Coordinate Transformation Method Research Articles

Control of MIMO linear plants with a guarantee for the controlled signals to stay in a given set

In this paper, we propose a new method for synthesizing the control of multi-input multi output linear plants with a guarantee of finding controlled signals in given sets under conditions of unknown bounded disturbances. The problem is solved in two stages. At the first stage, the coordinate transformation method is used to reduce the original constrained problem to the problem of studying the input-to-state stability of a new extended system without constraints. At the second stage, the control law for the extended system is obtained by solving a series of linear matrix inequalities. To illustrate the effectiveness of the proposed method, simulation in the MATLAB/Simulink is given. The simulation results show the presence of controlled signals in the given sets and the boundness of all signals in the control system. The proposed method is recommended for use in control problems where it is required to maintain controlled signals in given sets, for example, control of an electric power network, control of the reservoir pressure maintenance process, etc.

Stochastic Stability and Bifurcation of Centrifugal Governor System Subject to Color Noise

This paper presents a detailed investigation of stochastic stability and complex dynamics of a centrifugal governor system with approximately uniform color noise. The centrifugal governor system excited by noise is transformed into Itö equation using polar coordinate transformation and stochastic average method. According to the boundary conditions of attraction and repulsion, the stochastic stability is ensured. In addition, analyses concerning the influence of parameter variation and validity are carried out by employing numerical method. The results manifest that the effects of noise intensity and correlation time on stationary probability density are opposite. The amplitudes of probability density finally tend to a limit value, and the only limit cycle appears, which shows that when the bifurcation occurs, the trivial solution of the system converges to a limit cycle with a higher probability. Finally, the two-dimensional parameter bifurcation analysis of the centrifugal governor system subject to color noise excitation is studied. An interesting distribution characteristic is found that the periodic region is organized according to the sequence of Stern–Brocot trees, and this typical characteristic is a universal characteristic of the system on the two parameter planes. Furthermore, it is concluded that based on the largest Lyapunov exponent diagram and bifurcation diagram in two-dimensional parameter plane, the effects of noise intensity and correlation time on the periodic oscillation state are opposite, but both of them can transform the quasi-periodic oscillation into periodic oscillation. It should be emphasized that with the increase of noise intensity, the coexisting oscillation behavior of the centrifugal governor system will change, which is manifested by the destruction of coexisting attractors and the generation of chaotic attractors.

하이브리드 능동전력필터의 전력품질 개선을 위한 Coordinate Transformation 기법에 대한 성능 비교

In this paper, the performances of Coordinate transformation method for harmonic and reactive power compensation of hybrid active power filters were compared and analyzed. Recently, as the spread of power electronic devices is expanding, the occurrence of harmonics in the system is increasing, and the harmonics have a bad effect on the system and electrical equipment. As a measure against such harmonics, the parallel resonance problem of passive power filters among filters can be solved, and a hybrid active power filter with a small compensation capacity of the active power filter can be considered. However, In order to control the hybrid active power filter to the required power factor, it is necessary to control it through fast tracking even when the load changes. Therefore, in this paper, the performance was analyzed by applying the p-q theory method and the compensation current control method using d-q respectively to the hybrid active power filter. As a result of comparing and analyzing the effects through simulation, it was confirmed that using the p-q theory method quickly followed the target value with a relatively small error even with a variable load than using the d-q method.

Effects of airway deformation and alveolar pores on particle deposition in the lungs

The distal lung (G14–G23), which are composed of alveoli and bronchi, are responsible for almost all gas exchange and micro- and nanoparticle deposition in the lungs. In the existing research using computational fluid dynamics, the geometric modeling accuracy of the bronchial bifurcation structure is given priority, and then the alveoli are attached to bronchi as discrete spherical crowns. This method ignores the correlation between alveoli. In fact, the alveoli have a tessellated distribution, and adjacent alveoli are connected by several alveolar pores. Due to the huge number of alveoli, this seemingly small difference will be greatly amplified, which may lead to a large deviation in the prediction of the overall flow. Accordingly, the objective of this study is to construct a two-dimensional distal lung model including the bronchi, acini, and alveolar pores by using the methods of regular hexagonal tessellational subdivision, fusion, and coordinate transformation. A moving boundary is introduced to simulate the process of airflow and particle deposition in the distal lung, and the effects of bronchial deformation, respiratory frequency, and alveolar pores are obtained. The results show that there are significant differences in intrapulmonary flow patterns with and without alveolar pores. Alveolar pores can establish bypass ventilation downstream of a blockage, thus providing a pathway for particles to enter the airways downstream of the blockage. Changing the respiratory frequency and the amplitude of bronchial deformation will change the relative velocity between particles and moving wall, which, in turn, will change the particle deposition efficiency in the distal lung. To summarize this study, a geometric modeling method for the distal lung with alveolar pores is established, and the important roles of detailed characteristics of the distal lung are revealed. The findings of this study provide a reasonable hydrodynamic mechanism for the prevention of related respiratory diseases.

A Sun-Tracking Algorithm for Satellite-Borne Spectrometers Based on the Orbital Motion Model

To guarantee that a spectrometer can obtain effective solar spectral data, it is important that the two-dimensional turntable that carries the spectrometer tracks the sun with high accuracy for long time periods, such that the sun is always near the center of the field of view of the spectrometer. However, there is an offset lag problem for the tracking sensor, leading to an increase in the sun-tracking error and inaccuracies in solar spectrum data. To mitigate this problem, an on-axis tracking control algorithm—based on the orbital motion model—is proposed in this paper. First, the sun-tracking model of the spectrometer is established based on the coordinate transformation method, and the analytical relationship between the adjustment angle of the turntable and the solar vector in the orbit system is given by means of the inverse kinematics solution of the target model. Then, the predictive filtering algorithm of the target model is derived to acquire the target position, based on which, the on-axis tracking control algorithm of the spectrometer system is realized to compensate the offset lag and increase the sun-tracking accuracy. Finally, the simulation analysis and experimental verification were performed under the actual working conditions of an orbit. The simulation results demonstrate that the root-mean-square (RMS) of the target position deviation decreased from 2.08″ to 0.77″ after prediction filtering, and the RMS of the tracking error decreased from 7.14″ to 0.97″. The RMS of an orbit’s sun-tracking error decreased from 5.72″ to 1.43″ in the ground test. The simulation and experimental results verify that the algorithm proposed in this paper can improve the tracking accuracy of the spectrometer, providing a reference for the design of a spectrometer in orbit.

Boundary element analysis of thin structures using a dual transformation method for weakly singular boundary integrals

This paper focuses on the weakly singular integrals in thin structures of 3D boundary element method. In the pioneering woks for the weakly singular integrals, the singularities are eliminated through introducing transformations whose Jacobian at the singular point is zero. When using these methods for weakly singular boundary integrals on elements with a large-angle and large side length ratio, near singularity will appear. In this paper, a dual transformation method is proposed to accurately calculate weakly singular integrals in which the near singularity is also considered. The numerical implementation is divided into several steps. Firstly, the (α, β) coordinate transformation method is used to eliminate the weak singularity by introducing the α factors in the transformation Jacobian. Then extract the integral form with near singularities about β. Finally, a corresponding distance transformation is constructed to eliminate its near singularity. The results show that the proposed method can accurately integrate for arbitrary element shape and source point position. The dual transformation method may be a good choice to evaluate weakly singular integral for thin structural problem.

Coordinate transformation method for heat reallocation in the spiral water-cooled wall temperature calculation

Fireside metal temperature is quite important in the safety evaluation of boiler water-cooled wall. While little literature reported the accurate temperature calculation model for spiral water-cooled wall. This paper proposes a coordinate transformation method for heat reallocation in the spiral water-cooled wall temperature calculation. A computational fluid dynamics (CFD) model based on a 600 MW tangentially coal-fired boiler is used to provide the original heat flux distributions under various boiler loads. The reallocated heat distribution directly maps with the flow path of the spiral water-cooled wall. The combination of the heat reallocation model and thermal-hydraulic model is realized in MATLAB platform. The calculated temperature distributions at the outlet of the spiral water-cooled wall agree well with the in-situ data, and the maximum relative errors under 100% BMCR load and 75% THA load are 2.7% and 3.2%, respectively. The numerical results show that the working fluid flow rates of the divided loops are almost equal and the maximum metal temperatures of the spiral water-cooled wall are 732.1 K, 710.4 K, 760.9 K and 792.9 K under 100% BMCR, 75% THA, 50% THA and 35% BMCR loads, respectively. The local overheating is likely to occur in low boiler load. This model is intended to improve the metal temperature calculation method of the spiral water-cooled wall, which could benefit the safety monitoring of the boiler under variable loads.

Analytical Approach to the Coupled Effects of Slope Angle and Seepage on Shallow Lined Tunnel Response

The existing analytical models of shallow lined tunnels pay little attention to the coupled effects of slope angle and seepage, leading to an overestimation of tunnel stability. In order to overcome such a problem, based on the methods of coordinate transformation, complex function and conformal mapping, we attempt to provide an analytical approach to estimate the effective stress and deformation in shallow lined tunnels considering the corresponding influence factors in this study. First, the stress function is extended to the Laurent series in the complex plane, followed by Laplace transform and inverse transform methods on stress function, and the analytical solutions for stress and displacement fields around the tunnel are achieved during different stages. Then, Mein–Larson formula and G–A formula are used to obtain the pore water pressure and effective stress of surrounding rock and lining, considering the effects of rainfall and groundwater. The analytical solution provided in this study can be reduced without considering the lining support and slope angle effects. Furthermore, the rationality and effectiveness of the proposed solution are achieved by a comparison of numerical results. Finally, a comprehensive parametric investigation based on the proposed solution is performed, including buried depth, slope angle and rainfall intensity. The results show that the small change of stress and deformation of the ground surface is observed as the buried depth becomes more than 30[Formula: see text]m. If the slope angle varies within a range from 0 to 30[Formula: see text], the influence of slope angle change on the stress and deformation of surrounding rock can be generally neglected. When the rainfall intensity is greater than a certain threshold or rainfall time is shorter than a value, these two parameters are in a limited effect on the seepage change.

Stereo-vision-based multi-crop harvesting edge detection for precise automatic steering of combine harvester

With the development of the intelligent combine harvesters, the whole-field automatic harvesting has become feasible and includes driving straight along the unharvested crop edge and steering in the crop headland. Detecting the unharvested crop edge and the end of the cultivation crop, is the foundation of whole-field automatic harvesting. A rapid and robust detection method for detecting the harvesting edge for multiple crops based on stereo vision was developed. In order to improve the processing speed and keep the crop harvesting edge within the target region, a dynamic ROI (region of interest) extraction algorithm based on HSV (hue, saturation, and value) space scanning was developed. A coordinate transformation method was applied to generate a crop elevation image, and the unharvested crop area was obtained by the Ostu algorithm. Simultaneous detection of unharvested crop edge and crop end edge was realised by the method based on the horizontal length feature of the unharvested area contour. This enabled automatic driving along the unharvested crop edge, and automatic steering into the next harvest path according to the crop end edge. Finally, field tests with crops of paddy, oil-seed rape, and maize crops were carried out to test the system performance, and the accuracy of the detection was found to be higher than 98% for paddy and rape, and higher than 94% for maize with an average processing speed of 49 ms frame−1. The experiments showed that the proposed method exhibited high accuracy and efficiency and was suitable for various complex field environments.

Production decline analysis for a fractured vertical well with reorientated fractures in an anisotropic formation with an arbitrary shape using the boundary element method

In this work, theoretical models have been formulated, validated, and applied to evaluate the production decline performance of a fractured vertical well with reorientated fractures in an anisotropic formation with an arbitrary shape by using the boundary element method. More specifically, the coordinate transformation method was applied to convert the anisotropic system to an equivalent isotropic system, while a coupled matrix-fracture flow model is proposed in the Laplace domain. Then, the boundary element method is applied to solve the fluid flow problem in the matrix, while the Laplace-transform finite difference method is used to numerically obtain the pressure solutions for each fracture segment. Furthermore, the effect of orientated fractures can be examined by generating the Agarwal-Gardner type decline curves, during which two flow regimes including transient flow regime and boundary dominant flow regime can be found. The orientated fractures only affect the transient flow regimes and the boundary dominant flow can be affected by the area and shape of the reservoir. The fracture conductivity is found to be the most important parameter dominating the early production rate. The larger the anisotropic factor, the larger production rate during the early times. Also, the primary fracture angle is more sensitive than the orientated fracture angle. Subsequently, this newly proposed method has been validated and then extended to a field application, demonstrating that the production decline curves for a fractured well with reorientated fractures can be analyzed in a reasonable and accurate manner.

Influence of Charging Parameters on the Burden Flow Velocity and Distribution on the Blast Furnace Chute Based on Discrete Element Method

The charging operation is one of the four major blast-furnace (BF) smelting systems. The flow valve opening, chute angle, and chute rotating speed are the most important charging parameters in BF ironmaking. A method for determining the burden flow distribution area is proposed, and the coordinate transformation method is adopted to study the influence of charging parameters on the burden flow velocity and distribution at the end of the chute. Further details can be found in the article, number 2100332, by Ke Zhou and co-workers.

Effect of formation strength anisotropy on wellbore shear failure in bedding shale

The shale gas/oil is playing an important role in the current energy resources. However, the wellbore instability problems bring a high risk to drilling engineering especially in the formation with bedding planes. A normal wellbore stability analysis approach is based on elasticity, which is not enough to recognize the mechanisms. In this paper, the poroelasticity was adopted to present the hydro-mechanical coupling effect in shale formation, meanwhile, the permeability anisotropy which could affect the effective stresses around the well was considered. A three-dimensional finite difference model was developed to simulate arbitrary directional well in shale by the coordinate transformation method. The jointed material model was proposed to character the strength anisotropy and plastic behavior of bedding shale. Additionally, the effects of well trajectory, bedding plane orientation and mud weight on shale wellbore stability were discussed, thus some implications for improving wellbore stability in bedding shale formation were obtained from the proposed model. • The jointed material model is proposed to analyze the shear failure region in bedding shale. • The poroelastic theory is adopted to represent the hydro-mechanical coupling effect in the formation. • A finite difference three-dimensional model is established to simulate the wellbore failure behavior. • The effects of well trajectory, bedding plane orientation and mud weight on wellbore stability are evaluated.

Error Calibration for Full Tensor Magnetic Gradiometer Probe Based on Coordinate Transformation Method

In order to calibrate the zero offset error and triaxial non-orthogonal error of full tensor magnetic gradiometer (FTMG) probe composed of superconducting quantum interference device (SQUID) magnetometers, we propose a new calibration method in this article. With the help of the triaxial Helmholtz coil, we can generate a magnetic field with known parameters. By establishing the objective functions containing the error parameters for the outputs of the SQUIDs and solving them with the least-squares fitting algorithm, the included angle between the SQUID sensor and the Helmholtz coil can be obtained, then all the required error parameters can be calculated by coordinate transformation method. Compared with the traditional method, this method does not need to rotate the SQUID magnetometers-based probe to collect the data set for calibration, thus avoiding the influence of motion induced noise on the calibration results. In order to verify the effectiveness of the proposed method, we adopted the widely used ellipsoid fitting method as a comparison method and conducted field comparison experiments. The results show that the proposed calibration method is better than the traditional ellipsoid fitting calibration method under the same experimental environment. The root mean square errors of five independent magnetic gradient tensor components are reduced to 0.39, 0.35, 0.41, 0.31 and 0.57 nT/m from 1630.55, 756.59, 3097.56, 1051.09 and 1245.64 nT/m by the proposed method.

Space Vector Pulse-Width Modulation Control Strategy for Four-Leg Inverters Under Single Line-to-Ground Faults in Islanded Microgrids

In this paper, we propose a novel switching modulation scheme for three-phase four-leg inverters that enables the separation of the fault points occurring in AC distribution networks. The proposed method is aimed at continuously supplying normal voltage to the remaining healthy phases while applying zero voltage to any faulty phase when a single line-to-ground (SLG) fault occurs in the distribution network. This modulation scheme allows isolation without physically blocking the point of failure. This can prevent unnecessary continuous outages in the AC distribution network. To this end, we propose a novel coordinate transformation method to extract accurate values for the magnitude of unbalanced three-phase voltages. A novel space vector pulse-width modulation (SVPWM) method for switching schemes that are used under fault conditions is also presented. The proposed coordinate transformation considers a plane lying in a three-dimensional (3-D) space that describes the rotation of a three-phase voltage vector. This transformation converts a physical quantity that rotates in 3-D space into a value that moves in two-dimensional (2-D) space. Subsequently, the use of synchronous reference frame (SRF) transformation enables the detection and control of the voltage magnitude in case of an SLG fault. Additionally, switching vectors are selected to apply zero voltage to the faulty phase by analyzing the switching vector diagram of a four-leg inverter. Mathematical analyses conducted for the entire process are detailed herein. Further, the experimental results of four-leg inverters designed for the 10 kW class verify the proposed strategies.

Motion-Planning Algorithm for a Hyper-Redundant Manipulator in Narrow Spaces

In this study, a hyper-redundant manipulator was designed for detection and searching in narrow spaces for aerospace and earthquake rescue applications. A forward kinematics equation for the hyper-redundant manipulator was derived using the homogeneous coordinate transformation method. Based on the modal function backbone curve method and the known path, an improved modal method for the backbone curves was proposed. First, the configuration of the backbone curve for the hyper-redundant manipulator was divided into two parts: a mode function curve segment of the mode function and a known path segment. By changing the discrete points along the known path, the backbone curve for the manipulator when it reached a specified path point was dynamically obtained, and then the joint positions of the manipulator were fitted to the main curve by dichotomy. Combined with engineering examples, simulation experiments were performed using the new algorithm to extract mathematical models for external narrow space environments. The experimental results showed that when using the new algorithm, the hyper-redundant manipulator could complete the tasks of passing through curved pipes and moving into narrow workspaces. The effectiveness of the algorithm was also proven by these experiments.

English

As crops have different agricultural requirements in pot seedling and the parameters of the planting mechanism need to be repeatedly designed, this paper proposed a reverse design method for the classic gear five-bar planting mechanism based on the agronomic requirements for pot seedling planting. The mathematical model of the planting trajectory of the geared fivebar planting mechanism was constructed through homogeneous coordinate transformation method,; the conditions for the geared five-bar planting mechanism to achieve zero-speed planting were: the gear ratio of the gear pair is -2, and the difference in length between the planetary gear rod and the sun gear rod is equal to the ratio of the planting distance to 2π. Based on the agronomic parameters of pot seedlings (planting depth, planting distance), the parameters of the geared five-bar mechanism were reversed to realize the reverse design of the geared five-bar planting mechanism. Field test results: the average planting depth of tomato pot seedlings is 47mm, the planting distance is 203mm, and the uprightness of pot seedlings is 97.5%, which meets the agronomic requirements of planting tomato pot seedlings. Therefore, the proposed reverse design method of geared five-bar planting mechanism based on agronomic requirements can solve the problem of repeated design of planting mechanism due to different agricultural parameters of most crops, which can greatly reduce the workload of designing various crop planting mechanisms

Simulation of power distribution in prescription sunglasses using the coordinate transformation method

In this study, the whole-surface power distributions in prescription sunglasses at different face form angles were simulated using the coordinate transformation method. The lens was tilted with respect to the optical center by directly transforming its Cartesian coordinate system at the desired face form angle. The results show that prescription sunglasses display different whole-surface power maps compared to plano sunglasses. Moreover, when the tilt angle of the lens is high, a greater power error is observed in the temporal area of prescription sunglass lenses, which makes the power distribution more asymmetric.

Influence of Charging Parameters on the Burden Flow Velocity and Distribution on the Blast Furnace Chute Based on Discrete Element Method

The charging parameters at the top of a blast furnace are key factors that influence the burden flow trajectory and burden surface. To analyze the influence of the charging parameters on the burden flow velocity and distribution, a 1:8 bell‐less blast furnace scale discrete element method model is first established. The coordinate transformation method is adopted to obtain the position information of the particles relative to the chute, and a method for calculating the burden flow density based on the number of truncated particles is proposed to determine the burden flow distribution area. The influence of charging parameters, such as the flow valve opening, chute angle, and rotating speed on the burden flow velocity and distribution is analyzed. The results indicate that changing the charging parameters will change the burden flow velocity, and that the chute angle has the greatest influence on the burden flow velocity while the influence of the other two parameters is almost negligible. Increasing the flow valve opening, chute angle and rotating speed will increase the radial movement distance of the burden flow, whereas too large flow valve opening may reduce the radial movement distance.

Conceptual Design and Image Motion Compensation Rate Analysis of Two-Axis Fast Steering Mirror for Dynamic Scan and Stare Imaging System.

In order to enable the aerial photoelectric equipment to realize wide-area reconnaissance and target surveillance at the same time, a dual-band dynamic scan and stare imaging system is proposed in this paper. The imaging system performs scanning and pointing through a two-axis gimbal, compensating the image motion caused by the aircraft and gimbal angular velocity and the aircraft liner velocity using two two-axis fast steering mirrors (FSMs). The composition and working principle of the dynamic scan and stare imaging system, the detailed scheme of the two-axis FSM and the image motion compensation (IMC) algorithm are introduced. Both the structure and the mirror of the FSM adopt aluminum alloys, and the flexible support structure is designed based on four cross-axis flexural hinges. The Root-Mean-Square (RMS) error of the mirror reaches 15.8 nm and the total weight of the FSM assembly is 510 g. The IMC rate equations of the two-axis FSM are established based on the coordinate transformation method. The effectiveness of the FSM and IMC algorithm is verified by the dynamic imaging test in the laboratory and flight test.

From Centralized Protection to Distributed Edge Collaboration: A Location Difference-Based Privacy-Preserving Framework for Mobile Crowdsensing

Mobile Crowdsensing (MCS) has evolved into an effective and valuable paradigm to engage mobile users to sense and collect urban-scale information. However, users risk their location privacy while reporting data with actual sensing locations. Existing works of location privacy-preserving are primarily based on single-region location information, which rely on a trusted and centralized sensing platform and ignore the impact of regional differences on user privacy-preserving demands. To tackle this issue, we propose a Location Difference-Based Privacy-Preserving Framework (LDPF), leveraging the powerful edge servers deployed between users and the sensing platform to hide and manage users according to regional user characteristics. More specifically, for popular regions, based on the edge servers and the k-anonymity algorithm, we propose a Coordinate Transformation and Bit Commitment (CTBC) privacy-preserving method that effectively guarantees the privacy of location data without relying on a trusted sensing platform. For remote regions, based on a more realistic distance calculation mode, we design a Paillier Encryption Data Coding (PDC) privacy-preserving method that realizes the secure computation for users’ location and prevents malicious users from deceiving. The theoretical analysis and simulation results demonstrate the security and efficiency of the proposed framework in location difference-based privacy-preserving.