Nonlinear Dynamics of a Wave Solid-State Gyroscope Taking into Account the Electrical Resistance of an Oscillation Control Circuit

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.