Nonlinear Dynamics of a Wave Solid-State Gyroscope Taking into Account the Electrical Resistance of an Oscillation Control Circuit
Received 17 April 2023; accepted 22 May 2023; published 20 June 2023
2023, Vol. 19, no. 3, pp. 409-435
Author(s): Maslov D. A.
This article is concerned with investigating the nonlinear dynamics of the cylindrical resonator
of a wave solid-state gyroscope. The nonlinearity of oscillations caused by the nonlinear
properties of electrostatic control sensors is considered. This nonlinearity is derived by taking
into account the finite ratio of resonator flexure to the small gap of electrostatic control sensors.
The equations of the electromechanical system that in interconnected form describe the nonlinear
mechanical oscillations of the gyroscope resonator and electrical oscillations in the control circuit
are derived. The resulting differential equations belong to the class of Tikhonov systems, since
the equation of electrical processes in the control circuit is singularly perturbed. By taking into
account the low electrical resistance of the oscillation control circuit, which determines a small
parameter at the derivative in the singularly perturbed equation of electrical processes, the nonlinear
oscillations of the wave solid-state gyroscope resonator are studied. The small parameter
method is used to obtain a mathematical model of the resonator dynamics, which jointly takes
into account the nonlinearity of the resonator oscillations and the electrical resistance of the
oscillation control circuit. A special method is proposed to reduce the nonlinear equations of the
resonator dynamics to the standard form of the system of differential equations for averaging
and the equations of the dynamics of the wave solid-state gyroscope resonator are averaged. It is
shown that, in the case of nonlinear oscillations, consideration of the electrical resistance of the
oscillation control circuit does not affect the angular velocity of the gyroscope drift, but causes
slight dissipation of the oscillations, which also leads to an insignificant correction of the resonant
frequency.
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