Điều khiển phản hồi phi tuyến của chu kỳ giới hạn và sự hỗn loạn trong một bộ dao động cơ học: lý thuyết và thực nghiệm

Springer Science and Business Media LLC - Tập 104 - Trang 3223-3246 - 2021
Bhavik Patel1, Prasanjit Kumar Kundu1, Shyamal Chatterjee1
1Department of Mechanical Engineering, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, India

Tóm tắt

Mặc dù các kỹ sư tin rằng dao động tự kích thích và sự hỗn loạn là có hại, nhưng nghiên cứu gần đây đã tiết lộ rằng dao động chu kỳ và dao động hỗn loạn tự kích thích có thể được sử dụng một cách hiệu quả trong nhiều quá trình và thiết bị kỹ thuật mang lại lợi ích đáng kể. Do đó, một bộ điều khiển phản hồi phi tuyến đơn giản được đề xuất để tạo ra dao động chu kỳ và dao động hỗn loạn tự kích thích trong một bộ dao động cơ học. Các biểu thức phân tích liên quan đến biên độ của chu kỳ giới hạn và các tham số điều khiển được xác định bằng phương pháp nhiều thang thời gian. Kết quả phân tích được xác thực thông qua các mô phỏng số được thực hiện trong MATLAB–SIMULINK. Sự tồn tại của các dao động hỗn loạn được xác nhận qua các mô phỏng số. Một nghiên cứu tham số sâu rộng được thực hiện để làm sáng tỏ bản chất của các dao động hỗn loạn và sự phụ thuộc của chúng vào các tham số điều khiển. Các kết quả lý thuyết cuối cùng được xác thực qua các thí nghiệm. Thông thường, có thể quan sát rằng cùng một bộ điều khiển có thể được sử dụng để kích thích cả dao động chu kỳ và dao động hỗn loạn chỉ bằng cách đảo ngược pha của bộ điều khiển. Đây có thể là ví dụ đầu tiên cho thấy cùng một bộ điều khiển có thể được ứng dụng để tạo ra dao động chu kỳ và dao động hỗn loạn trong một hệ thống cơ học. Các phát hiện của bài báo được cho là có thể ứng dụng trong các hệ thống cơ học vĩ mô và vi mô.

Từ khóa


Tài liệu tham khảo

van der Pol, B.: LXXXVIII On “relaxation-oscillations.” Lond. Edinb. Dublin. Philos. Mag. J. Sci. 2, 978–992 (1926). https://doi.org/10.1080/14786442608564127 Rayleigh, L.: XXXIII On maintained vibrations. Lond. Edinb. Dublin Philos. Mag. J. Sci. 15, 229–235 (1883). https://doi.org/10.1080/14786448308627342 Babitsky, V.I.: Autoresonant mechatronic systems. Mechatronics 5, 483–495 (1995). https://doi.org/10.1016/0957-4158(95)00026-2 Pelgné, G., Kamnev, E., Brissaud, D., Gouskov, A.: Self-excited vibratory drilling: A dimensionless parameter approach for guiding experiments. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 219, 73–86 (2005). https://doi.org/10.1243/095440505X8118 Chaodong, L., Xiaojing, H.: A bio-mimetie pipe crawling microrobot driven based on self-excited vibration. In: 2007 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 984–988 (2007). doi: https://doi.org/10.1109/ROBIO.2007.4522297 Lee, Y., Lim, G., Moon, W.: A piezoelectric micro-cantilever bio-sensor using the mass-micro-balancing technique with self-excitation. Microsyst. Technol. 13, 563–567 (2007). https://doi.org/10.1007/s00542-006-0216-x Batako, A.D., Babitsky, V.I., Halliwell, N.A.: A self-excited system for percussive-rotary drilling. J. Sound Vib. 259, 97–118 (2003). https://doi.org/10.1006/jsvi.2002.5158 Babitsky, V., Astashev, V.: Nonlinear dynamics and control of ultrasonically assisted machining. J. Vib. Control. 13, 441–460 (2007). https://doi.org/10.1177/1077546307074222 Kwaśniewki, J., Dominik, I., Lalik, K.: Application of self-oscillating system for stress measurement in metal. J. Vibroeng. 14, 61–66 (2012) Ono, K., Takahashi, R., Shimada, T.: Self-excited walking of a biped mechanism. Int. J. Rob. Res. 20, 953–966 (2001). https://doi.org/10.1177/02783640122068218 Ono, K., Furuichi, T., Takahashi, R.: Self-excited walking of a biped mechanism with Feet. Int. J. Rob. Res. 23, 55–68 (2004). https://doi.org/10.1177/0278364904038888 Luo, J., Su, Y., Ruan, L., Zhao, Y., Kim, D., Sentis, L., Fu, C.: Robust bipedal locomotion based on a hierarchical control structure. Robotica 37, 1750–1767 (2019). https://doi.org/10.1017/S0263574719000237 Malas, A., Chatterjee, S.: Generating self-excited oscillation in a class of mechanical systems by relay-feedback. Nonlinear Dyn. 76, 1253–1269 (2014). https://doi.org/10.1007/s11071-013-1208-x Malas, A., Chatterjee, S.: Modal self-excitation by nonlinear acceleration feedback in a class of mechanical systems. J. Sound Vib. 376, 1–17 (2016). https://doi.org/10.1016/j.jsv.2016.04.029 Malas, A., Chatterjee, S.: Amplitude controlled adaptive feedback resonance in a single degree-of-freedom mass-spring mechanical system. Proc. Eng. 144, 697–704 (2016). https://doi.org/10.1016/j.proeng.2016.05.070 Malas, A., Chatterjee, S.: Modeling and design of direct nonlinear velocity feedback for modal self-excitation in a class of multi degrees-of-freedom mechanical systems. JVC/J. Vib. Control. 23, 656–672 (2017). https://doi.org/10.1177/1077546315582292 Malas, A., Chatterjee, S.: Analysis and synthesis of modal and non-modal self-excited oscillations in a class of mechanical systems with nonlinear velocity feedback. J. Sound Vib. 334, 296–318 (2015). https://doi.org/10.1016/j.jsv.2014.09.011 Aguilar, L.T., Boiko, I., Fridman, L., Iriarte, R.: Generating self-excited oscillations via two-relay controller. IEEE Trans. Automat. Contr. 54, 416–420 (2009). https://doi.org/10.1109/TAC.2008.2009615 Nakamura, T., Yabuno, H., Yano, M.: Amplitude control of self-excited weakly coupled cantilevers for mass sensing using nonlinear velocity feedback control. Nonlinear Dyn. 99, 85–97 (2020). https://doi.org/10.1007/s11071-019-05287-w Urasaki, S., Yabuno, H.: Identification method for backbone curve of cantilever beam using van der Pol-type self-excited oscillation. Nonlinear Dyn. (2020). https://doi.org/10.1007/s11071-020-05945-4 Tanaka, Y., Kokubun, Y., Yabuno, H.: Proposition for sensorless self-excitation by a piezoelectric device. J. Sound Vib. 419, 544–557 (2018). https://doi.org/10.1016/j.jsv.2017.11.033 Mouro, J., Tiribilli, B., Paoletti, P.: Nonlinear behaviour of self-excited microcantilevers in viscous fluids. J. Micromech. Microeng. 27, 095008 (2017). https://doi.org/10.1088/1361-6439/aa7a6f Yabuno, H., Higashino, K., Kuroda, M., Yamamoto, Y.: Self-excited vibrational viscometer for high-viscosity sensing. J. Appl. Phys. 116, 124305 (2014). https://doi.org/10.1063/1.4896487 Endo, D., Yabuno, H., Higashino, K., Yamamoto, Y., Matsumoto, S.: Self-excited coupled-microcantilevers for mass sensing. Appl. Phys. Lett. 106, 223105 (2015). https://doi.org/10.1063/1.4921082 Mouro, J., Tiribilli, B., Paoletti, P.: A versatile mass-sensing platform with tunable nonlinear self-excited microcantilevers. IEEE Trans. Nanotechnol. (2018). https://doi.org/10.1109/TNANO.2018.2829404 Endo, D., Yabuno, H., Yamamoto, Y., Matsumoto, S.: Mass sensing in a liquid environment using nonlinear self-excited coupled-microcantilevers. J. Microelectromech. Syst. 27, 774–779 (2018). https://doi.org/10.1109/JMEMS.2018.2866877 Lin, Y., Yabuno, H., Liu, X., Yamamoto, Y., Matsumoto, S.: Highly sensitive AFM using self-excited weakly coupled cantilevers. Appl. Phys. Lett. 115, 133105 (2019). https://doi.org/10.1063/1.5115836 Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141 (1963). https://doi.org/10.1175/1520-0469(1963)020%3c0130:DNF%3e2.0.CO;2 Barboza, R.U.Y.: Dynamics of a hyperchaotic lorenz system. Int. J. Bifurc. Chaos 17, 4285–4294 (2007). https://doi.org/10.1142/S0218127407019950 Wang, X., Wang, M.: A hyperchaos generated from Lorenz system. Phys. A Stat. Mech. Appl. 387, 3751–3758 (2008). https://doi.org/10.1016/j.physa.2008.02.020 Wang, Bo H. (Seoul, KR), Koh, Seok B. (Seoul, KR), Ahn, Seung K. (Seoul, KR), Roychowdhury, Shounak (Seoul, K.: “Chaos washing machine and a method of washing thereof,” http://www.freepatentsonline.com/5560230.html (1996) Nomura, H., Wakami, N., Aihara, K.: Time-series analysis of behavior of a two-link nozzle in a dishwasher. Electron. Commun. Jpn. Part III Fundam. Electron. Sci. 79, 88–97 (1996). https://doi.org/10.1002/ecjc.4430790909 Tani, J.: Proposal of chaotic steepest descent method for neural networks and analysis of their dynamics. Electron. Commun. Jpn. Part III Fundam. Electron. Sci. 75, 62–70 (1992). https://doi.org/10.1002/ecjc.4430750406 Moreno-Valenzuela, J., Torres-Torres, C.: Adaptive chaotification of robot manipulators via neural networks with experimental evaluations. Neurocomputing 182, 56–65 (2016). https://doi.org/10.1016/j.neucom.2015.11.085 Miranda-Colorado, R., Aguilar, L.T., Moreno-Valenzuela, J.: A model-based velocity controller for chaotisation of flexible joint robot manipulators. Int. J. Adv. Robot. Syst. 15, 172988141880252 (2018). https://doi.org/10.1177/1729881418802528 Aihara, K.: Chaos and Its Applications. Procedia IUTAM. 5, 199–203 (2012). https://doi.org/10.1016/j.piutam.2012.06.027 Fortuna, L., Frasca, M., Rizzo, A.: Chaotic pulse position modulation to improve the efficiency of sonar sensors. IEEE Trans. Instrum. Meas. 52, 1809–1814 (2003). https://doi.org/10.1109/TIM.2003.820452 Sahin, S., Kavur, A.E., Demiroglu Mustafov, S., Seydibeyoglu, O., Baser, O., Isler, Y., Guzelis, C.: Spatiotemporal chaotification of delta robot mixer for homogeneous graphene nanocomposite dispersing. Rob. Auton. Syst. 134, 103633 (2020). https://doi.org/10.1016/j.robot.2020.103633 Brandt, M.E., Chen, G.: Bifurcation control of two nonlinear models of cardiac activity. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 44, 1031–1034 (1997). https://doi.org/10.1109/81.633897 Georgiou, I.T., Schwartz, I.B.: Dynamics of large scale coupled structural/mechanical systems: a singular perturbation/proper orthogonal decomposition approach. SIAM J. Appl. Math. 59, 1178–1207 (1999). https://doi.org/10.1137/S0036139997299802 Gao, Y., Chau, K.T.: Chaotification of permanent-magnet synchronous motor drives using time-delay feedback. In: IECON Proceedings (Industrial Electronics Conference), pp. 762–766. IEEE (2002) Cuomo, K.M., Oppenheim, A.V.: Circuit implementation of synchronised chaos with applications to communications. Phys. Rev. Lett. 71, 65–68 (1993). https://doi.org/10.1103/PhysRevLett.71.65 Fedula, M., Hovorushchenko, T., Nicheporuk, A., Martynyuk, V.: Chaos-based signal detection with discrete-time processing of the Duffing attractor. East. Eur. J. Enterp. Technol. 4, 44–51 (2019). https://doi.org/10.15587/1729-4061.2019.175787 Zhou J, Xu D, Li Y: Chaotifing duffing-type system with large parameter range based on optimal time-delay feedback control. In: 2010 International workshop on chaos-fractal theories and applications, pp. 121–126. IEEE (2010) Li, Y., Xu, D., Fu, Y., Zhou, J.: Chaotification of a nonlinear vibration isolation system by dual time delayed feedback control. Int. J. Bifurc. Chaos 23, 1–20 (2013). https://doi.org/10.1142/S021812741350096X Chai K., Li S., Lou J.J., Yu X., Liu Y.S., Yang C.Q.: Line spectra chaotification of the nonlinear vibration isolation system on the flexible foundation based on the open-plus-nonlinear-closed-loop method. J. Vib. Control. 107754632093376 (2020). https://doi.org/10.1177/1077546320933762 Zhang, J., Tang, T., Fang, W.: Line spectrum chaotification on QZS systems with time-delay control. Complexity 2020, 1–14 (2020). https://doi.org/10.1155/2020/1932406 Chen, G., Shi, Y.: Introduction to anti-control of discrete chaos: Theory and applications. Philos. Trans. R Soc. A Math. Phys. Eng. Sci. 364, 2433–2447 (2006). https://doi.org/10.1098/rsta.2006.1833 Chen, Q., Hong, Y., Chen, G.: Chaotic behaviors and toroidal/spherical attractors generated by discontinuous dynamics. Phys. A Stat. Mech. Appl. 371, 293–302 (2006). https://doi.org/10.1016/j.physa.2006.03.047 Zhang, Y., Liu, X., Zhang, H., Jia, C.: Constructing chaotic systems from a class of switching systems. Int. J. Bifurc. Chaos 28, 1850032 (2018). https://doi.org/10.1142/S0218127418500323 Ueta, T., Chen, G.: Bifurcation Analysis of Chen’s equation. Int. J. Bifurc. Chaos. 10, 1917–1931 (2000). https://doi.org/10.1142/S0218127400001183 Kwiatkowski, R.: Dynamic analysis of double pendulum with variable mass and initial velocities. Proc. Eng. 136, 175–180 (2016). https://doi.org/10.1016/j.proeng.2016.01.193 Johnson, M.A., Moon, F.C.: Experimental characterisation of quasiperiodicity and chaos in a mechanical system with delay. Int. J. Bifurc. Chaos. 09, 49–65 (1999). https://doi.org/10.1142/S0218127499000031 Buscarino, A., Famoso, C., Fortuna, L., Frasca, M.: A New Chaotic electro-mechanical oscillator. Int. J. Bifurc. Chaos. 26, 1650161 (2016). https://doi.org/10.1142/S0218127416501613 Salcedo, A., Alvarez, J.: Oscillations in first-order, continuous-time systems via time-delay feedback. Complexity 2018, 1–14 (2018). https://doi.org/10.1155/2018/2178031 Choi, I.: Interactive exploration of a chaotic oscillator for generating musical signals in real-time concert performance. J. Frankl. Inst. 331, 785–818 (1994). https://doi.org/10.1016/0016-0032(94)90089-2 Geiyer, D., Kauffman, J.L.: Chaotification as a means of broadband energy harvesting with piezoelectric materials. J. Vib. Acoust. Trans. ASME. 137, 1–8 (2015). https://doi.org/10.1115/1.4030024 Buscarino, A., Fortuna, L., Frasca, M., Muscato, G.: Chaos does help motion control. Int. J. Bifurc. Chaos 17, 3577–3581 (2007). https://doi.org/10.1142/S0218127407019391 Madan R.N.: Front matter. In: Chua’s circuit: a paradigm for chaos, pp. i–xliii. World Scientific (1993) Luo, Y., He, Z., Che, X., Zeng, B.: The research of mechanism synthesis based on mechanical fractional order chaos system methods. In: 2009 Fifth international conference on natural computation, pp. 509–512. IEEE (2009) Li, C., Xu, L., Zhang, J.: Bifurcation and chaotic vibration for an electro-mechanical integrated harmonic piezodrive system. J. Mech. Sci. Technol. 30, 2961–2970 (2016). https://doi.org/10.1007/s12206-016-0605-8 Lu, K., Yang, Q., Chen, G.: Singular cycles and chaos in a new class of 3D three-zone piecewise affine systems. Chaos 29, 043124 (2019). https://doi.org/10.1063/1.5089662 Natiq, H., Said, M.R.M., Ariffin, M.R.K., He, S., Rondoni, L., Banerjee, S.: Self-excited and hidden attractors in a novel chaotic system with complicated multistability. Eur. Phys. J. Plus. 133, 1–2 (2018). https://doi.org/10.1140/epjp/i2018-12360-y Ablay, G.: Chaos in PID controlled nonlinear systems. J. Electr. Eng. Technol. 10, 1843–1850 (2015). https://doi.org/10.5370/JEET.2015.10.4.1843 Strogatz, S.H.: Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, 2nd edn. Westview Press, Boulder (2015) Friedrich, H., Nayfeh, A.H.: Introduction to perturbation techniques. Wiley, New York. XIV, 519 S., £ 16.00. ISBN 0–471–08033–0. ZAMM - Zeitschrift für Angew. Math. und Mech. 61, 666–666 (1981). https://doi.org/10.1002/zamm.19810611224