Geodesic
The linearization for wave solid-state gyroscope resonator oscillations and electrostatic control sensors forces
Russian journal of nonlinear dynamics, Tome 13 (2017) no. 3, pp. 413-421.

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A wave solid-state gyroscope with a cylindrical resonator and electrostatic control sensors is considered. The gyroscope dynamics mathematical model describing nonlinear oscillations of the resonator under voltage on the electrodes is used. The reference voltage causes a cubic nonlinearity and the alternating voltage causes a quadratic nonlinearity of the control forces. Various regimes of supplying voltage to gyro sensors are investigated. For the linearization of oscillations the form of voltages on the electrodes is presented. These voltages compensate for both nonlinear oscillations of the resonator caused by electrostatic sensors and those caused by other physical and geometric factors. It is shown that the control forces have a nonlinearity that is eliminated by the voltage applied to the electrode system according to a special law. The proposed method can be used to eliminate nonlinear oscillations and to linearize power characteristics of sensors for controlling wave solid-state gyroscopes with hemispherical, cylindrical and ring resonators.
Keywords: wave solid-state gyroscope, cylindrical resonator, nonlinear oscillations. 
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D. A. Maslov; I. V. Merkuryev. The linearization for wave solid-state gyroscope resonator oscillations and electrostatic control sensors forces. Russian journal of nonlinear dynamics, Tome 13 (2017) no. 3, pp. 413-421. http://geodesic.mathdoc.fr/item/ND_2017_13_3_a7/

[1] Peshekhonov V. G., “Gyroscopic navigation systems: Current status and prospects”, Gyroscopy and Navigation, 2:3 (2011), 111–118 | DOI

[2] Jeanroy A., Bouvet A., Remillieux G., “HRG and marine applications”, Gyroscopy and Navigation, 5:2 (2014), 67–74 | DOI

[3] Meyer D., Rozelle D., “Milli-HRG inertial navigation system”, Gyroscopy and Navigation, 3:4 (2012), 227–234 | DOI

[4] Basarab M. A., Lunin B. S., Matveev V. A., Fomichev A. V., Chumankin E. A., Yurin A. V., “Miniature gyroscope based on elastic waves in solids for small spacecraft”, Vestn. MGTU, Ser. Priborostroenie, 2014, no. 4, 80–96 (Russian)

[5] Zhuravlev V. F., Klimov D. M., Wave solid-state gyroscopes, Nauka, Moscow, 1985 (Russian)

[6] Zhuravlev V. Ph., “Theoretical foundations of wave solid gyroscope (WSG),”, Mech. Solids, 28:3 (1993), 3–15

[7] Egarmin N. E., “Nonlinear effects in dynamics of rotating circular ring”, Izv. Akad. Nauk. Mekh. Tverd. Tela, 1993, no. 3, 50–59 (Russian)

[8] Matveev V. A., Lipatnikov V. I., Alekhin A. V., Designing of a wave solid-state gyroscope, MGTU, Moscow, 1997, 168 pp. (Russian)

[9] Merkuryev I. V., Podalkov V. V., The dynamics of MEMS and wave solid-state gyroscopes, Fizmatlit, Moscow, 2009 (Russian)

[10] Maslov A. A., Maslov D. A., 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 | DOI | MR

[11] De S. K., Aluru N. R., “Complex nonlinear oscillations in electrostatically actuated microstructures”, J. Microelectromech. Syst., 15:2 (2006), 355–369 | DOI

[12] Rhoads J., Shaw S., Turner K., Moehlis J., DeMartini B., Zhang W., “Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators”, J. Sound Vibration, 296:4–5 (2006), 797–829 | DOI

[13] Sharma M., Sarraf E. H., Baskaran R., Cretu E., “Parametric resonance: Amplification and damping in MEMS gyroscopes”, Sens. Actuators A Phys., 177 (2012), 79–86 | DOI

[14] Zhuravlev V. Ph., “The controlled Foucault pendulum as a model of a class of free gyros”, Mech. Solids, 42:6 (1997), 21–28 | MR

[15] Maslov D. A., 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)

[16] Maslov A. A., Maslov D. A., Merkuryev I. V., “Parameter identification of a hemispherical resonator gyro with nonlinearity of the resonator”, Pribory i sistemy. Upravlenie, kontrol, diagnostika, 2014, no. 5, 18–23 (Russian)

[17] Maslov D. A., “Parameters identification for the gyro with a cylindrical resonator allowing for nonlinearity impact on the forcing action amplitude”, Mashinostr. i inzh. obraz., 2017, no. 1, 24–31 (Russian)

[18] Tarasov A. N., Control system for micromechanical vibrating gyroscopes with combined excitation and measurements frequencies, Cand. Tech. Sci. Dissertation, Bauman Moscow State Technical University, Moscow, 2015, 190 pp.

[19] Zhuravlev V. Ph., Linch D. D., “Electric model of a hemispherical resonator gyro”, Mech. Solids, 30:5 (1995), 10–21