Can Describing Function Technique predict Bifurcations in Thermoacoustic Systems?

2010 ◽  
Author(s):  
Priya Subramanian ◽  
Vikrant Gupta ◽  
Bharat Tulsyan ◽  
Raman Sujith
Keyword(s):  
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.

A new direct statistical analysis of nonlinear systems: CAUTDET

2017 ◽  
Vol 233 (1) ◽  
pp. 382-389
Author(s):  
Hong-Xia Li ◽  
Hui-Jie Li ◽  
Yuan-Li Cai
Keyword(s):  
Nonlinear System ◽  
System Analysis ◽  
Covariance Analysis ◽  
Function Technique ◽  
Analysis Method ◽  
Describing Function ◽  
Analysis Problem ◽  
Unscented Transform ◽  
Time Calculation ◽  
System Input

This paper investigates the nonlinear system analysis problem for achieving higher computational efficiency and accuracy. A novel and efficient technique, covariance analysis unscented transform describing function technique (CAUTDET), is proposed. This method combines linear system covariance analysis algorithm with describing function method based on unscented transform. Furthermore, the quasi-linearization of the nonlinear system are derived to approximate the nonlinearity, while there is no requirement of the probability density function of the nonlinear system input and needs only one time calculation. Moreover, the proposed technique can be viewed as a generalization method of the nonlinear system design and analysis. Finally, simulations are presented to illustrate the effectiveness of the presented analysis method.

Stability of a Proportional Valve Control System With Backlash and Saturation

2013 ◽  
Author(s):  
Nader Moustafa ◽  
Roger Fales
Keyword(s):  
Limit Cycle ◽  
Function Analysis ◽  
Linear Part ◽  
Open Loop ◽  
Function Technique ◽  
Main Stage ◽  
Describing Function ◽  
Nonlinear Part ◽  
The Stability ◽  
Limit Cycle Behavior

In this work, the describing function technique is used to study the stability of a nonlinear system. All of dynamic systems in industrial and fluid power systems are nonlinear and include uncertainties to some degree. Thus, unexpected changes in the stability can be exhibited and can lead these systems to become unstable or exhibit oscillatory behavior. Engineers have developed nonlinear mathematical models to be able to predict whether or not a designed system will be exposed to such an oscillation before considering building and implementing the system. The focus of this study is to predict the existence of nonlinear oscillation behavior in a dynamic system using a simplified approach. A nonlinear model validation of a solenoid operated proportional control valve was performed using open loop testes. The type of two-stage hydraulic valve considered in this research is used to control the velocity of hydraulic cylinders. The pilot valve, which is the focus of this research, is a pressure control 3-way valve. A number of 30 replications of this pilot spool valve were studied and tested experimentally along with a single main stage valve. The model consists of linear and nonlinear parts. The linear part of the model was developed by linearizing the nonlinear governing equations at nominal conditions. The nonlinear part was constructed by analyzing open loop experimental test data. The data showed that two major nonlinearities are found that are key to describing the behavior of the system: saturation of the current input and backlash hysteresis behavior. These nonlinearities were considered to be the cause of limit cycle behavior. Each one of these nonlinearities was represented by its describing function and limit cycles were predicted using the describing function analysis method. In using the describing function method, the complexities of working with the nonlinear physics based model to determine limit cycle behavior were avoided.

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