scholarly journals Stabilization of an Unconventional Large Airship when Hovering

2021 ◽  
Vol 11 (8) ◽  
pp. 3551
Author(s):  
Naoufel Azouz ◽  
Mahmoud Khamlia ◽  
Jean Lerbet ◽  
Azgal Abichou
Keyword(s):  
Feedback Control ◽  
Dynamic Model ◽  
Linear Equations ◽  
Energy Optimization ◽  
Numerical Algorithms ◽  
Control Law ◽  
Control Allocation ◽  
Optimization Constraints ◽  
Loading And Unloading ◽  
Non Linear Equations

In this paper, we present the stabilization of an unconventional unmanned airship above a loading and unloading area. The study concerns a quad-rotor flying wing airship. This airship is devoted to freight transport. However, during the loading and unloading phases, the airship is very sensitive to squalls. In this context, we present in this paper the dynamic model of the airship, and we propose a strategy for controlling it under the effects of a gust of wind. A feedforward/feedback control law is proposed to stabilize the airship when hovering. As part of the control allocation, the non-linear equations between the control vectors and the response of the airship actuators are highlighted and solved analytically through energy optimization constraints. A comparison with classical numerical algorithms was performed and demonstrated the power and interest of our analytic algorithm.

Design Optimization of Valveless DTH Pneumatic Hammers by a Weighted Pseudo-Gradient Search Method

1998 ◽  
Vol 120 (4) ◽  
pp. 687-694 ◽  
Author(s):  
L. E. Chiang ◽  
E. B. Stamm
Keyword(s):  
Dynamic Model ◽  
Linear Equations ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Variables ◽  
Standard Procedures ◽  
Non Linear ◽  
Predicted Values ◽  
Gradient Search Method ◽  
Non Linear Equations

A design methodology for Down-The-Hole (DTH) pneumatic hammers used for rock drilling is proposed which renders an optimal design for a given set of constraints. A generic non-linear dynamic model developed by the authors is used to compute the hammer performance. This model consists of a set of six differential equations plus a set of twenty non-linear polynomial equations. In addition there are parameter range restrictions given by fabrication and operational standard procedures. In any given application, magnitudes such as power, impact energy, frequency, efficiency and mass flow may be sought for optimality. However these magnitudes must be computed by integration after solving the dynamic model over an entire cycle, thus traditional optimization methods for non-linear equations that are based in gradient information are not suitable. Hence a method that uses secant information is used to approximate the gradient of the space of design variables. Several prototypes using this optimization method have been designed and field tested. The results are in agreement with predicted values.

scholarly journals Design of Optimal Hybrid Position/Force Controller for a Robot Manipulator Using Neural Networks

2007 ◽  
Vol 2007 ◽  
pp. 1-23 ◽  
Author(s):  
Vikas Panwar ◽  
N. Sukavanam
Keyword(s):  
Neural Network ◽  
Feedback Control ◽  
Dynamic Model ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Optimal Feedback Control ◽  
Control Law ◽  
State Variables ◽  
Bounded Control ◽  
Optimal Feedback

The application of quadratic optimization and sliding-mode approach is considered for hybrid position and force control of a robot manipulator. The dynamic model of the manipulator is transformed into a state-space model to contain two sets of state variables, where one describes the constrained motion and the other describes the unconstrained motion. The optimal feedback control law is derived solving matrix differential Riccati equation, which is obtained using Hamilton Jacobi Bellman optimization. The optimal feedback control law is shown to be globally exponentially stable using Lyapunov function approach. The dynamic model uncertainties are compensated with a feedforward neural network. The neural network requires no preliminary offline training and is trained with online weight tuning algorithms that guarantee small errors and bounded control signals. The application of the derived control law is demonstrated through simulation with a 4-DOF robot manipulator to track an elliptical planar constrained surface while applying the desired force on the surface.

scholarly journals A master exceptional field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin
Keyword(s):  
Field Theory ◽  
Gauge Invariance ◽  
Sigma Model ◽  
Linear Equations ◽  
Field Theories ◽  
Gauge Invariant ◽  
Non Linear ◽  
Non Linear Equations

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

scholarly journals Framework for Reconstruction of Pseudo Quad Polarimetric Imagery from General Compact Polarimetry

2021 ◽  
Vol 13 (3) ◽  
pp. 530
Author(s):  
Junjun Yin ◽  
Jian Yang
Keyword(s):  
Linear Equations ◽  
Estimation Method ◽  
Data Sets ◽  
Reconstruction Procedure ◽  
Component Decomposition ◽  
Reconstruction Methods ◽  
Sar Imagery ◽  
Key Aspects ◽  
Non Linear Equations ◽  
Reconstruction Model

Pseudo quad polarimetric (quad-pol) image reconstruction from the hybrid dual-pol (or compact polarimetric (CP)) synthetic aperture radar (SAR) imagery is a category of important techniques for radar polarimetric applications. There are three key aspects concerned in the literature for the reconstruction methods, i.e., the scattering symmetric assumption, the reconstruction model, and the solving approach of the unknowns. Since CP measurements depend on the CP mode configurations, different reconstruction procedures were designed when the transmit wave varies, which means the reconstruction procedures were not unified. In this study, we propose a unified reconstruction framework for the general CP mode, which is applicable to the mode with an arbitrary transmitted ellipse wave. The unified reconstruction procedure is based on the formalized CP descriptors. The general CP symmetric scattering model-based three-component decomposition method is also employed to fit the reconstruction model parameter. Finally, a least squares (LS) estimation method, which was proposed for the linear π/4 CP data, is extended for the arbitrary CP mode to estimate the solution of the system of non-linear equations. Validation is carried out based on polarimetric data sets from both RADARSAT-2 (C-band) and ALOS-2/PALSAR (L-band), to compare the performances of reconstruction models, methods, and CP modes.

scholarly journals Striated Tire Yaw Marks—Modeling and Validation

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4309
Author(s):  
Wojciech Wach ◽  
Jakub Zębala
Keyword(s):  
Vehicle Dynamics ◽  
Linear Equations ◽  
Tire Model ◽  
Vehicle Accidents ◽  
The Road ◽  
Variable Curvature ◽  
Macro Scale ◽  
On The Road ◽  
Multi Body ◽  
Non Linear Equations

Tire yaw marks deposited on the road surface carry a lot of information of paramount importance for the analysis of vehicle accidents. They can be used: (a) in a macro-scale for establishing the vehicle’s positions and orientation as well as an estimation of the vehicle’s speed at the start of yawing; (b) in a micro-scale for inferring among others things the braking or acceleration status of the wheels from the topology of the striations forming the mark. A mathematical model of how the striations will appear has been developed. The model is universal, i.e., it applies to a tire moving along any trajectory with variable curvature, and it takes into account the forces and torques which are calculated by solving a system of non-linear equations of vehicle dynamics. It was validated in the program developed by the author, in which the vehicle is represented by a 36 degree of freedom multi-body system with the TMeasy tire model. The mark-creating model shows good compliance with experimental data. It gives a deep view of the nature of striated yaw marks’ formation and can be applied in any program for the simulation of vehicle dynamics with any level of simplification.

scholarly journals Compartmental Learning versus Joint Learning in Engineering Education

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 662
Author(s):  
María Jesús Santos ◽  
Alejandro Medina ◽  
José Miguel Mateos Roco ◽  
Araceli Queiruga-Dios
Keyword(s):  
Engineering Students ◽  
Chemical Engineering ◽  
Linear Equations ◽  
Mathematical Software ◽  
Mathematical Concepts ◽  
Joint Learning ◽  
The University ◽  
Academic Year ◽  
Non Linear Equations ◽  
Mathematics And Physics

Sophomore students from the Chemical Engineering undergraduate Degree at the University of Salamanca are involved in a Mathematics course during the third semester and in an Engineering Thermodynamics course during the fourth one. When they participate in the latter they are already familiar with mathematical software and mathematical concepts about numerical methods, including non-linear equations, interpolation or differential equations. We have focused this study on the way engineering students learn Mathematics and Engineering Thermodynamics. As students use to learn each matter separately and do not associate Mathematics and Physics, they separate each matter into different and independent compartments. We have proposed an experience to increase the interrelationship between different subjects, to promote transversal skills, and to make the subjects closer to real work. The satisfactory results of the experience are exposed in this work. Moreover, we have analyzed the results obtained in both courses during the academic year 2018–2019. We found that there is a relation between both courses and student’s final marks do not depend on the course.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

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