On the Application of the Describing Function Technique to the Bifurcation Analysis of Nonlinear Systems

2007 ◽  
Vol 54 (4) ◽  
pp. 343-347 ◽  
Author(s):  
Valentina Lanza ◽  
Michele Bonnin ◽  
Marco Gilli
Keyword(s):  
Nonlinear Systems ◽  
Bifurcation Analysis ◽  
Function Technique ◽  
Describing Function

Vehicle-Follower Longitudinal Control for Automated Transit Vehicles

1977 ◽  
Vol 99 (4) ◽  
pp. 241-248 ◽  
Author(s):  
R. J. Caudill ◽  
W. L. Garrard
Keyword(s):  
Steady State ◽  
Function Technique ◽  
Steady State Response ◽  
Describing Function ◽  
Transient Responses ◽  
Longitudinal Control ◽  
Transit Systems ◽  
State Response ◽  
Acceleration And Deceleration ◽  
And Control

This paper examines the effects of spacing policy and control system nonlinearities on the dynamic response of strings of automated transit vehicles operating under automatic velocity and spacing control. Both steady-state and transient responses are studied. Steady-state response is examined by a modification of the describing function technique and transient response is studied by Liapunov procedures. It is shown that a nonlinearity commonly encountered in automated transit vehicles, a limiter on acceleration and deceleration, can result in string instabilities even though a linearized analysis indicates that the string is stable. Although this paper is specifically focused on automated transit systems, some of the results obtained also appear to be applicable to strings of automobiles on freeways.

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