Article considers the solution of dynamic problems using of numerical approximations based on a matrix description of systems and matrix operators for devices of automatic control systems. The results of approximate calculations in the decomposition of signals in basis function systems based on Walsh functions and shifted orthogonal Legendre polynomials for different dimensions of the basis are presented. Optimal sizes of bases without loss of calculation accuracy are found.

The report considers a design concept for precision test benches for verification of gyroscopic devices with digital control systems and inertial sensing elements as modern mechatronic control systems – i.e. primary standards, the design solutions of which include derived special cases of secondary standards with inertial sensing elements and digital control systems, both previously proposed by the authors and novel designs, which can be realized using the proposed design principles.

This paper presents a study of the robust characteristics of a compensation silicon pendulous accelerometer based on a central composite design. It is shown that a modern compensation pendulous accelerometer is a complex electromechanical system having dynamic characteristics that depend on a variety of parameters of both its electronic and mechanical parts. The proposed research methodology is used to draw conclusions about the most significant design elements of a pendulous accelerometer affecting the development of robust characteristics of the device's automatic control system.

This article discloses the problem of terminal control of a movable object, represented by a system of second-order differential equations in the form of a state space - the occurrence of self-oscillations at the control endpoint. The Kalman filter is used as a state observer, ensuring the elimination of self-oscillations at the control endpoint. Mathematical modeling with the constructed Kalman filter to confirm the achievement of the goal was carried out.

This article discusses to implement with practical confirmation the applicability of the method based on correction circuit parameter selection using mathematical model of pendulum compensation accelerometer and software tools. Using this method certain values of the correcting circuit parameters were obtained. Simulation of the pendulum compensation accelerometer with correction circuit having the given parameter and experimental evaluation have been carried out. The experimental results coincided with the simulation results.

The regression model of the torque sensor current of the pendulum accelerometer is presented in this article. The factor design experiment method for to determine the most important parameters is used. The regression model of the torque sensor current from the most important parameters of the accelerometer was obtained.

This article covers a specific end-to-end design technology. This technology is based on constructing a mathematical model of a uniaxial gyroscopic stabiliser (UGS) by transforming a physical model of an object created in SolidWorks using standard Matlab tools. Mathematical modelling was carried out to verify the stability of the obtained model. The main stages of end-to-end design (CAD-design) of a dynamic system are formed using the example of a uniaxial gyroscopic stabiliser. Conclusions were drawn on the application of the proposed technology in the design of dynamic systems and the synthesis of control laws. Application of the proposed end-to-end design technology will reduce the number of errors and the design time of dynamic systems and the control law building. An application for the operating system was developed to automate the end-to-end design process.

This article discusses the synthesis of a static regulator based on LMI-control with varying the correction coefficient. The mathematical modeling of the proposed regulator was carried out. Conclusions about the application of the proposed method are drawn.

We present the results of magnetovariational soundings at two sites (Tiksi Observatory and Kotelny Island in the Laptev Sea region of the Arctic) and their three-dimensional (3D) inversion using the ModEM program. In the models obtained by the inversion, the conductive heterogeneities are present in the regions of the both sites down to a depth of 200 km in the region of the observatory and 100 km beneath the Kotelny Island. The geoelectric heterogeneities in the model in the region of the observatory are most contrasting and voluminous, whereas beneath the island they are more localized. The correlation between the locations of these heterogeneities at both sites and the features of the geological and geophysical structure of the region is noted. It is shown that the applied algorithm of data processing eliminates the effect of the polar electrojet which provides the possibility to study the geoelectric structure of the region by magnetovariational method.

This article presents a method of sequential approximations to solve the nonlinear terminal control problem. The “ideal” model of a uniaxial gyrostabilizer is used for the synthesis of the terminal law of control. Components of moment disturbances are presented as uncertainties. The mathematical modeling of terminal control with disturbances was conducted.

—We consider results of magnetotelluric and magnetovariational soundings in the period range 10 < T ≪ 20 000 s in the North Vietnam area. The simple structure of magnetovariational responses is shown, which generally reflects the electrically conductive quasi-two-dimensional structure of the Earth’s crust. Impedance responses form as a superposition of responses of local complex subsurface and quasi-two-dimensional regional deep-seated structures. Separation of local and regional effects made it possible to construct a geoelectrical depth model of the regional tectonosphere, whose main elements are electrically conductive subvertical trans-lithospheric faults and high-resistivity disturbances of the conductive asthenosphere. These elements, favoring the flow of telluric currents induced in deep-seated electrically conductive systems into the sedimentary cover, form zones of abnormal apparent-resistivity curves. The apparent resistivity monotonously increases with increasing the period up to 20,000 s. We called the combination of such elements of the geoelectrical model a ultradeep fluid–fault system (UDFFS). The modeling has established the location of three orthogonally intersecting UDFFS of NE and SE strikes in the North Vietnam area. It shows that conductive (fluid-saturated) translithospheric faults extending to the base of the sedimentary sequence control the location of petroleum fields and ore deposits. A method for separating local and regional magnetotelluric effects is proposed. It permits one to determine reliably the main strikes of a regional two-dimensional structure and the configuration of the apparent-resistivity curves along them.

Results of magnetic-variation sounding on the opposite shores of the Tatar Strait are presented. The resulting frequency dependences of tippers serve as a basis for 3D inversion carried out using the ModEM software. The inversion yields horizontal and vertical sections of the Tatar Strait in a 400x400 x400 km area along the x, y, and z axes, respectively. A conductive zone is revealed near the continental shore, and its central part has an electric resistivity of 0.5 Ohnrm at a depth of 5-7 km. The zone reaches 20-40 km across and vanishes in the lower crust. Along the shore, an anomaly begins north of the Datta Village and extends to the area south of the town of Sovetskaya Gavan. There is a similar anomaly that is isometric in the horizontal plane and less contrasting, which exists near Sakhalin Island at depths of 8-12 km, where the crust resistivity is 15 Ohnrm. The position of the anomaly matches the nearby zone of local M= 4-6 earthquakes in the upper crust. At depths greater than 10 km beneath the strait, these anomalies merge and the electrical resistivity increases. In the lower crust and in the upper mantle beneath the strait, the section is characterized by a resistivity of 30-60 Ohnrm. At depths greater than 100 km, there is a conductive layer submerging beneath the 'Tatar Strait from the Sea of Okhotsk, with conductive branches running from it beneath the Tatar Strait south and north of the Datta Village. The possible causes of near-shore conductive anomalies are discussed.

This paper discusses “supersoft” control of final parameters in a single-axis gyrostabilizer, providing the required precision and “softness” of the gyro-stabilized platform (GSP) rotation from arbitrary initial position to the preset final state. The problems of the synthesis of “supersoft” terminal regulators for GSP and gyro unit (GU) are presented. The mathematical simulation of “supersoft” control is carried out. The conclusions on application of “supersoft” control of final parameters in a single-axis gyrostabilizer are drawn.

This paper considers the possibility of improving the quality of control parameters of the sensitive element in a float type gyroscope - angular rate sensor. The electronics unit of the sensor contains a nominal regulator, synthesized using the method of targeted frequency characteristics and represents a serial connection of aperiodic and boosting links. This report also considers a dynamic output regulator based on the method of invariant ellipsoids that was synthesized for the studied angular rate sensor. The results of mathematical modeling of the response of the sensitive element to different types of external disturbances are presented for the two types of regulators. Comparison of the results shows the advantages of the dynamic regulator over the nominal one.

This paper shows the process of determining the permissible overloads acting on the sensitive element of the pendulum compensating accelerometer. The sensing element is a pendulum made of monocrystalline silicon in the form of a plate. The estimation of permissible overloads was carried out by the method of finite element analysis using modern computer aided design software. To check the adequacy of the results obtained, physical experiments were carried out, during which the pendulums were loaded along one of the axes.

Large steeply dipping geoelectrical structures penetrating the whole lithosphere and extending deeply beneath it are detected on Sakhalin Island by magnetotelluric soundings. The fault system that forms this structure contributes to the flow of telluric currents from the deep horizons of the tectonosphere to the near-surface layers. As a result, the electrical component across the strike of the structure is very sensitive to the presence of conducive galvanically coupled vertical and horizontal elements (objects) in the section through which currents flow. This phenomenon provides the basis for a new approach to a detailed study of the block structure of the lithosphere and its upper part, the Earth’s crust. Based on this effect, which has not been studied earlier in the magnetotelluric works, the block structure of the Earth’s crust on southern Sakhalin is examined. It is found that the interblock joints characterized by a relatively low level of specific electrical resistivity, which indicates their fluid saturation, are fragments of regional or higher-order faults. The location of the foci of crustal earthquakes is closely related to these fragments. It is shown that the urban district of Yuzhno-Sakhalinsk is situated in the area of a triple junction of geoelectrical blocks in the Earth’s crust.

This paper discusses combined terminal control of the gyro-stabilized platform (GSP) in the "coarse" alignment mode providing the required precision and "softness" of GSP turn from arbitrary initial position to the preset final state. The stages of control are described. The mathematical simulation of combined terminal control of the GSP are carried out. Conclusions on application of combined terminal control of GSP are drawn.

In this paper, an example of a simplified representation of a uniaxial gyrostabilizer shows an algorithm for <;<;cross-cutting>> design of dynamic systems, which based on interaction between CAD-systems and mathematical software packages.