scholarly journals Effect of East Gyro Drift and Initial Azimuth Error on the Compass Azimuth Alignment Convergence Time

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dongxu He ◽  
Xinle Zang ◽  
Lei Ge
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Oscillation Period ◽  
Inverse Laplace Transform ◽  
Convergence Time ◽  
Initial Error ◽  
Error Band ◽  
Alignment System ◽  
The Time Domain ◽  
Gyro Drift

The effect of gyro constant drift and initial azimuth error on the convergence time of compass azimuth is analyzed in this article. Using our designed compass azimuth alignment system, we obtain the responses of gyro constant drift and initial azimuth error in the frequency domain. The corresponding response function in the time domain is derived using the inverse Laplace transform, and its convergence time is then analyzed. The analysis results demonstrate that the convergence time of compass azimuth alignment is related to the second-order damping oscillation period, the gyro constant drift, and the initial azimuth error. In this study, the error band is set to 0.01° to determine convergence. When the gyro drift is less than 0.05°/h, compass azimuth alignment can converge within 0.9 damping oscillation periods. When the initial azimuth error is less than 5°, compass azimuth alignment can converge within 1.4 damping oscillation periods. When both conditions are met, the initial error plays a major role in convergence, while gyro drift has a smaller effect on convergence time. Finally, the validity of our method is verified using simulations.

ON THE PHENOMENOLOGY OF ELECTRICAL RELAXATION IN ROCKS

Geophysics ◽  
1973 ◽  
Vol 38 (1) ◽  
pp. 37-48 ◽  
Author(s):  
R. T. Shuey ◽  
M. Johnson
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Decay Time ◽  
Inverse Laplace Transform ◽  
Current Response ◽  
Initial Value ◽  
Real Frequency ◽  
Voltage Curve ◽  
Decay Times ◽  
The Time Domain

The work of Keller (1959) with decay‐time distributions is extended by incorporating ideas developed by Gross (1953) for viscoelasticity. In addition to the usual premises of linear systems theory, we introduce the postulate that the response is nonresonant. Mathematically, this postulate is that the frequency response, continued off the real frequency axis, is an analytic function of the complex variable ω, except, possibly, at purely imaginary frequencies. The singularities in the response at purely imaginary frequencies are identified with decay times. There are two decay‐time distribution functions, one associated with resistivity and one associated with conductivity. The former is the inverse Laplace transform of the voltage response to a current step, and the latter is the inverse Laplace transform of the current response to a voltage step. These two decay spectra are not the same; in the normal situation where resistivity decreases and conductivity increases with increasing (real) frequency, the conductivity decay times are shorter than the corresponding resistivity decay times. There are several relations between the resistivity decay spectrum and the usual IP measures. The initial value of the time‐domain voltage curve is proportional to the integral over the spectrum of resistivity decay times. The area under the time‐domain voltage curve, divided by its initial value, is the mean of the distributed resistivity decay times. Finally, PFE and phase shift are roughly proportional to the strength of the resistivity decay in the relevant spectral region.

Thermoelastic Interactions in a Slim Strip Due to a Moving Heat Source Under Dual-Phase-Lag Heat Transfer

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Nantu Sarkar ◽  
Sudip Mondal
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Laplace Transform ◽  
Time Domain ◽  
Generalized Thermoelasticity ◽  
Inverse Laplace Transform ◽  
Phase Lag ◽  
Dual Phase ◽  
Moving Heat Source ◽  
Transient Phenomena

Abstract Following the link of work of He and Cao (2009, Math. Comput. Modell., 49(7–8), 1719–1720), we employ the theory of generalized thermoelasticity with dual-phase-lag (DPL) to study the transient phenomena in a thin slim strip due to a moving heat source. Both ends of the strip are assumed to be fixed and thermally insulated. Using Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the strip are carried out and presented graphically. The effect of moving heat source speed on temperature, stress, and displacement is studied. The temperature, displacement, and stress in the strip are found to be decreasing at large source speed.

Time-domain study of transient fields for a thin circular loop antenna

2002 ◽  
Vol 80 (9) ◽  
pp. 995-1003 ◽  
Author(s):  
S T Bishay ◽  
G M Sami
Keyword(s):  
Time Domain ◽  
Analytical Form ◽  
Loop Antenna ◽  
Inverse Laplace Transform ◽  
Wave Number ◽  
Earth Model ◽  
Circular Loop ◽  
Wave Forms ◽  
Displacement Currents ◽  
The Time Domain

The transient fields in the time-domain of a thin circular loop antenna on a two-layer conducting earth model are expressed in analytical form. In these expressions, the displacement currents both in the two-layer ground and in the air region are taken into consideration. The closed-form expressions of the time-domain are obtained as the inverse Laplace transform of the derived full-wave time-harmonic solution. These time-domain solutions are obtained as a summation of wave-guide modes plus contributions from branch cuts in the complex plane of the longitudinal wave number. Numerical examples are given to indicate the important features in the wave forms of the surface fields due to step and pulsed current excitation. These features provide the means of detecting the earth's stratification, measuring the overburden height, and determining the ratio of the conductivities of the layers. PACS Nos.: 41.20Jb, 42.25Bs, 42.25Gy, 44.05+e

scholarly journals The Mathematical Models of Lattice Functions in Modelling of Control System

2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Mathematical Models ◽  
Control Systems ◽  
Time Domain ◽  
Discrete Control ◽  
Automatic Control Systems ◽  
The Laplace Transform ◽  
Lattice Function ◽  
The Time Domain

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

Three effective inverse Laplace transform algorithms for computing time-domain electromagnetic responses

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. E113-E128 ◽  
Author(s):  
Jianhui Li ◽  
Colin G. Farquharson ◽  
Xiangyun Hu
Keyword(s):  
Laplace Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Computing Time ◽  
Inverse Laplace Transform ◽  
Double Precision ◽  
Horizontal Electric Dipole ◽  
Time Domain Electromagnetic ◽  
Double Precision Arithmetic ◽  
Efficient Option

The inverse Laplace transform is one of the methods used to obtain time-domain electromagnetic (EM) responses in geophysics. The Gaver-Stehfest algorithm has so far been the most popular technique to compute the Laplace transform in the context of transient electromagnetics. However, the accuracy of the Gaver-Stehfest algorithm, even when using double-precision arithmetic, is relatively low at late times due to round-off errors. To overcome this issue, we have applied variable-precision arithmetic in the MATLAB computing environment to an implementation of the Gaver-Stehfest algorithm. This approach has proved to be effective in terms of improving accuracy, but it is computationally expensive. In addition, the Gaver-Stehfest algorithm is significantly problem dependent. Therefore, we have turned our attention to two other algorithms for computing inverse Laplace transforms, namely, the Euler and Talbot algorithms. Using as examples the responses for central-loop, fixed-loop, and horizontal electric dipole sources for homogeneous and layered mediums, these two algorithms, implemented using normal double-precision arithmetic, have been shown to provide more accurate results and to be less problem dependent than the standard Gaver-Stehfest algorithm. Furthermore, they have the capacity for yielding more accurate time-domain responses than the cosine and sine transforms for which the frequency-domain responses are obtained by interpolation between a limited number of explicitly computed frequency-domain responses. In addition, the Euler and Talbot algorithms have the potential of requiring fewer Laplace- or frequency-domain function evaluations than do the other transform methods commonly used to compute time-domain EM responses, and thus of providing a more efficient option.

Preliminary Tests of Application of RV3 Robot for IMU Testing and Calibration

2017 ◽  
Author(s):  
Jacek Rapinski ◽  
Michal Smieja
Keyword(s):  
High Precision ◽  
Time Domain ◽  
Reference Data ◽  
Industrial Robot ◽  
Preliminary Test ◽  
Trajectory Design ◽  
Dynamic Conditions ◽  
The Time Domain ◽  
Gyro Drift ◽  
Automatic Station

The procedure of calibration of IMU sensors is a very challenging and time consuming task. In order to simplify this process a proposition of an automatic station for IMU calibration is presented in this paper. The use of industrial robot allows for unlimited test trajectory design with high precision reference data. In the article a test stand based on the industrial Mitsubishi RV3 robot is presented. The preliminary test included series of movements of ADIS 16354 6DOF IMU sensor mounted on the robot header. The data gained simultaneously from the IMU sensor and the the robot header trajectory were recorded with the PC. Next, the obtained sets of data in the time domain were translated to the unified coordinates and compared. Finally the differences betwen information comming from both sources were calculated and sensor gyro drift was estimated. The results presented in the the paper show that assumed conception makes it possible to determine the drift of the gyroscope in dynamic conditions.

scholarly journals Determination of the response of a class of nonlinear time invariant systems

1981 ◽  
Vol 4 (3) ◽  
pp. 615-623
Author(s):  
Sudhangshu B. Karmakar
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Inverse Laplace Transform ◽  
New Approach ◽  
Functional Expansion ◽  
Expansion Time ◽  
Time Domain Response ◽  
The Time Domain ◽  
Time Invariant

This paper illustrates by means of a simple example a new approach for the determination of the time domain response of a class of nonlinear systems. The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional expansion. Each of the components in the expansion is first transformed into a multidimensional frequency domain and then to a single dimensional frequency domain by the technique of association of variables. By taking into consideration the conditions for the rapid convergence of the functional expansion the response of the system in the frequency domain can effectively be obtained by taking only the first few terms of the expansion. Time domain response is then found by inverse Laplace transform.

Sign in / Sign up

Export Citation Format

Share Document