scholarly journals A Simple Time Domain Collocation Method to Precisely Search for the Periodic Orbits of Satellite Relative Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Xiaokui Yue ◽  
Xuechuan Wang ◽  
Honghua Dai
Keyword(s):  
Motion Control ◽  
Periodic Orbits ◽  
Relative Motion ◽  
Time Domain ◽  
Initial Conditions ◽  
Closed Orbit ◽  
Numerical Approach ◽  
Fuel Saving ◽  
Satellite Relative Motion ◽  
The Time Domain

A numerical approach for obtaining periodic orbits of satellite relative motion is proposed, based on using the time domain collocation (TDC) method to search for the periodic solutions of an exactJ2nonlinear relative model. The initial conditions for periodic relative orbits of the Clohessy-Wiltshire (C-W) equations or Tschauner-Hempel (T-H) equations can be refined with this approach to generate nearly bounded orbits. With these orbits, a method based on the least-squares principle is then proposed to generate projected closed orbit (PCO), which is a reference for the relative motion control. Numerical simulations reveal that the presented TDC searching scheme is effective and simple, and the projected closed orbit is very fuel saving.

Experimental Validation of a Dynamic Simulation

1990 ◽  
Author(s):  
K. Harold Yae ◽  
Su-Tai Chern ◽  
Howyoung Hwang
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Simulation ◽  
Time Domain ◽  
Experimental Validation ◽  
Initial Conditions ◽  
Hydraulic Cylinder ◽  
Force Output ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
The Time Domain

Abstract Using forward and inverse dynamic analysis, the dynamic simulation of a backhoe has been compared with experiments. In the experiment, recorded were the configuration and force histories; that is, velocity and position, and force output from the hydraulic cylinder-all were measured in the time domain. When the experimental force history is used as driving force in the simulation, forward dynamic analysis produces a corresponding motion history. And when the experimental motion history is used as if a prescribed trajectory, inverse dynamic analysis generates a corresponding force history. Therefore, these two sets of motion and force histories — one set from experiment, and the other from the simulation that is driven forward and backward with the experimental data — are compared in the time domain. The comparisons are discussed in regard to the effects of variations in initial conditions, friction, and viscous damping.

scholarly journals Application of nonlinear dynamics methods for quantitative and qualitative evaluation of properties of 2D models of S-chaos

2021 ◽  
Vol 16 (91) ◽  
pp. 125-143
Author(s):  
Aleksei A. Gavrishev ◽  
Keyword(s):  
Nonlinear Dynamics ◽  
Lower Bound ◽  
Time Domain ◽  
Initial Conditions ◽  
Qualitative Evaluation ◽  
Recurrence Analysis ◽  
Combined Application ◽  
Student Version ◽  
The Time Domain ◽  
Property Characteristic

In this article, based on the mathematical, numerical and computer modeling carried out by the combined application of E&F Chaos, Past, Fractan, Visual Recurrence Analysis, Eviews Student Version Lite programs, some of the well-known 2D models of S-chaos are modeled, the data obtained are studied using nonlinear dynamics methods and the fact of their relation or non-relation to chaotic (quasi-chaotic) processes is established. As a result, it was found that the time diagrams obtained for the studied 2D models of S-chaos have a complex noise-like appearance and are continuous in the time domain. The resulting spectral diagrams have both a complex noise-like and regular appearance and are continuous in the spectral regions. The obtained values of BDS-statistics show that some of the time implementations can be attributed to chaotic (quasi-chaotic) processes. Also, the obtained values of BDS-statistics show that the studied 2D models of S-chaos have a property characteristic of classical chaotic (quasi-chaotic) processes: the slightest change in the initial conditions leads to the generation of a new set of signals. The obtained values of the lower bound of the KS-entropy show that the studied models also have the properties of chaotic (quasi-chaotic). Taking into account the conducted research and data from known works [1–5], it is possible to conclude that 2D models of S-chaos can relate to chaotic (quasi-chaotic) processes.

Thermoacoustic interplay between intrinsic thermoacoustic and acoustic modes: non-normality and high sensitivities

2019 ◽  
Vol 878 ◽  
pp. 190-220 ◽  
Author(s):  
Francesca M. Sogaro ◽  
Peter J. Schmid ◽  
Aimee S. Morgans
Keyword(s):  
Time Domain ◽  
Time Scale ◽  
Initial Conditions ◽  
Normal Modes ◽  
Time Domain Analysis ◽  
Normal Behaviour ◽  
Optimal Perturbation ◽  
Acoustic Modes ◽  
Energy Growth ◽  
The Time Domain

This study analyses the interplay between classical acoustic modes and intrinsic thermoacoustic (ITA) modes in a simple thermoacoustic system. The analysis is performed using a frequency-domain low-order network model as well as a time-domain spatially discretised model. Anti-correlated modal sensitivities are found to arise due to a pairwise interplay between acoustic and ITA modes. The magnitude of the sensitivities increases as the interplay between the modes grows stronger. The results show a global behaviour of the modes linked to the presence of exceptional points in the spectrum. The time-domain analysis results in a delay-differential equation and allows the investigation of non-normal behaviour and its consequences. Pseudospectral analysis reveals that energy amplification is crucially linked to an interplay between acoustic and ITA modes. While higher non-orthogonality between two modes is correlated with peaks in modal sensitivity, transient energy growth does not necessarily involve the most sensitive modes. In particular, growth estimates based on the Kreiss constant demonstrate that transient amplification relies critically on the proximity of the non-normal modes to the imaginary axis. The time scale for transient amplification is identified as the flame time delay, which is further corroborated by determining the optimal initial conditions responsible for the bulk of the non-modal energy growth. The flame is identified as an active and dominant contributor to energy gain. The frequency of the optimal perturbation matches the acoustic time scale, once more confirming an interplay between acoustic and ITA structures. Flame-based amplification factors of two to five are found, which are significant when feeding into the acoustic dynamics and eventually triggering nonlinear limit-cycle behaviour.

A standard finite‐difference scheme for the time‐domain computation of anelastic wavefields

Geophysics ◽  
1994 ◽  
Vol 59 (2) ◽  
pp. 290-296 ◽  
Author(s):  
E. S. Krebes ◽  
Gerardo Quiroga‐Goode
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Time Domain ◽  
Finite Difference Scheme ◽  
Initial Conditions ◽  
Homogeneous Medium ◽  
Standard Technique ◽  
Equation Of Motion ◽  
Central Difference ◽  
The Time Domain

We show that the finite‐differencing technique based on the consecutive application of the central difference operator to spatial derivatives, a standard well‐known technique that has been commonly used in the seismological literature for solving the elastic equation of motion, can also be used to obtain a stable time‐domain, finite‐difference scheme for solving the anelastic equation of motion. We compare the results of the scheme for a heterogeneous medium with those of the time‐domain finite‐difference scheme previously developed by Emmerich and Korn and find that they agree very closely. We show, analytically, that in the case of a homogeneous medium, the two schemes give identical numerical results for certain zero initial conditions. The scheme based on the standard technique uses more computer time and memory than the scheme of Emmerich and Korn. However, from a theoretical viewpoint, it is easier to analyze, as it is developed solely with a familiar standard method.

Frequency Constrained Adaptive PID Laws for Motion Control Systems

2017 ◽  
Author(s):  
Tesheng Hsiao ◽  
Chung-Chiang Cheng
Keyword(s):  
Frequency Domain ◽  
Control Systems ◽  
Motion Control ◽  
Time Domain ◽  
Pid Controller ◽  
Tracking Performance ◽  
Tracking Errors ◽  
Pid Tuning ◽  
The Time Domain ◽  
Tuning Methods

The proportional-integral-derivative (PID) controller is widely used in motion control systems due to its simplicity and effectiveness. To achieve satisfactory performance, the PID parameters must be properly tuned. Although numerous PID tuning methods were investigated in the past, most of them were based on either time-domain or frequency-domain responses, while integration of features in both domains for PID tuning was less addressed. However, many industrial practitioners still found it difficult to compromise multiple conflicting control objectives, such as fast responses, small overshoot and tracking errors, and good robustness, with PID controllers. Moreover, it is desirable to adjust PID parameters online such that plant variations and unexpected disturbances can be compensated for more efficiently. In view of these requirements, this paper proposes an adaptive PID control law that updates its parameters online by minimizing the time-domain tracking errors subject to frequency-domain constraints that are imposed for loop shaping. By combining optimization criteria in both time and frequency domains for online parameter adjustment, the proposed PID controller can achieve good tracking performance with adequate robustness margin. Then the proposed PID law is applied to control an XZ-table driven by AC servo motors. Experimental results show that the tracking performance of the proposed controller is superior to that of a constant-gain PID controller whose parameters were tuned by the commercial Matlab/Simulink PID tuner.

A note on the calibration of the electromagnetic seismograph

1973 ◽  
Vol 63 (3) ◽  
pp. 1145-1155
Author(s):  
Hans Jarosch ◽  
A. R. Curtis
Keyword(s):  
Time Domain ◽  
Initial Conditions ◽  
System Parameters ◽  
Electromagnetic Seismograph ◽  
The Time Domain ◽  
Explicit Expressions

abstract Explicit expressions are given for the response in the time domain of a zerocoupled seismometer-galvanometer combination for a step of acceleration as initial conditions. The results may be directly applied for computing the system parameters.

Variational Solution for an Initial Conditions Problem

1997 ◽  
Vol 50 (11S) ◽  
pp. S50-S55 ◽  
Author(s):  
C. P. Filipich ◽  
M. B. Rosales
Keyword(s):  
Finite Number ◽  
Classical Solution ◽  
Time Domain ◽  
Initial Conditions ◽  
Boundary Value ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impulse Load ◽  
Initial Conditions Problem ◽  
The Time Domain

An initial conditions problem is addressed by first transforming it into a boundary value one. An appropriate functional and an extremizing sequence are proposed. The methodology has been previously named WEM (Whole Element Method) by the authors. In the present paper, this name is justified since division of the time domain is avoided even when loads with finite number of impulses of arbitrary duration are involved. The method is theoretically founded by theorems and corolaries. Their statements are included in the work. A numerical example of an undamped single degree of freedom (SDOF) system subjected to a rectangular impulse load is carried out. Comparison is made with the well-known classical solution.

scholarly journals Transient Response Estimation of an Offshore Wind Turbine Support System

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 891 ◽  
Author(s):  
Fushun Liu ◽  
Xingguo Li ◽  
Zhe Tian ◽  
Jianhua Zhang ◽  
Bin Wang
Keyword(s):  
Wind Turbine ◽  
Frequency Domain ◽  
Transient Response ◽  
Time Domain ◽  
Initial Conditions ◽  
Offshore Wind ◽  
Offshore Wind Turbines ◽  
Domain Method ◽  
The Time Domain ◽  
External Loads

To obtain reliable estimations of the dynamic responses of high-rising marine structures such as offshore wind turbines with obvious nonzero initial conditions, traditional frequency-domain methods cannot be employed because they provide only steady-state results. A novel frequency-domain transient response estimation method for offshore wind turbines is presented in this paper. This method builds upon a recent, significant theoretical development, which found that expressions of external loads in the frequency domain can be obtained by discretizing their eigenvalues and corresponding complex coefficients rather than directly by discrete Fourier transform (DFT) analysis, which makes it possible to deal with nonzero conditions in the frequency domain. One engineering advantage of this approach is its computational efficiency, as the motion equations of the system can be solved in the frequency domain. In order to demonstrate this approach, a case of a monopile-supported wind turbine with nonzero initial conditions was investigated. The numerical results indicate that the approach matches well with the time-domain method, except for a small, earlier portion of the estimated responses. A second case study of a sophisticated, jacket support wind turbine, involving practical issues such as complex external loads and computation efficiency, is also discussed, and comparisons of the results with the time-domain method and traditional frequency-domain method using the commercial software ANSYS are included here.

Sign in / Sign up

Export Citation Format

Share Document