Impact Factor

    Increase in the Accuracy of the Parameters Identification for a Vibrating Ring Microgyroscope Operating in the Forced Oscillation Mode with Nonlinearity Taken into Account

    2018, Vol. 14, no. 3, pp.  377-386

    Author(s): Maslov D. A., Merkuryev I. V.

    The dynamics of a vibrating ring microgyroscope operating in the forced oscillation mode is investigated. The elastic and viscous anisotropy of the resonator and the nonlinearity of oscillations are taken into consideration. Additional nonlinear terms are suggested for the mathematical model of resonator dynamics. In addition to cubic nonlinearity, nonlinearity of the fifth degree is considered. By using the Krylov – Bogolyubov averaging method, equations containing parameters characterizing damping, elastic and viscous anisotropy, as well as coefficients of oscillation nonlinearity are deduced. The parameter identification problem is reduced to solving an overdetermined system of algebraic equations that are linear in the parameters to be identified. The proposed identification method allows testing at large oscillation amplitudes corresponding to a sufficiently high signal-to-noise ratio. It is shown that taking nonlinearities into account significantly increases the accuracy of parameter identification in the case of large oscillation amplitudes.
    Keywords: parameter identification, vibrating ring microgyroscope, nonlinear oscillations
    Citation: Maslov D. A., Merkuryev I. V., Increase in the Accuracy of the Parameters Identification for a Vibrating Ring Microgyroscope Operating in the Forced Oscillation Mode with Nonlinearity Taken into Account, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 3, pp.  377-386

    Download File
    PDF, 542.86 Kb


    [1] Zhuravlev, V. F. and Klimov, D. M., Wave Solid State Gyroscope, Nauka, Moscow, 1985, 126 pp. (Russian)
    [2] Zhuravlev, V. Ph., “Theoretical Foundations of Wave Solid Gyroscope (WSG)”, Mech. Solids, 28:3 (1993), 3–15; Izv. Akad. Nauk. Mekh. Tverd. Tela, 1993, no. 3, 15–26
    [3] Zhuravlev, V. Ph., “The Controlled Foucault Pendulum As a Model of a Class of Free Gyros”, Mech. Solids, 42:6 (1997), 21–28  mathscinet; Izv. Akad. Nauk. Mekh. Tverd. Tela, 1997, no. 6, 27–35 (Russian)
    [4] Zhuravlev V. F., “The Task of Identification Errors of the Generalized Foucault Pendulum”, Mech. Solids, 2000, no. 5, 5–9  zmath; Izv. Ross. Akad. Nauk. Mekh. Tverd. Tela, 2000, no. 5, 186–192 (Russian)
    [5] Zhbanov, Yu. K. and Zhuravlev, V. F., “On Balancing of the Wave Solid State Gyroscope”, Mech. Solids, 30:4 (1998), 851–859; Izv. Akad. Nauk. Mekh. Tverd. Tela, 1998, no. 4, 4–16 (Russian)
    [6] Matveyev, V. A., Lipatnikov, V. I., and Alekhin, A. V., Design of a Wave Solid-State Gyroscope, MGTU, Moscow, 1998, 168 pp. (Russian)
    [7] Merkuryev, I. V. and Podalkov, V. V., Dynamics of the Micromechanical and Wave Solid-State Gyroscopes, Fizmatlit, Moscow, 2009, 228 pp. (Russian)
    [8] Gavrilenko, A. B., Merkuryev, I. V., and Podalkov, V. V., “Experimental Methods for the Determination Viscoelastic Anisotropy Parameters of the Wave Solid-State Gyroscope Resonator”, Vestn. MPEI, 15:5 (2010), 13–19 (Russian)
    [9] De, S. K. and Aluru, N. R., “Complex Nonlinear Oscillations in Electrostatically Actuated Microstructures”, J. Microelectromech. Syst., 15:2 (2006), 355–369  crossref
    [10] Rhoads, J. F., Shaw, S. W., Turner, K. L., Moehlis, J., DeMartini, B. E., and Zhang, W., “Generalized Parametric Resonance in Electrostatically Actuated Microelectromechanical Oscillators”, J. Sound Vibration, 296:4–5 (2006), 797–829  crossref  adsnasa
    [11] Chavarette, F. R., Balthazar, J. M., Guilherme, I. R., do Nascimento, O. S., and Peruzzi, N. J., “A Reducing of Chaotic Behavior to a Periodic Orbit, of a Combdriver Drive System (MEMS) Using Particle Swarm Optimization”, Proc. of the 9th Brazilian Conf. on Dynamics Control and Their Applications (Serra Negra, 2010), 378–383
    [12] Maslov, A. A., Maslov, D. A., and Merkurev, I. V., “Parameter Identification of Hemispherical Resonator Gyro with the Nonlinearity of the Resonator”, Pribory i Sistemy. Upravlenie, Kontrol, Diagnostika, 2014, no. 5, 18–23 (Russian)
    [13] Maslov, A. A., Maslov, D. A., and Merkuryev, I. V., “Nonlinear Effects in Dynamics of Cylindrical Resonator of Wave Solid-State Gyro with Electrostatic Control System”, Gyroscopy and Navigation, 6:3 (2015), 224–229  crossref  mathscinet; Giroskopiya i Navigatsiya, 2015, no. 1, 71–80 (Russian)  crossref
    [14] Bogolubov, N. N. and Mitropolskiy, Yu. A., Asymptotic Methods in the Theory of Nonlinear Oscillations, Nauka, Moscow, 1974, 503 pp. (Russian)  mathscinet
    [15] Ivchenko, G. I. and Medvedev, Yu. I., Introduction to Mathematical Statistics, 2nd ed., URSS, Moscow, 2017, 608 pp. (Russian)  mathscinet
    [16] Gavrilenko, A. B., Merkuryev, I. V., Podalkov, V. V., and Sbytova, E. S., Micromechanical Systems Dynamics, MPEI, Moscow, 2016, 60 pp. (Russian)
    [17] Raspopov, V. Ya. and Yershov, R. V., “Solid-State Wave Gyroscopes with Ring Resonator”, Datchiki i Sistemy, 2009, no. 5, 61–72 (Russian)
    [18] Maslov, D. A. and Merkuryev, I. V., “Compensation of Errors Taking into Account Nonlinear Oscillations of the Vibrating Ring Microgyroscope Operating in the Angular Velocity Sensor Mode”, Nelin. Dinam., 13:2 (2017), 227–241 (Russian)  mathnet  crossref  mathscinet

    Creative Commons License
    This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License