scholarly journals Stability Analysis of a Predecessor-Following Platoon of Vehicles With Two Time Delays

2015 ◽  
Vol 27 (1) ◽  
pp. 35-46 ◽  
Author(s):  
Ali Ghasemi ◽  
Saeed Rouhi
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Disturbance Attenuation ◽  
One Dimension ◽  
String Stability ◽  
Characteristic Roots ◽  
Vehicle Platoon ◽  
Velocity Information ◽  
The Stability ◽  
Lead Vehicle

The problem of controlling a platoon of vehicles moving in one dimension is considered so that they all follow a lead vehicle with constant spacing between successive vehicles. The stability and the string stability of a platoon of vehicles with two independent and uncertain delays, one in the inter-vehicle distance and the other in the relative velocity information channels, are considered. The main objectives of this paper are: (1) using a simplifying factorization procedure and deploying the cluster treatment of characteristic roots (CTCR) paradigm to obtain exact stability boundaries in the domain of the delays, and (2) for the purpose of disturbance attenuation, the string stability analysis is examined. Finally, a simulation example of multiple vehicle platoon control is used to demonstrate the effectiveness of the proposed method.

Stability analysis of bidirectional adaptive cruise control with asymmetric information flow

2014 ◽  
Vol 229 (2) ◽  
pp. 216-226 ◽  
Author(s):  
Ali Ghasemi ◽  
Reza Kazemi ◽  
Shahram Azadi
Keyword(s):  
Stability Analysis ◽  
Adaptive Cruise Control ◽  
Disturbance Attenuation ◽  
Time Lags ◽  
Cruise Control ◽  
String Stability ◽  
Control Laws ◽  
Vehicle Platoon ◽  
Negative Effect ◽  
The Stability

Stability and the string stability of a platoon of adaptive cruise control (ACC) vehicles using a constant spacing are investigated. Due to realistic design and execution, negative effect of tracking lag parameter on the stability is examined. An efficient analytical approach is presented in order to obtain a sufficient stability condition in the domain of the control parameters. The stability criterion is examined using a partial differential equation (PDE) approximation using large number of vehicles subjected to the time lags in vehicle dynamics and heterogeneity in the control laws, which allows asymmetry in the use of front and back information. The string stability analysis is performed to evaluate the disturbance attenuation. Finally, an example of multiple vehicle platoon control is presented, which demonstrates the effectiveness and the robustness of the proposed method.

scholarly journals Directional Control of a Platoon of Vehicles for Comfort Specification by Considering Parasitic Time Delays and Lags

2013 ◽  
Vol 25 (5) ◽  
pp. 413-420
Author(s):  
Ali Ghasemi
Keyword(s):  
Time Delays ◽  
One Dimension ◽  
Control Parameters ◽  
String Stability ◽  
Physical Systems ◽  
Directional Control ◽  
Practical Design ◽  
Negative Effect ◽  
Dynamic Variables ◽  
Lead Vehicle

The problem of controlling a string of vehicles moving in one dimension is considered so that they all follow a lead vehicle with a constant spacing between successive vehicles. This paper is concerned by considering both effect of the parasitic time delays and lags and comfort specification. The Contribution of this paper is two-fold. Firstly, most physical systems often involve parasitic time delays and lags. Due to practical design and implementation, the negative effect of the parasitic time delays and lags on the string stability be taken into account Secondly, the aim here, however, is specifically to consider the restrictions which need to be imposed on the control parameters, in order to be well-suited with bounds on the dynamic variables as well as the requirement for string stability. At the end the robustness against the noise in the measurement signals factors are studied.

Stability of a Consensus Protocol for Second Order Agents With Multiple Time Delays

2011 ◽  
Author(s):  
Rudy Cepeda-Gomez ◽  
Nejat Olgac
Keyword(s):  
Information Exchange ◽  
Time Delays ◽  
Second Order ◽  
Multiple Time ◽  
State Transformation ◽  
Consensus Protocol ◽  
Position Information ◽  
Characteristic Roots ◽  
Velocity Information ◽  
The Stability

In this study we consider the consensus problem for a group of second order agents interacting under a fixed, undirected communication topology. Communication lines are affected by two rationally independent delays. The first delay is assumed to be in the position information channels whereas the second one is in the velocity information exchange. The delays are assumed to be uniform throughout the entire network. We first reduce the complexity of the problem, by performing a state transformation that allows the decomposition of the characteristic equation of the system into a set of second order factors. The stability of the resulting subsystems is analyzed exactly and exhaustively in the domain of the time delays using the Cluster Treatment of Characteristic Roots (CTCR) paradigm. CTCR is a recent method which declares the stability features of the system for any composition of the time delays. Example cases are provided to verify the analytical conclusions.

Preserving Stability Under Communication Delays in Multi Agent Systems

2013 ◽  
Author(s):  
Hossein Rastgoftar ◽  
Suhada Jayasuriya
Keyword(s):  
Time Delays ◽  
Communication Delays ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Continuum Approach ◽  
Position Information ◽  
Characteristic Roots ◽  
Multi Agent ◽  
Velocity Information ◽  
The Stability

The effect of time delays on the stability of a recently proposed continuum approach for controlling a multi agent system (MAS) evolving in n-D under a special local inter-agent communication protocol is considered. There a homogenous map determined by n+1 leaders is learned by the follower agents each communicating with n+1 adjacent agents. In this work both position and velocity information of adjacent agents are used for local control of follower agents whereas in previous work [1, 2] only position information of adjacent agents was used. Stability of the proposed method under a time delay h is studied using the cluster treatment of characteristic roots (CTCR) [3]. It is shown that the stability of MAS evolution can be preserved when (i) the velocity of any follower agent is updated using both position and velocity of its adjacent agents at time (t-h); and (ii) the communication matrix has real eigenvalues. In addition, it is shown that when there is no communication delay, deviations from a selected homogenous map during transients may be minimized by updating only the position of a follower using both position and velocity of its adjacent agents.

Kernel and Offspring Concepts for the Stability Robustness of Multiple Time Delayed Systems (MTDS)

2006 ◽  
Vol 129 (3) ◽  
pp. 245-251 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
Characteristic Root ◽  
Invariance Property ◽  
Multiple Time ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Robustness ◽  
The Stability

A novel treatment for the stability of linear time invariant (LTI) systems with rationally independent multiple time delays is presented in this paper. The independence of delays makes the problem much more challenging compared to systems with commensurate time delays (where the delays have rational relations). We uncover some wonderful features for such systems. For instance, all the imaginary characteristic roots of these systems can be found exhaustively along a set of surfaces in the domain of the delays. They are called the “kernel” surfaces (curves for two-delay cases), and it is proven that the number of the kernel surfaces is manageably small and bounded. All possible time delay combinations, which yield an imaginary characteristic root, lie either on this kernel or its infinitely many “offspring” surfaces. Another hidden feature is that the root tendencies along these surfaces exhibit an invariance property. From these outstanding characteristics an efficient, exact, and exhaustive methodology results for the stability assessment. As an added uniqueness of this method, the systems under consideration do not have to be stable for zero delays. Several example case studies are presented, which are prohibitively difficult, if not impossible to solve using any other peer methodology known to the authors.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

Chatter in Turning Process Incorporating the Effect of Ploughing Force

1999 ◽  
Author(s):  
Z. C. Wang ◽  
W. L. Cleghorn ◽  
S. D. Yu
Keyword(s):  
Stability Analysis ◽  
Cutting Force ◽  
Force Model ◽  
Turning Process ◽  
Cutting Force Model ◽  
Stability Curve ◽  
Characteristic Roots ◽  
The Laplace Transform ◽  
Machining System ◽  
The Stability

Abstract In this paper, the stability analysis of turning process is performed based on a new cutting force model which includes the effect of ploughing force. This approach utilized the Laplace transform to identify the characteristic roots of the examined machining system. The stability of the machining system can then be determined by examining the locations of the characteristic roots. The stability curve for a specific turning process can then be plotted. The effect of different cutting force models on the stability is also investigated. The results clearly demonstrate some chatter phenomena observed by other researchers.

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