The Effect of Time Delay on the Stability Control of Trailers

2020 ◽  
Author(s):  
Hanna Zs. Horvath ◽  
Denes Takacs
Keyword(s):  
Time Delay ◽  
Control Algorithm ◽  
Lateral Displacement ◽  
Stability Control ◽  
Vertical Position ◽  
Control Torque ◽  
Yaw Rate ◽  
The Stability ◽  
Yaw Angle ◽  
Theoretical Results

Abstract The instability of the car-trailer systems very often leads to the snaking and/or rocking motions of trailers. In order to reduce the safety risk of these unwanted vibrations, stability control can be applied. In this paper, we use a spatial trailer model to analyze the effect of a possible control algorithm, which actuates by means of braking. For the sake of simplicity, the dynamics of the towing vehicle is modeled by the lateral displacement of the tow hitch that is supported laterally by a spring and damper. The longitudinal speed of the vehicle is kept constant. The effect of the braking forces are emulated in our study via a control torque, which is proportional to the yaw angle and the yaw rate. The time delay of the controller is also considered. Linear stability charts are constructed in the plane of the different system parameters. Linearly stable and unstable parameter domains are identified both for the vertical position of the center of gravity and the control gains. Numerical simulations are used to validate the theoretical results.

scholarly journals Simulation analysis of efficiency and stability for vehicle’s ABS control on combined steering and braking maneuvers

2019 ◽  
Vol 272 ◽  
pp. 01024 ◽  
Author(s):  
Feng YU ◽  
Jun XIE
Keyword(s):  
High Speed ◽  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Simulation Analysis ◽  
Stability Control ◽  
Vehicle Stability ◽  
Slip Ratio ◽  
Braking Performance ◽  
Braking System ◽  
The Stability

Eight degrees of freedom vehicle model was established. Using the method of fuzzy control, the ABS control algorithm was designed based on slip ratio. Simulation analysis was done at speed of 15m/s, 20m/s, 25m/s under turning braking. The results show that the vehicle braking performance and vehicle stability at middle or low speed was improved by using the ABS controller, but qualitative analysis shows that phenomenon of vehicle instability was appeared at high-speed conditions. The turning braking stability under ABS controller was judged quantificationally by the stability judging formula. The results show that the requirements of stability control could not meet with only Anti-lock Braking System.

scholarly journals EFFECT OF TIME DELAY ON SPATIAL PATTERNS IN A AIRAL INFECTION MODEL WITH DIFFUSION

2016 ◽  
Vol 21 (2) ◽  
pp. 143-158
Author(s):  
Jia Liu ◽  
Qunying Zhang ◽  
Canrong Tian
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Viral Infection ◽  
Spatial Patterns ◽  
Infection Model ◽  
The Stability ◽  
Manifold Theory ◽  
Viral Infection Model ◽  
Theoretical Results

This paper is concerned with the dynamics of a viral infection model with diffusion under the assumption that the immune response is retarded. A time delay is incorporated into the model described the delayed immune response after viral infection. Based upon a stability analysis, we demonstrate that the appearance, or the absence, of spatial patterns is determined by the delay under some conditions. Moreover, the spatial patterns occurs as a consequence of Hopf bifurcation. By applying the normal form and the center manifold theory, the direction as well as the stability of the Hopf bifurcation is explored. In addition, a series of numerical simulations are performed to illustrate our theoretical results.

Lyapunov Optimal Feedback Control of a Nonlinear Inverted Pendulum

1989 ◽  
Vol 111 (4) ◽  
pp. 554-558 ◽  
Author(s):  
M. J. Anderson ◽  
W. J. Grantham
Keyword(s):  
Feedback Control ◽  
Control Algorithm ◽  
Inverted Pendulum ◽  
Optimal Feedback Control ◽  
Vertical Position ◽  
Control Torque ◽  
Potential Wells ◽  
Optimal Feedback ◽  
Almost All ◽  
Nonlinear Gravity

Lyapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which “rocks” the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Lyapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.

scholarly journals Analysis of a Delayed Internet Worm Propagation Model with Impulsive Quarantine Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Yu Yao ◽  
Xiaodong Feng ◽  
Wei Yang ◽  
Wenlong Xiang ◽  
Fuxiang Gao
Keyword(s):  
Time Delay ◽  
Propagation Model ◽  
The Novel ◽  
Worm Propagation ◽  
Internet Worm ◽  
Internet Worms ◽  
The Stability ◽  
And Control ◽  
Theoretical Results ◽  
Significant Attention

Internet worms exploiting zero-day vulnerabilities have drawn significant attention owing to their enormous threats to Internet in the real world. To begin with, a worm propagation model with time delay in vaccination is formulated. Through theoretical analysis, it is proved that the worm propagation system is stable when the time delay is less than the thresholdτ0and Hopf bifurcation appears when time delay is equal to or greater thanτ0. Then, a worm propagation model with constant quarantine strategy is proposed. Through quantitative analysis, it is found that constant quarantine strategy has some inhibition effect but does not eliminate bifurcation. Considering all the above, we put forward impulsive quarantine strategy to eliminate worms. Theoretical results imply that the novel proposed strategy can eliminate bifurcation and control the stability of worm propagation. Finally, simulation results match numerical experiments well, which fully supports our analysis.

Technology Research Vehicle Braking Stability Control

2014 ◽  
Vol 602-605 ◽  
pp. 1219-1222
Author(s):  
Ya Rong Liu
Keyword(s):  
Vehicle Dynamics ◽  
Fuzzy Controller ◽  
Control Variable ◽  
Stability Control ◽  
Technology Research ◽  
Dynamics Model ◽  
Sideslip Angle ◽  
Yaw Rate ◽  
The Stability ◽  
And Control

In this paper, the stability of the car when braking, the establishment of a complete vehicle dynamics model to analyze the main causes and influencing factors of automobile brake instability. Select the vehicle yaw rate and sideslip angle as the control variable, meaning the use of certain applications of fuzzy control theory, the ESP fuzzy controller, and control strategy simulation with.

Bifurcation Analysis in a Lotka-Volterra Model with Delay

2012 ◽  
Vol 594-597 ◽  
pp. 2693-2696
Author(s):  
Chang Jin Xu
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Volterra Model ◽  
The Stability ◽  
Theoretical Results

In this paper, a Lotka-Volterra model with time delay is considered. The stability of the equilibrium of the model is investigated and the existence of Hopf bifurcation is proved. Numerical simulations are performed to justify the theoretical results. Finally, main conclusions are included.

scholarly journals Hopf Bifurcation of an Improved SLBS Model under the Influence of Latent Period

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Chunming Zhang ◽  
Wanping Liu ◽  
Jing Xiao ◽  
Yun Zhao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Center Manifold ◽  
Center Manifold Theorem ◽  
Local Hopf Bifurcation ◽  
Dynamical Behaviors ◽  
Latent Time ◽  
Normal Form Method ◽  
The Stability ◽  
Theoretical Results

A model applicable to describe the propagation of computer virus is developed and studied, along with the latent time incorporated. We regard time delay as a bifurcating parameter to study the dynamical behaviors including local asymptotical stability and local Hopf bifurcation. By analyzing the associated characteristic equation, Hopf bifurcation occurs when the time delay passes through a sequence of critical values. A formula for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions is given by using the normal form method and center manifold theorem. Finally, illustrative examples are given to support the theoretical results.

scholarly journals Bifurcation dynamics in a fractional-order oregonator model including time delay

2021 ◽  
Vol 87 (2) ◽  
pp. 397-414
Author(s):  
Changjin Xu ◽  
◽  
Wei Zhang ◽  
Chaouki Aouiti ◽  
Zixin Liu ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Mathematical Models ◽  
Fractional Order ◽  
Vital Role ◽  
Chemical Models ◽  
Set Up ◽  
The Stability ◽  
Oregonator Model ◽  
Theoretical Results

Setting up mathematical models to describe the interaction of chemical variables has been a hot issue in chemical and mathematical areas. Nevertheless, many mathematical models are only involved with the integer-order differential equation case. The fruits on fractional-order chemical models are very scarce. In this present work, on the basis of the previous studies, we set up a novel fractional-order delayed Oregonator model. Selecting the time delay as bifurcation parameter, we obtain novel delay-independent bifurcation conditions that guarantee the stability and the appearance of Hopf bifurcation for the fractional-order delayed Oregonator model. The study shows that time delay plays a vital role in controlling the stability and the appearance of Hopf bifurcation of the considered fractional-order delayed Oregonator model. In order to verify the rationality of theoretical results, computer simulations are carried out.

scholarly journals Stability control of a novel multidimensional fractional-order financial system with time‐delay via impulse control

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhe Zhang ◽  
Jing Zhang ◽  
Fan Yong Cheng ◽  
Feng Liu ◽  
Can Ding
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Impulse Control ◽  
Impulsive Control ◽  
Financial System ◽  
Stability Control ◽  
Two Dimensions ◽  
State Variable ◽  
The Stability ◽  
System With Time Delay

AbstractThis paper is concerned about the impulsive control of a class of novel nonlinear fractional-order financial system with time-delay. Considering the variation of every states in the fractional-order financial system in the real world has certain delay for various reasons, thus we add corresponding delay on every state variable. Different from the traditional method of stability judgment, we choose two dimensions of time and space to analyze, which makes the process more accurate. In addition, the sufficient condition of the stability criterion for the fractional-order financial system based on impulsive control is derived. Moreover, the impulsive control can not only make the fractional-order financial system stable in different time delay but also in the different fractional operator. Consequently, the impulsive control has generality, universality and strong applicability. In the end, some numerical simulation examples are provided to verify the effectiveness and the benefit of the proposed method.

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