scholarly journals Mathematical Modeling of the Coaxial Quadrotor Dynamics for Its Attitude and Altitude Control

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1232
Author(s):  
Wojciech Giernacki ◽  
Jarosław Gośliński ◽  
Jagoda Goślińska ◽  
Tadeo Espinoza-Fraire ◽  
Jinjun Rao
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Viscous Friction ◽  
Control Techniques ◽  
Aerial Vehicle ◽  
Altitude Control ◽  
Selection Of ◽  
Three Dimensional Space

In this paper, an easily implementable coaxial quadrotor model and its validation on data from a real unmanned aerial vehicle (UAV), are presented. The proposed mathematical model consists of two parts: description of orientation and position of the UAV in the three-dimensional space. It takes into consideration the gyroscopic effect, influence of the Coriolis force, viscous friction and a several drag-like effects (blade flapping, rotor drag, translational drag and profile drag). In contrast to multirotor models available in the literature, this one is characterized by complementarity in relation to the available control techniques. Depending on selection of these techniques, the model can be narrowed (simplified) to meet the needs without the loss of behaviour adequacy to a real UAV.

scholarly journals A Predictive Control Strategy for Aerial Payload Transportation with an Unmanned Aerial Vehicle

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1822
Author(s):  
Norberto Urbina-Brito ◽  
María-Eusebia Guerrero-Sánchez ◽  
Guillermo Valencia-Palomo ◽  
Omar Hernández-González ◽  
Francisco-Ronay López-Estrada ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Predictive Control ◽  
Control Strategy ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Lagrange Formulation ◽  
Aerial Vehicle ◽  
Load Swing ◽  
The Mathematical Model ◽  
Three Dimensional Space

This paper presents the results of a model-based predictive control (MPC) design for a quadrotor aerial vehicle with a suspended load. Unlike previous works, the controller takes into account the hanging payload dynamics, the dynamics in three-dimensional space, and the vehicle rotation, achieving a good balance between fast stabilization times and small swing angles. The mathematical model is based on the Euler–Lagrange formulation and considers the dynamics of the vehicle, the cable, and the load. Then, the mathematical model is represented as an input-affine system to obtain the linear model for the control design. A constrained MPC strategy was designed and compared with an unconstrained MPC and an algorithm from the literature for the case of study. The constraints to be considered include the limits on the swing angles and the quadrotor position. The constrained control algorithm was constructed to stabilize the aerial vehicle. It aims to track a trajectory reference while attenuating the load swing, considering a maximum swing range of ±10∘. Numerical simulations were carried out to validate the control strategy.

scholarly journals Development of a Mathematical Model for Tracking Movement of a Human Limb in Three-Dimensional Space Using MEMS Sensors

2021 ◽  
Vol 11 (3) ◽  
pp. 74-82
Author(s):  
N.I. Levonovich
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Practical Importance ◽  
Three Dimensional ◽  
Suitable Model ◽  
Mems Sensors ◽  
Model Experiments ◽  
Human Limb ◽  
Tracking Movement ◽  
Three Dimensional Space

This article discusses the development of a mathematical model for a device capable of tracking the movements of a human limb based on the readings of microelectromechanical sensors. For developing and selecting the most suitable model, experiments were conducted based on publicly available components. The result obtained is of practical importance since it can be used to create a device.

scholarly journals Multi-Analytical Approach for Asbestos Minerals and Their Non-Asbestiform Analogues: Inferences from Host Rock Textural Constraints

Fibers ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 42 ◽  
Author(s):  
Gaia Maria Militello ◽  
Andrea Bloise ◽  
Laura Gaggero ◽  
Gabriele Lanzafame ◽  
Rosalda Punturo
Keyword(s):  
Energy Dispersive Spectrometry ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Instrumental Approach ◽  
X Ray ◽  
Transmission Electron ◽  
Analytical Protocol ◽  
Non Destructive ◽  
Selection Of ◽  
Three Dimensional Space

Asbestos is a hazardous mineral, as well as a common and well-known issue worldwide. However, amphiboles equal in composition but not in morphology, as well as the fibrous antigorite and lizardite, are not classified as asbestos even if more common than other forms of the mineral. Still, their potential hazardous properties requires further exploration. The proposed multi-instrumental approach focuses on the influence of textural constraints on the subsequent origin of asbestiform products in massive rock. This aspect has a significant effect on diagnostic policies addressing environmental monitoring and the clinical perspective. Concerning minerals that are chemically and geometrically (length > 5 μm, width < 3 μm and length:diameter > 3:1) but not morphologically analogous to regulated asbestos, the debate about their potential hazardous properties is open and ongoing. Therefore, a selection of various lithotypes featuring the challenging identification of fibrous phases with critical counting dimensions was investigated; this selection consisted of two serpentinites, one metabasalt and one pyroxenite. The analytical protocol included optical microscopy (OM), scanning and transmission electron microscopy combined with energy dispersive spectrometry (SEM/EDS; TEM/EDS), micro-Raman spectroscopy and synchrotron radiation X-ray microtomography (SR X-ray μCT). The latter is an original non-destructive approach that allows the observation of the fiber arrangement in a three-dimensional space, avoiding morphological influence as a result of comminution.

scholarly journals Construction of Shale Gas Well

2018 ◽  
Vol 35 ◽  
pp. 01003
Author(s):  
Aneta Sapińska-Śliwa ◽  
Rafał Wiśniowski ◽  
Krzysztof Skrzypaszek
Keyword(s):  
Economic Analysis ◽  
Shale Gas ◽  
Input Data ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Trajectory Design ◽  
Gas Well ◽  
Profile Type ◽  
Selection Of ◽  
Three Dimensional Space

The paper describes shale gas borehole axes trajectories (vertical, horizontal, multilateral). The methodology of trajectory design in a two-and three-dimensional space has been developed. The selection of the profile type of the trajectory axes of the directional borehole depends on the technical and technological possibilities of its implementation and the results of a comprehensive economic analysis of the availability and development of the field. The work assumes the possibility of a multivariate design of trajectories depending on the accepted (available or imposed) input data.

scholarly journals A proposal method for reducing the order of general heat conduction equation

2018 ◽  
Vol 20 ◽  
pp. 02014
Author(s):  
Thanh-Phong Tran
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Transfer Process ◽  
Heat Conduction Equation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Heat Transfer Process ◽  
Unknown Parameters ◽  
Simulation Experiments ◽  
Three Dimensional Space

In the context of investigating methods dedicated to identifying unknown parameters of the system described by partial differential equations, particularly in the field of heat transfer, it has been realized that the heat transfer process in particular three-dimensional features is really complex and takes longer to calculate. Therefore, an equivalent mathematical model which is simpler proposed to reduce the calculation time and the costs of experimental activities. We observe that the mathematical models of the diffusion equation can be minimized in three-dimensional space into a similar two-dimensional pattern within certain limits did not change the physical properties of heat transfer process. A mathematical model and the numerical results of simulation experiments in order to prove effectiveness the proposed method will be presented in detail in this article.

A Fast Digital 3D-SVPWM Algorithm for Four-Leg Converter

2014 ◽  
Vol 541-542 ◽  
pp. 494-497
Author(s):  
Peng Xian Song ◽  
Ping Wang ◽  
Yao Hua Li
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Coordinate Transformation ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Vector Pwm ◽  
Space Vector ◽  
Computational Burden ◽  
Three Phase ◽  
Three Dimensional Space

The three-phase four-leg converter can be obtained by adding a bridge into the traditional three-phase three-leg converter. The average mathematical model of three-phase four-leg converter is described in this paper. The three-dimensional space vector PWM (3D-SVPWM) is analyzed. For simplifying the modulation, a fast digital SVPWM algorithm which eliminates coordinate transformation and saves calculating time was proposed. The feasibility of the proposed modulation technique is verified by computer simulation. These results show that the proposed fast digital 3D-SVPWM technique can be easily implemented without conventional computational burden.

Static and Dynamic Behaviours of Three-Tower Suspension Bridges and the Structure Selection of the Mid-Tower

2010 ◽  
Vol 163-167 ◽  
pp. 2343-2349 ◽  
Author(s):  
Peng Liang ◽  
Xiang Nan Wu ◽  
Yue Xu
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Comprehensive Analysis ◽  
Suspension Bridges ◽  
Finite Element Models ◽  
Structure Selection ◽  
Main Cable ◽  
Main Girder ◽  
Selection Of ◽  
Three Dimensional Space

In order to discuss the mechanical behaviour differences between the two-tower and three-tower suspension bridges, based on the Taizhou Yangtze River Bridge, three dimensional space finite element models of two-tower, three-tower with concrete mid-tower and with steel mid-tower were constructed. Through the comprehensive analysis, main conclusions are got as follows: due to the mid-tower lack of effective restraint from side cable, compared with two-tower suspension bridges, three-tower suspension bridges have lower total stiffness and natural frequency, with larger deflection-to-span ratio of main girder. So, some factors such as anti-slipping safety factor between the main cable and saddle, deflection-to-span ratio of main girder and force in mid-tower, which are not important in two-tower design, become controlling ones in three-tower suspension bridges. These factors are related to anti-pushing rigidity of mid-tower, but in contradictory demanding for the rigidity of mid-tower. After comprehensive analysis, steel tower with shape of upside-down ‘Y’ meets all demands, and then, was selected as appropriate structure for the mid-tower.

Deposit Digitizing for JiaYaShan Ore Block in LanPing Pb-Zn Mine

2012 ◽  
Vol 229-231 ◽  
pp. 2047-2051
Author(s):  
Yu Jian Li ◽  
Wen Chang Li ◽  
Yong Feng Yan
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Dynamic Management ◽  
Systematic Analysis ◽  
Use Of Resources ◽  
Deposit Model ◽  
Ore Block ◽  
Three Dimensional Space

Lanping Pb-Zn mine is the biggest Pb-Zn mine of China. It is necessary for the mine to digital. On the basis of systematic analysis of and research on Jiayashan ore block in Lanping pb-zn mine, Mine Mathematical Model software, Surpac software and Micrmine software from abroad for digitization ware used to study this deposit. Finally, a three-dimensional space deposit model was established. As a result, the dynamic management of mine has been realized, the degree of automation and systematize have been increased for mining production, the scientific help have been presented for making use of resources sufficiently and reasonably.

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