Closure to “Discussion of ‘Stability of a Nonlinear Feedback System in the Presence of Gaussian Noise’” (1962, ASME J. Basic Eng., 84, pp. 69–70)

1962 ◽  
Vol 84 (1) ◽  
pp. 70-70
Author(s):  
Rangasami Sridhar ◽  
Rufus Oldenburger
Keyword(s):  
Gaussian Noise ◽  
Feedback System ◽  
Nonlinear Feedback

Stability of a Nonlinear Feedback System in the Presence of Gaussian Noise

1962 ◽  
Vol 84 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Rangasami Sridhar ◽  
Rufus Oldenburger
Keyword(s):  
Gaussian Noise ◽  
Natural Extension ◽  
Feedback System ◽  
Frequency Component ◽  
Analog Computer ◽  
Nonlinear Feedback ◽  
Feedback Systems ◽  
Describing Function ◽  
Power Spectral ◽  
Describing Function Method

A stability criterion for certain types of nonlinear feedback systems in the presence of Gaussian noise is established here. This criterion may be considered as a natural extension of the describing function method. It is assumed that the lowest frequency component in the power spectral density of the noise is at least ten times higher than the highest significant frequency of the system. The method developed here is applicable to feedback systems with just one instantaneous, nonmemory type nonlinearity in the loop. The results mentioned in this paper have been experimentally verified on an analog computer. The theory explained here may be used by the designer to predict the manner in which noise will affect the performance of a system.

scholarly journals A Flexible Nonlinear Feedback System That Captures Diverse Patterns of Adaptation and Rebound

2008 ◽  
Vol 10 (1) ◽  
pp. 70-83 ◽  
Author(s):  
Johan Gabrielsson ◽  
Lambertus A. Peletier
Keyword(s):  
Feedback System ◽  
Nonlinear Feedback

An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity

2017 ◽  
Vol 24 (13) ◽  
pp. 2760-2781
Author(s):  
Xiao-Xiao Liu ◽  
Xing-Min Ren
Keyword(s):  
Nonlinear Control ◽  
Vibration Suppression ◽  
Estimation Method ◽  
Feedback System ◽  
Random Excitation ◽  
Point Estimation ◽  
Maximum Principles ◽  
Moving Mass ◽  
Nonlinear Feedback ◽  
Point Estimation Method

This paper addresses the vibration control of single-span beams subjected to a moving mass by coupling the saturated nonlinear control and an improved point estimation method (IPEM). An optimal nonlinear feedback control law, for a kind of uncertain linear system with actuator nonlinearities, is derived using the combination of Pontryagin's maximum principles and the improved point estimation method. The stability of the feedback system is guaranteed using a Lyapunov function. In order to obtain the instantaneously probabilistic information of output responses, a novel moment approach is presented by combining the improved point estimation method, the maximum entropy methodology and the probability density evolution theory. In addition to the consideration of stochastic system parameters, the external loadings are considered as a nonstationary random excitation and a moving sprung mass, respectively. The proposed strategy is then used to perform vibration suppression analysis and parametric sensitivity analysis of the given beam. From numerical simulation results, it is deduced that the improved point estimation method is a priority approach to the optimal saturated nonlinear control of stochastic beam systems. This observation has widespread applications and prospects in vehicle–bridge interaction and missile–gun systems.

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