Stability Analysis of High-Performance Drones With Suspended Payloads

2019 ◽  
Author(s):  
Samantha Hoang ◽  
Yifeng Liu ◽  
Alberto Aliseda ◽  
I. Y. Shen
Keyword(s):  
Stability Analysis ◽  
Nonlinear System ◽  
High Performance ◽  
Initial Conditions ◽  
Wind Disturbance ◽  
External Disturbances ◽  
Nonlinear Simulations ◽  
Linearized System ◽  
Payload Mass ◽  
The Stability

Abstract This paper studies the stability of a system consisting of a drone with a heavy payload through both linear stability analysis and nonlinear simulations. The stability is studied with respect to two payload parameters: the length of the arm the payload is suspended from and the mass of the payload. Linearizing the drone-payload system around vertical flight results in a linearized system that is marginally stable with five negative, real eigenvalues and seven zero-eigenvalues. The presence of seven zero-eigenvalues makes it difficult to predict the stability of the nonlinear system so nonlinear simulations are completed to understand how the drone-payload system reacts to external disturbances. To directly study the severity of the nonlinear system’s instability, the system is subjected to an initial, one-second wind disturbance that induces different initial conditions on the system. The results of the nonlinear simulations indicate that the presence of a suspended payload will always cause the drone-payload system to be unstable. Both an increase in the length of the payload arm and the payload mass will individually increase the deviation of the system from the expected path.

Dynamics and Stability of a Nonlinear Brake Model

2001 ◽  
Author(s):  
Jörg Wauer ◽  
Jürgen Heilig
Keyword(s):  
Stability Analysis ◽  
Lyapunov Exponent ◽  
Nonlinear Model ◽  
Numerical Evaluation ◽  
Critical Speed ◽  
Initial Conditions ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Pad ◽  
The Stability

Abstract The dynamics of a nonlinear car disc brake model is investigated and compared with a simplified linear model. The rotating brake disc is approximated by a rotating ring. The brake pad is modeled as a point mass which is in contact with the rotating ring and visco-elastically suspended in axial and circumferential direction. The stability analysis for the nonlinear model is performed by a numerical evaluation of the top Lyapunov-exponent. Several parameter studies for the nonlinear model are discussed. It is shown that dynamic instabilities of the nonlinear model are estimated at subcritical rotating speeds lower than 10% of the critical speed. Further, the sensitivity of the nonlinear model to the initial conditions and the stiffness ratios is demonstrated.

scholarly journals Three-dimensional modeling and time-delay stability analysis for robotics docking simulation

2019 ◽  
Vol 233 (14) ◽  
pp. 5438-5455
Author(s):  
Prateek Sazawal ◽  
Daniel Choukroun ◽  
Heike Benninghoff ◽  
Eberhard Gill
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Nonlinear System ◽  
Contact Force ◽  
System Model ◽  
Model Parameters ◽  
Force Model ◽  
Hardware In The Loop ◽  
Contact Force Model ◽  
The Stability

Hardware-in-the-loop simulations of two interacting bodies are often accompanied by a time delay. The time delay, however small, may lead to instability in the hardware-in-the-loop system. The present work investigates the source of instability in a two spacecraft system model with a time-delayed contact force feedback. A generic compliance-device-based contact force model is proposed with elastic, viscous, and Coulomb friction effects in three dimensions. A 3D nonlinear system model with time delay is simulated, and the effect of variations in contact force model parameters is studied. The system is then linearized about a nominal state to determine the stability regions in terms of parameters of the spring-dashpot contact force model by the pole placement method. Furthermore, the stability analysis is validated for the nonlinear system by energy observation for both the stable and unstable cases.

scholarly journals Stability study of finite-difference-based lattice Boltzmann schemes with upwind differences of high order approximation

2015 ◽  
pp. 196-204
Author(s):  
Г.В. Кривовичев ◽  
С.А. Михеев
Keyword(s):  
Stability Analysis ◽  
Finite Difference ◽  
Linear Approximation ◽  
Lattice Boltzmann ◽  
Initial Conditions ◽  
Order Approximation ◽  
Stability Study ◽  
High Order Approximation ◽  
Spatial Variables ◽  
The Stability

Исследуется устойчивость трехслойных конечно-разностных решеточных схем Больцмана третьего и четвертого порядков аппроксимации по пространственным переменным. Проводится анализ устойчивости по начальным условиям с использованием линейного приближения. Для исследования используется метод Неймана. Показано, что устойчивость схем можно улучшить за счет аппроксимации конвективных членов во внутренних узлах сеточного шаблона. В этом случае удается получать большие по площади области устойчивости, чем при аппроксимации в граничных узлах шаблона. The stability of three-level finite-difference-based lattice Boltzmann schemes of third and fourth orders of approximation with respect to spatial variables is studied. The stability analysis with respect to initial conditions is performed on the basis of a linear approximation. These studies are based on the Neumann method. It is shown that the stability of the schemes can be improved by the approximation convective terms in internal nodes of the grid stencils in use. In this case the stability domains are larger compared to the case of approximation in boundary nodes.

Symmetry Properties in the Symmetry-Breaking of Nonsmooth Dynamical Systems

2009 ◽  
Vol 5 (1) ◽  
Author(s):  
Alessio Ageno ◽  
Anna Sinopoli
Keyword(s):  
Group Theory ◽  
Stability Analysis ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Simply Supported ◽  
Symmetry Properties ◽  
Existence Conditions ◽  
Asymmetric Responses ◽  
The Stability ◽  
Nonsmooth Dynamical Systems

In this paper, the block simply supported on a harmonically moving ground is assumed as a system well representing a typical nonsmooth dynamical behavior. The aim of the work is to carry out the existence conditions of asymmetric responses; an analysis that comes first in any stability investigation. By using simple definitions belonging to the symmetry group theory, it is possible to completely clarify the relationships between the various initial conditions that allow simple asymmetric responses, and to develop tools, which will be very useful in the stability analysis of more complex asymmetric responses.

scholarly journals Stability of Vertically Traveling, Pre-tensioned, Heavy Cables

2018 ◽  
Vol 13 (8) ◽  
Author(s):  
Abhinav Ravindra Dehadrai ◽  
Ishan Sharma ◽  
Shakti S. Gupta
Keyword(s):  
Stability Analysis ◽  
Governing Equation ◽  
Initial Conditions ◽  
Slenderness Ratio ◽  
Equation Of Motion ◽  
Rate Of Change ◽  
Bending Rigidity ◽  
Stable Regime ◽  
Varying Coefficients ◽  
The Stability

We study the stability of a pre-tensioned, heavy cable traveling vertically against gravity at a constant speed. The cable is modeled as a slender beam incorporating rotary inertia. Gravity modifies the tension along the traveling cable and introduces spatially varying coefficients in the equation of motion, thereby precluding an analytical solution. The onset of instability is determined by employing both the Galerkin method with sine modes and finite element (FE) analysis to compute the eigenvalues associated with the governing equation of motion. A spectral stability analysis is necessary for traveling cables where an energy stability analysis is not comprehensive, because of the presence of gyroscopic terms in the governing equation. Consistency of the solution is checked by direct time integration of the governing equation of motion with specified initial conditions. In the stable regime of operations, the rate of change of total energy of the system is found to oscillate with bounded amplitude indicating that the system, although stable, is nonconservative. A comprehensive stability analysis is carried out in the parameter space of traveling speed, pre-tension, bending rigidity, external damping, and the slenderness ratio of the cable. We conclude that pre-tension, bending rigidity, external damping, and slenderness ratio enhance the stability of the traveling cable while gravity destabilizes the cable.

scholarly journals On the Global Stability Analysis of Corona Virus Disease (COVID-19) Mathematical Model

2021 ◽  
pp. 81-87
Author(s):  
William Atokolo ◽  
Achonu Omale Joseph ◽  
Rose Veronica Paul ◽  
Abdul Sunday ◽  
Thomas Ugbojoide Onoja
Keyword(s):  
Stability Analysis ◽  
Global Stability ◽  
Initial Conditions ◽  
Virus Disease ◽  
Disease Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Stability Analysis ◽  
Corona Virus ◽  
The Stability

In this present work, we investigated the Global Stability Analysis of Corona virus disease model formulated by Atokolo et al in [11]. The COVID‑19 pandemic, also known as the coronavirus pandemic, is an ongoing pandemic that is ravaging the whole world. By constructing a Lyapunov function, we investigated the stability of the model Endemic Equilibrium state to be globally asymptotically stable. This results epidemiologically implies that the COVID-19 will invade the population in respective of the initial conditions (population) considered.

Adaptive fault-tolerant flutter control considering related failure

2021 ◽  
pp. 095441002110180
Author(s):  
Mingzhou Gao
Keyword(s):  
Stability Analysis ◽  
Control Method ◽  
Fault Tolerant ◽  
Fault Tolerant Control ◽  
Control Law ◽  
Cubic Nonlinearity ◽  
External Disturbances ◽  
Lyapunov Stability Analysis ◽  
Simulation Results ◽  
The Stability

This article proposes a novel adaptive fault-tolerant control method for suppressing flutter and compensating for related failure in a flutter system. Considering cubic nonlinearity, external disturbances, and related failure, the flutter dynamic model was established firstly. Then, an adaptive fault-tolerant control law was proposed on basis of this model to compensate for related failure and suppress flutter. By Lyapunov stability analysis, the stability of proposed control law was proved in detail. On the last, simulation results further proved the effectiveness of the control law which can not only suppress flutter and compensate for related failure successfully but also has good robustness for external disturbances and system perturbation.

Control and synchronization for two Chua systems based on intuitionistic fuzzy control scheme: A comparative study

2021 ◽  
pp. 014233122098142
Author(s):  
Mohamed Hamdy ◽  
Mohamed Magdy ◽  
Salah Helmy
Keyword(s):  
Fuzzy Control ◽  
Comparative Study ◽  
Chaotic Systems ◽  
Initial Conditions ◽  
External Disturbances ◽  
Intuitionistic Fuzzy ◽  
Control Scheme ◽  
Simulation Results ◽  
The Stability ◽  
Control And Synchronization

This paper presents control and synchronization for two nonlinear chaotic systems in the presence of uncertainties and external disturbances based on an intuitionistic fuzzy control (IFC) scheme. Two classes of Chua and cubic Chua oscillators have been formulated as master and slave respectively. The master and slave systems have different initial conditions and parameters, which leads to the butterfly effect that rules the chaotic systems’ behaviour. IFC scheme is chosen as a different method that has not been used before to control and synchronize Chua and cubic Chua oscillators. The main objective of the IFC scheme is to collect more information about the system and provide flexibility for the controller that increases the robustness of the control system to uncertainties in the structure of the chaotic systems. The stability analysis of the overall system is guaranteed using Routh-Hurwitz and Lyapunov criteria. The simulation results accomplished to evaluate the effectiveness of the proposed control and to demonstrate its reliability to control Chua’s circuit system with a comparative study.

Asymptotic Stability of the Sphere's Rolling Equilibrium

2021 ◽  
pp. 1-8
Author(s):  
Tuhin Das
Keyword(s):  
Stability Analysis ◽  
Horizontal Plane ◽  
Stable Equilibrium ◽  
Initial Conditions ◽  
Theoretical Development ◽  
Asymptotically Stable ◽  
Inclined Plane ◽  
Pure Rolling ◽  
Simulation Results ◽  
The Stability

Abstract The classical phenomenon of a sphere transitioning from sliding to rolling during its motion on a horizontal plane is investigated from a novel system theoretic perspective. Specifically, the transition is studied as a problem in stabilization, an approach not reported in the literature. The main contribution of this paper is in proving that pure rolling is an asymptotically stable equilibrium within the state-space of a sliding sphere. It is shown that the stabilization of this equilibrium from arbitrary initial conditions occurs through the natural interplay between the friction force and moment that result from sliding. Simulation results confirm the theoretical development. The stability analysis is extended to motion on an inclined plane.

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