Relationship between the Steady-Handling Characteristics of Automobiles and Their Stability

1973 ◽  
Vol 15 (5) ◽  
pp. 326-328 ◽  
Author(s):  
R. S. Sharp
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Degree Of Freedom ◽  
Nonlinear Region ◽  
Handling Characteristics ◽  
Yield Information ◽  
Turning Motion ◽  
The Stability ◽  
Three Degree Of Freedom

Analyses of the steady-state handling behaviour of an automobile and the stability of its steady-turning motion, based on a three degree of freedom mathematical model, are used to show that the steady behaviour and the stability are related similarly in the nonlinear region as in the well documented linear one. It is concluded that analysis and measurement of the steady behaviour will yield information on the stability of automobiles.

Multivariable Control Design for a Bilateral Telemanipulator

2003 ◽  
Author(s):  
Kevin B. Fite ◽  
Michael Goldfarb
Keyword(s):  
Impedance Control ◽  
Singular Values ◽  
Degree Of Freedom ◽  
Stability Robustness ◽  
Remote Environment ◽  
And Performance ◽  
The Stability ◽  
Three Degree Of Freedom ◽  
And Control ◽  
Control Methodology

This paper presents an architecture and control methodology for a multi-degree-of-freedom teleoperator system. The approach incorporates impedance control of the telemanipulator pair and formulates the system as a single feedback loop encompassing the human operator, telemanipulator, and remote environment. In so doing, multivariable Nyquist-like techniques are used to design compensation for enhanced stability robustness and performance. A measure of the transparency exhibited by the multivariable teleoperator system is attained using matrix singular values. The approach is experimentally demonstrated on a three degree-of-freedom scaled telemanipulator pair with a highly coupled environment. Using direct measurement of the power delivered to the operator to assess the system’s stability robustness, along with the proposed measure of multivariable transparency, the loop-shaping compensation is shown to improve the stability robustness by a factor of almost two and the transparency by more than a factor of five.

QUALITATIVE ANALYSIS OF A MATHEMATICAL MODEL FOR CAPILLARY FORMATION IN TUMOR ANGIOGENESIS

2003 ◽  
Vol 13 (01) ◽  
pp. 19-33 ◽  
Author(s):  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Qualitative Analysis ◽  
Transition Probability ◽  
Steady State Solution ◽  
State Solution ◽  
Transition Probability Density ◽  
Capillary Formation ◽  
Long Time ◽  
The Stability

Qualitative analysis of a mathematical model for capillary formation is presented under assumptions that enzyme and fibronectin concentrations are in quasi-steady state. The aim of this paper is to prove mathematically that the long-time tendency of endothelial cells will be towards the transition probability density function of enzyme and fibronectin. Endothelial cell steady-state solution is obtained and a numerical simulation is provided to show that there is a close agreement between the steady-state solution obtained analytically and the numerically calculated steady-state of the related initial value problem, which provides strong evidence for the stability of this steady-state.

A Stability Analysis of the Wheel Shimmy

2012 ◽  
Author(s):  
Giandomenico Di Massa ◽  
Stefano Pagano ◽  
Salvatore Strano ◽  
Mario Terzo
Keyword(s):  
Stability Analysis ◽  
Degree Of Freedom ◽  
Experimental Investigations ◽  
Classical Stability ◽  
Low Degree ◽  
Oscillation Modes ◽  
Non Linear ◽  
The Stability ◽  
Three Degree Of Freedom ◽  
Wheel Shimmy

The wheel shimmy is a classical non-linear problem. The most frequently used approach to study this phenomena is based on linearized low degree of freedom models, that from one side, thanks the simplicity of the equations of the motion, allows to evaluate the stability with classical stability-analysis approach, but from the other side it limits the study about the equilibrium point. In this paper a stability-analysis, based on a three degree of freedom non-linear analytical model, is presented. Starting from the system numerical response, adopting a time-domain modal analysis method, the modal parameters were identified. The proposed procedure, through a 3 degree of freedom nonlinear representation of the castor, highlights the three main castor oscillation modes whose characteristics can then be identified with a method applicable even for experimental investigations.

The Steady-State Response of a Two-Degree-of-Freedom Bilinear Hysteretic System

1965 ◽  
Vol 32 (1) ◽  
pp. 151-156 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Degree Of Freedom ◽  
Finite Limit ◽  
Steady State Response ◽  
Varying Parameters ◽  
Hysteretic System ◽  
State Response ◽  
The Stability ◽  
Two Degree Of Freedom

The method of slowly varying parameters is used to obtain an approximate solution for the steady-state response of a two-degree-of-freedom bilinear hysteretic system. The stability of the system is investigated and it is shown that such a system exhibits unbounded amplitude resonance when the level of excitation is increased beyond a certain finite limit.

DISC BRAKE SQUEAL ANALYSIS USING NONLINEAR MATHEMATICAL MODEL

2021 ◽  
Vol 263 (2) ◽  
pp. 4773-4778
Author(s):  
Akif Yavuz ◽  
Osman Taha Sen
Keyword(s):  
Mathematical Model ◽  
Sliding Friction ◽  
Nonlinear Behavior ◽  
Friction Model ◽  
Degree Of Freedom ◽  
Computational Techniques ◽  
Brake Disc ◽  
Disc Brake ◽  
Brake Squeal ◽  
The Stability

Many academics have examined the disc brake squeal problem with experimental, analytical, and computational techniques, but there is as yet no method to completely understand disc brake squeal. This problem is not fully understood because a nonlinear problem. A mathematical model was created to understand the relationship between brake disc and pad thought to cause the squeal phenomenon. For this study, two degree of freedom model is adopted where the disc and the pad are modeled. The model represents pad and disc as single degree of freedom systems that are connected together through a sliding friction interface. This friction interface is defined by the dynamic friction model. Using this model, linear and nonlinear analyzes were performed. The stability of the system under varying parameters was examined with the linear analysis. Nonlinear analysis was performed to provide more detailed information about the nonlinear behavior of the system. This analysis can provide information on the size of a limit cycle in phase space and hence whether a particular instability is a problem. The results indicate that with the decrease in the ratio of disc to pad stiffness and disc to pad mass, the system is more unstable and squeal noise may occur.

The Steady-State Response of the Double Bilinear Hysteretic Model

1965 ◽  
Vol 32 (4) ◽  
pp. 921-925 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Steady State Solution ◽  
Degree Of Freedom ◽  
State Solution ◽  
Steady State Response ◽  
Hysteretic Model ◽  
Jump Phenomenon ◽  
State Response ◽  
The Stability

The steady-state response of a one-degree-of-freedom double bilinear hysteretic model is investigated and it is shown that this model gives rise to the jump phenomenon which is associated with certain nonlinear systems. The stability of the steady-state solution is discussed and it is shown that the model predicts an unbounded resonance for finite excitation.

scholarly journals A Mathematical Model for the Eradication of Anopheles Mosquito and Elimination of Malaria

2020 ◽  
pp. 1-14
Author(s):  
Atanyi Yusuf Emmanuel ◽  
Abam Ayeni Omini
Keyword(s):  
Mathematical Model ◽  
Life Cycle ◽  
Steady State ◽  
Stability Analysis ◽  
Equilibrium State ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Anopheles Mosquito ◽  
Model Parameters ◽  
The Stability

A mathematical model to eliminate malaria by breaking the life cycle of anopheles mosquito using copepods at larva stage and tadpoles at pupa stage was derived aimed at eradicating anopheles pupa mosquito by introduction of natural enemies “copepods and tadpoles” (an organism that eats up mosquito at larva and pupa stage respectively). The model equations were derived using the model parameters and variables. The stability analysis of the free equilibrium states was analyzed using equilibrium points of Beltrami and Diekmann’s conditions for stability analysis of steady state. We observed that the model free equilibrium state is stable which implies that the equilibrium point or steady state is stable and the stability of the model means, there will not be anopheles adult mosquito in our society for malaria transmission. The ideas of Beltrami’s and Diekmann conditions revealed that the determinant and trace of the Jacobian matrix were greater than zero and less than zero respectively implying that the model disease free equilibrium state is stable. Hence, the number of larva that transforms to pupa is almost zero while the pupa that develop to adult is zero meaning the life-cycle is broken at the larva and pupa stages with the introduction of natural enemy. Maple was used for the symbolic and numerical solutions.

Stability Analysis of a Bilateral Teleoperating System

1993 ◽  
Vol 115 (3) ◽  
pp. 419-426 ◽  
Author(s):  
Y. Strassberg ◽  
A. A. Goldenberg ◽  
J. K. Mills
Keyword(s):  
Feedback Linearization ◽  
Closed Loop ◽  
Tracking Error ◽  
Degree Of Freedom ◽  
Closed Loop System ◽  
Control Scheme ◽  
Feedback Linearization Control ◽  
Small Gain ◽  
The Stability ◽  
Three Degree Of Freedom

In this paper the stability of a control scheme for bilateral master-slave teleoperation is investigated. Given the nominal models of the master and slave dynamics, and using an approximate feedback linearization control, based on the earlier work of Spong and Vidyasagar, 1987, a robust closed-loop system (position and force) can be obtained with a multiloop version of the small gain theorem. It is shown that stable bilateral teleoperating systems can be achieved under the assumption that the deviation of the models from the actual systems satisfies certain norm inequalities. We also show that, using the proposed scheme, the tracking error (position/velocity and force/torque) is bounded and it can be made arbitrarily small. The control scheme is illustrated using the simulation of a three-degree-of-freedom master-slave teleoperator (three-degree-of-freedom master and three-degree-of-freedom slave).

Analysis on steady-state vibration induced by backlash in machine tool rotary table

2016 ◽  
Vol 231 (22) ◽  
pp. 4163-4171 ◽  
Author(s):  
Xiao Yang ◽  
Dun Lu ◽  
Jun Zhang ◽  
Wanhua Zhao
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Machine Tool ◽  
Mechanical System ◽  
Dynamic Behavior ◽  
Critical Region ◽  
Stability Region ◽  
Rotary Table ◽  
Motion Controller ◽  
The Stability

This paper presents a mathematical model of a machine tool rotary table with backlash to describe the dynamic behavior of the mechanical system and the motion controller. The accuracy of this model is verified by experiments. The steady-state vibration under different conditions is simulated to investigate its mechanism and change rule. The results show that the steady-state vibration is attributed to the alternate impact of transmission components. Based on the different performances of the steady-state vibration for different control gains and different motion directions, the concept of stability region in the plane of control gains is presented. In the critical region, the steady-state vibration only occurs when the table moves toward backlash. The complex contact regimes may lead to a significant increase in the amplitude of the steady-state vibration. Besides, the influences of the load and the magnitude of backlash on the steady-state vibration and the stability region are also discussed.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

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