Dmitry Maslov
ul. Krasnokazarmennaya 14, Moscow, 111250, Russia
National Research University “Moscow Power Engineering Institute”
Bibliometric IDs:
ScopusPublications:
Maslov D. A.
Nonlinear Dynamics of a Wave SolidState Gyroscope Taking into Account the Electrical Resistance of an Oscillation Control Circuit
2023, Vol. 19, no. 3, pp. 409435
Abstract
This article is concerned with investigating the nonlinear dynamics of the cylindrical resonator
of a wave solidstate 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 solidstate 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 solidstate 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.

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
2018, Vol. 14, no. 3, pp. 377386
Abstract
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 signaltonoise ratio. It is shown that taking nonlinearities
into account significantly increases the accuracy of parameter identification in the case of large
oscillation amplitudes.

Maslov D. A., Merkuryev I. V.
The linearization for wave solidstate gyroscope resonator oscillations and electrostatic control sensors forces
2017, Vol. 13, No. 3, pp. 413421
Abstract
A wave solidstate 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 solidstate gyroscopes with hemispherical, cylindrical and ring resonators. 
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
2017, Vol. 13, No. 2, pp. 227241
Abstract
The dynamics of a vibrating ring microgyroscope resonator with openloop and closed feedback is investigated. We use a mathematical model of forced oscillations for thin elastic resonator, taking into account the nonlinearity coefficient, uneven stiffness, difference in Qfactors and control impact parameters. Using the Krylov–Bogolyubov averaging method, the resonator dynamics in slow variables measured by microgyroscope electronics has been investigated. Formulas with algorithmic compensation of the above defects for determining the angular velocity of the resonator under nonlinear oscillations and without feedback have been obtained. Control signals taking into account the defects are presented for feedback of the microgyroscope operating in the compensation mode of the angular velocity sensor. Numerical modeling of angular velocity determination in the operation modes considered has been carried out.
