mirzaei, M., M. Soltani, N. K. Poulsen, and H. H. Niemann. 2013. “An MPC approach to individual pitch control of wind turbines using uncertain LIDAR measurements.” In Proc., 2013 European Control Conf., ECC 2013, 490–495. New York: IEEE.
Muralt, P. 2000. “Ferroelectric thin films for micro-sensors and actuators: A review.” J. Micromech. Microeng. 10 (2): 136–146. https://doi.org/10.1088/0960-1317/10/2/307.
Nguyen, B. P., Y. Ho, Z. Wu, and C. Chui. 2012. “Implementation of model predictive control with modified minimal model on low-power RISC microcontrollers.” In Proc., 3rd Symp. on Information and Communication Technology, 165–171. New York: ACM.
Nocedal, J., and S. J. Wright. 2006. Numerical optimization. New York: Springer.
Ogata, K. 1995. Discrete-time control systems. Upper Saddle River, NJ: Prentice-Hall International.
Park, G., T. Rosing, M. D. Todd, C. R. Farrar, and W. Hodgkiss. 2008. “Energy harvesting for structural health monitoring sensor networks.” J. Infrastruct. Syst. 14 (1): 64–79. https://doi.org/10.1061/(ASCE)1076-0342(2008)14:1(64).
Pascucci, C. A., A. Bemporad, S. Bennani, and M. Rotunno. 2014. “Embedded MPC for space applications.” In Proc., 2nd IAA Conf. on Dynamics and Control of Space Systems. Paris: IAA.
Ramadass, Y. K., and A. P. Chandrakasan. 2010. “An efficient piezoelectric energy harvesting interface circuit using a bias-flip rectifier and shared inductor.” IEEE J. Solid-State Circuits 45 (1): 189–204. https://doi.org/10.1109/JSSC.2009.2034442.
Rao, C. V., S. J. Wright, and J. B. Rawlings. 1998. “Application of interior-point methods to model predictive control.” J. Optim. Theory Appl. 99 (3): 723–757. https://doi.org/10.1023/A:1021711402723.
Richalet, J., A. Rault, J. L. Testud, and J. Papon. 1978. “Model predictive heuristic control: Applications to industrial processes.” Automatica 14 (5): 413–428. https://doi.org/10.1016/0005-1098(78)90001-8.
Roundy, S., and P. K. Wright. 2004. “A piezoelectric vibration based generator for wireless electronics.” Smart Mater. Struct. 13 (5): 1131–1142. https://doi.org/10.1088/0964-1726/13/5/018.
Shen, W., and S. Zhu. 2015. “Harvesting energy via electromagnetic damper: Application to bridge stay cables.” J. Intell. Mater. Syst. Struct. 26 (1): 3–19. https://doi.org/10.1177/1045389X13519003.
Skop, R. A., and S. Balasubramanian. 1997. “A new twist on an old model for vortex-excited vibrations.” J. Fluids Struct. 11 (4): 395–412. https://doi.org/10.1006/jfls.1997.0085.
Soman, S. S., H. Zareipour, O. Malik, and P. Mandal. 2010. “A review of wind power and wind speed forecasting methods with different time horizons.” In Proc., North American Power Symp. 2010, 1–8. New York: IEEE.
Song, D., J. Yang, X. Fan, Y. Liu, A. Liu, G. Chen, and Y. H. Joo. 2018. “Maximum power extraction for wind turbines through a novel yaw control solution using predicted wind directions.” Energy Convers. Manage. 157 (Feb): 587–599. https://doi.org/10.1016/j.enconman.2017.12.019.
Torres, E. O., and G. A. Rincón-Mora. 2008. “Energy-harvesting system-in-package microsystem.” J. Energy Eng. 134 (4): 121–129. https://doi.org/10.1061/(ASCE)0733-9402(2008)134:4(121).
Zhang, L. B., A. Abdelkefi, H. L. Dai, R. Naseer, and L. Wang. 2017. “Design and experimental analysis of broadband energy harvesting from vortex-induced vibrations.” J. Sound Vib. 408 (Nov): 210–219. https://doi.org/10.1016/j.jsv.2017.07.029.
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Published In
Journal of Energy Engineering
Volume 146 • Issue 5 • October 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jul 2, 2019
Accepted: Mar 31, 2020
Published online: Jun 18, 2020
Published in print: Oct 1, 2020
Discussion open until: Nov 18, 2020
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