scholarly journals Optimal Aerial Guidance in General Wind Fields

2020 ◽  
Author(s):  
Ely Paiva ◽  
Guilherme Pereira
Keyword(s):  
Analytical Solution ◽  
Minimum Principle ◽  
Wind Fields ◽  
Control Effort ◽  
Optimal Guidance ◽  
Guidance Algorithm ◽  
Point To Point ◽  
Iterative Procedures ◽  
Derivatives Of ◽  
Wind Perturbation

<div>This paper presents an optimal guidance approach</div><div>for a UAV point-to-point navigation in 2D, under wind perturbation, with a general desired airspeed profile. A cost function weighting the travel time and the control effort is minimized through the Pontryagin’s Minimum Principle, involving the derivatives of the airspeed velocities. Two iterative procedures for a guidance algorithm under general wind fields were developed, including an analytical solution for the optimal heading in minimum-time paths. Different cases from the literature are compared and a hard wind scenario test is presented.</div>

scholarly journals Optimal Aerial Guidance in General Wind Fields

2020 ◽  
Author(s):  
Ely Paiva ◽  
Guilherme Pereira
Keyword(s):  
Analytical Solution ◽  
Minimum Principle ◽  
Wind Fields ◽  
Control Effort ◽  
Optimal Guidance ◽  
Guidance Algorithm ◽  
Point To Point ◽  
Iterative Procedures ◽  
Derivatives Of ◽  
Wind Perturbation

<div>This paper presents an optimal guidance approach</div><div>for a UAV point-to-point navigation in 2D, under wind perturbation, with a general desired airspeed profile. A cost function weighting the travel time and the control effort is minimized through the Pontryagin’s Minimum Principle, involving the derivatives of the airspeed velocities. Two iterative procedures for a guidance algorithm under general wind fields were developed, including an analytical solution for the optimal heading in minimum-time paths. Different cases from the literature are compared and a hard wind scenario test is presented.</div>

scholarly journals An analytical solution for solving a new wave equation within Lorenzo-Hartley kernel

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 3739-3744
Author(s):  
Feng Gao
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Fractional Order ◽  
New Wave ◽  
Liouville Type ◽  
Derivatives Of

In this article we investigate the general fractional-order derivatives of the Riemann-Liouville type via Lorenzo-Hartley kernel, general fractional-order integrals and the new general fractional-order wave equation defined on the definite domain with the analytical soluton.

An Analytical Solution of the Generalized Phase-Lagging Equation for Ultra-Fast Heat Transfer in One-Dimensional Semi-Infinite Domain

2012 ◽  
Author(s):  
Vladimir Kulish ◽  
Kirill V. Poletkin
Keyword(s):  
Analytical Solution ◽  
Domain Boundary ◽  
Integral Form ◽  
Solution Procedure ◽  
Generalized Derivatives ◽  
Infinite Domain ◽  
One Dimensional ◽  
Confluent Hypergeometric Functions ◽  
The Laplace Transform ◽  
Derivatives Of

The paper presents an integral solution of the generalized one-dimensional phase-lagging heat equation with the convective term. The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of non-integer orders). Confluent hypergeometric functions, known as Whittaker’s functions, appear in the course of the solution procedure, upon applying the Laplace transform to the original transport equation. The analytical solution of the problem is written in the integral form and provides a relationship between the local values of the temperature and heat flux. The solution is valid everywhere within the domain, including the domain boundary.

Quadrotor Thrust Vectoring Control with Time and Jerk Optimal Trajectory Planning in Constant Wind Fields

2018 ◽  
Vol 06 (01) ◽  
pp. 15-37 ◽  
Author(s):  
João Paulo Silva ◽  
Christophe De Wagter ◽  
Guido de Croon
Keyword(s):  
Trajectory Planning ◽  
Aerodynamic Drag ◽  
A Priori ◽  
Euler Angle ◽  
Flight Test ◽  
Wind Fields ◽  
Thrust Vectoring ◽  
Point Tracking ◽  
Aerodynamic Properties ◽  
Point To Point

This paper proposes a trajectory planning and control strategy to optimally visit a given set of waypoints in the presence of wind. First, aerodynamic properties of quadrotors which affect trajectory planning and tracking performance are investigated. Blade flapping, induced and parasitic drag are derived and an extended method to identify all coefficients from flight test data is developed. Then, a three-step approach is suggested to optimize the trajectory. These steps reduce the size of the optimization problem and thereby increase computational efficiency while still guaranteeing near optimal results. The trajectories are optimized for minimal aerodynamic drag and minimal jerk. The derived smooth trajectory generation is compared with traditional trajectory planning consisting of discrete point to point tracking followed by low-pass filtering. The new trajectories yield a clear reduction in maximal needed thrust and in Euler angle aggressiveness. A thrust vectoring controller is designed, which exploits the a priori trajectory information and identified aerodynamic properties. Its performance is compared to a standard PID controller and results show a reduction in tracking delay and an increase in thrust and attitude angle margins, which overall enable faster flight.

Optimization of aerospace aircraft guidance to the landing area

2021 ◽  
Author(s):  
A.Yu. Melnikov ◽  
S.N. Ilukhin
Keyword(s):  
Maximum Principle ◽  
Boundary Value ◽  
Flight Simulation ◽  
Motion Model ◽  
Algorithm Efficiency ◽  
Simulation Procedure ◽  
Optimal Guidance ◽  
Guidance Algorithm ◽  
The Pontryagin Maximum Principle ◽  
Significant Factors

The article considers a technique for constructing an optimal guidance procedure for an aerospace aircraft. The technique is based on the adaptation of the Pontryagin maximum principle for the considered class of problems. At the same time the guidance accuracy is ensured by solving a boundary value problem, which is periodically performed during the flight. The developed procedure for predicting the final parameters of the optimal flight according to a simplified motion model is presented, which also makes it possible to determine the value of the actual miss. A detailed mathematical description of the proposed technique is given. The feasibility of the proposed technique is ensured by minimizing the amount of computational operations. The guidance algorithm efficiency is illustrated by a numerical example with a flight simulation procedure taking into account all significant factors. The paper also provides examples of solving boundary value problems and the results of modeling the optimal guidance.

Observing Profiles of Derived Kinematic Field Quantities Using a Network of Profiling Sites

2021 ◽  
Keyword(s):  
Great Plains ◽  
Weather Prediction ◽  
Numerical Weather Prediction Model ◽  
Strong Correlations ◽  
Wind Fields ◽  
Large Area ◽  
Southern Great Plains ◽  
Atmospheric Radiation Measurement ◽  
Derivatives Of ◽  
Good Agreement

Abstract Observations of thermodynamic and kinematic parameters associated with derivatives of the thermodynamics and wind fields, namely advection, vorticity, divergence, and deformation, can be obtained by applying Green’s Theorem to a network of observing sites. The five nodes that comprise the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) profiling network, spaced 50 -80 km apart, are used to obtain measurements of these parameters over a finite region. To demonstrate the applicability of this technique at this location, it is first applied to gridded model output from the High Resolution Rapid Refresh (HRRR) numerical weather prediction model, using profiles from the locations of ARM network sites, so that values calculated from this method can be directly compared to finite difference calculations. Good agreement is found between both approaches as well as between the model and values calculated from the observations. Uncertainties for the observations are obtained via a Monte Carlo process in which the profiles are randomly perturbed in accordance with their known error characteristics. The existing size of the ARM network is well-suited to capturing these parameters, with strong correlations to model values and smaller uncertainties than a more closely-spaced network, yet it is small enough that it avoids the tendency for advection to go to zero over a large area.

Stresses in anisotropic media with particular reference to problems of rock mechanics

1966 ◽  
Vol 1 (2) ◽  
pp. 172-182 ◽  
Author(s):  
O. C. Zienkiewicz ◽  
Y. K. Cheung ◽  
K. G. Stagg
Keyword(s):  
Analytical Solution ◽  
Good Accuracy ◽  
Transverse Isotropy ◽  
Individual Element ◽  
Stress Distributions ◽  
Axis Orientation ◽  
Point To Point ◽  
The Individual ◽  
Stratified Rock ◽  
At Will

The recently developed finite element method of numerical stress analysis has been previously applied to the analysis of the stress distribution in isotropically elastic materials and is here extended to deal with a particular form of anisotropy. The case of anisotropy considered is that generally referred to as transverse isotropy, i.e. where the material is isotropic in the yz plane but non-isotropic with respect to directions normal to this plane. The analysis is restricted to the consideration of two-dimensional plane strain problems in the xy plane. The individual element axis orientation may be varied at will with respect to the overall co-ordinate system so that problems may be treated where the direction of isotropy varies from point to point within the material. It is suggested that this system of anisotropy is particularly relevant to the analysis of stress distributions in stratified rock masses. Previous approaches to this problem are outlined in Appendix 1. A series of illustrative examples are shown, first, to compare the numerical solution to a problem with a known analytical solution to that analytical solution and, second, to show the application to more complex situations with no known analytical solutions. It is concluded from the first comparison that the method is capable of giving good accuracy.

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