Abstract
The article is devoted to rejection of unwanted dynamic reactions of flexible structures. The problem of vibrationless movement of an elastic object when natural oscillations are absent and the reaction of the system does not exceed the static reaction is considered. To analyze the oscillations of the system, the maximum response spectrum and the residual spectrum are used. The vibrationless movement property is defined as restrictions on these spectra specified by the control signal. The problem of vibrationless movement is solved by input shaping methods. The shaping filter built on fixed values of the eigenfrequencies of the system is unstable when the frequencies deviate from the set values. To solve this problem, robust modifications of the method are proposed. The high complexity of the considered problem requires computer modeling. In particular, using computer modeling, the problem of the choice of a shaping filter with the property of maximum robustness is solved.
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References
Genta, G.: Vibration Dynamics and Control. Springer, New York (2009)
Akulenko, L.D.: Boundary kinematic control of a distributed oscillatory system. J. Appl. Math. Mech. 71(6), 862–868 (2007)
Gannel, L.V., Formal’skii, A.M.: Control for minimizing vibrations in systems with compliant elements. Journal of Computer and Systems Sciences International 52(1), 117–128 (2013).
Smith, O.J.M.: Posicast control of damped oscillatory systems. Proc. IRE 45(9), 1249–1255 (1957)
Singhose, W.: Command shaping for flexible systems: a review of the first 50 years. Int. J. Precis. Eng. Man. 10(4), 153–168 (2009)
Prourzin, V.A.: Control of elastic plant movement without excilation on eigen-oscilation. Autom. Remote Control 78(12), 2141–2153 (2017)
Singh, T., Vadali, S.R.: Robust time-optimal control: a frequency domain approach. J. Guidance Control Dyn. 17, 346–353 (1994)
Vaughan, J., Yano, A., Singhose, W.: Comparison of robust input shapers. J. Sound Vib. 315, 797–815 (2008)
Pao, L., Lau, M.: Robust input shaper control design for parameter variations in flexible structures. J. Dyn. Syst. Meas. Contr. 122, 63–70 (2000)
Sung, Y.G., Singhose, W.: Robustness analysis of input shaping commands for two-mode flexible systems. IET Control Theor. Appl. 3, 722–730 (2009)
Prourzin, V.A.: Equivalent gaming formulations of the problem of designing the maximum robust controls. Autom. Remote Control 66(8), 1305–1315 (2005)
Shevlyakov, G.L., Vil’chevski, N.O.: Robustness in Data Analysis: Criteria and Methods. VSP, Utrecht-Boston-Tokio (2002)
Shevlyakov, G.L., Vil’chevski, N.O.: Robustness in Data Analysis. De Gruyter, Boston (2011)
Shevlyakov, G.L., Oja, H.: Robust Correlation: Theory and Applications. Wiley, New York (2016)
Weaver, Jr., W., Timoshenko, S.P., Young, D.H.: Vibration Problems in Engineering. Wiley & Sons, New York (1990)
Prourzin, V.A.: A constrained scalar control for the motion of a system of oscillators with damping residual oscillations. J. Comput. Syst. Sci. Int. 46(4), 521–531 (2007)
Prourzin, V.A.: A problem of optimal shock isolation of elastic objects. Mech. Solids 39(2), 22–29 (2004)
Boltyanskii, V.G.: Matematicheskie metody optimal’nogo upravleniya (Mathematical Methods of Optimal Control). Nauka, Moscow (1969)
Singhose, W., Seering, W., Singer, N.: Input shaping for vibration reduction with specified insensitivity to modeling errors. In: Proc. Japan-USA Sym. on Flexible Automation, pp. 307–313 (1996)
Park, U.H., Lee, J.W., Lim, B.D., Sung, Y.G.: Design and sensitivity analysis of an input shaping filter in the ZPlane. J. Sound Vib. 243, 157–171 (2001)
Bhat, S.P., Miu, D.K.: Precise point-to-point positioning control of flexible structures. ASME J. Dyn. Syst. Meas. Control 112(4), 667–674 (1990)
Singh, T., Heppler, G.R.: Shaped input control of a system with multiple modes. ASME J. Dyn. Syst. Meas. Control 115, 341–347 (1993)
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Prourzin, V.A., Kim, K., Shevlyakov, G. (2021). Computer Modeling of Robust Control of Vibrationless Movement of Multi-mode Flexible Structures. In: Voinov, N., Schreck, T., Khan, S. (eds) Proceedings of International Scientific Conference on Telecommunications, Computing and Control. Smart Innovation, Systems and Technologies, vol 220. Springer, Singapore. https://doi.org/10.1007/978-981-33-6632-9_13
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DOI: https://doi.org/10.1007/978-981-33-6632-9_13
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