Transient Response of Nonlinear Systems to Stationary Random Excitation

1975 ◽  
Vol 42 (4) ◽  
pp. 891-893 ◽  
Author(s):  
S. R. Soni ◽  
K. Surendran
Keyword(s):  
Nonlinear Systems ◽  
Transient Response ◽  
Perturbation Technique ◽  
Random Excitation ◽  
Second Order ◽  
Mean Square ◽  
Restoring Force ◽  
Random Inputs ◽  
Nonlinear Restoring Force ◽  
Second Order Systems

Transient response of second-order systems with a slightly nonlinear restoring force is analyzed for random inputs using perturbation technique. Mean square responses, up to the second-order of correction, are obtained for white and exponentially decaying correlation functions.

scholarly journals On an extension of the stochastic linearization

1993 ◽  
Vol 15 (4) ◽  
pp. 1-6
Author(s):  
Di Paola Mario ◽  
Nguyen Dong Anh
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Equation ◽  
Random Excitation ◽  
Linearization Method ◽  
Mean Square ◽  
Fundamental Idea ◽  
Stochastic Linearization ◽  
The Mean ◽  
The Difference

Stochastic linearization method is one of the most useful tools for analysis of nonlinear systems under random excitation. The fundamental idea of the classical stochastic linearization consists in replacing the original nonlinear equation by a linear one in such a way that the difference between two equations is minimized in the mean square value. In this paper a new version of the stochastic linearization is proposed. It is shown that for two nonlinear systems considered the new version gives good results for both the weak and strong nonlinearities.

Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation

1970 ◽  
Vol 37 (3) ◽  
pp. 612-616 ◽  
Author(s):  
L. L. Bucciarelli ◽  
C. Kuo
Keyword(s):  
Narrow Band ◽  
Random Excitation ◽  
Second Order ◽  
Envelope Function ◽  
Order System ◽  
Mean Square ◽  
Forcing Function ◽  
Mean Square Response ◽  
Noise Function ◽  
The Mean

The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.

Placing Minimum Phase Zeros to Shape Transient Response: Generalization From Control of Hybrid Power Systems

2017 ◽  
Author(s):  
Bilal S. Salih ◽  
Tuhin K. Das
Keyword(s):  
Power Systems ◽  
Transient Response ◽  
Transfer Functions ◽  
Higher Order ◽  
Second Order ◽  
Step Response ◽  
Minimum Phase ◽  
Hybrid Power Systems ◽  
Hybrid Power ◽  
Second Order Systems

Conservation of energy can be applied in designing control of hybrid power systems to manage power demand and supply. In practice, it can be used for designing decentralized controllers. In this paper, this idea is analyzed in a generalized theoretical framework. The problem is transformed to that of using minimum phase zeros to generate a specific type of transient response admitted by dynamical systems. Here, the transient step response is shaped using an underlying conservation principle. In this paper, emphasis is placed on second order systems. However, the analysis can be extended to higher order transfer functions. Analytical results relating zero location to the matched/ mismatched areas of the transient response are established for a class of second order systems. A combination of feedback and feedforward actions are shown to achieve the desired zero placement/addition and the desired transient response. The proposed analysis promises extension to nonlinear systems. Optimization studies also seem appropriate, especially for higher order transfer functions.

scholarly journals Linearization of randomly excited nonlinear systems by using local mean square error criterion

2000 ◽  
Vol 22 (2) ◽  
pp. 111-123 ◽  
Author(s):  
Luu Xuan Hung
Keyword(s):  
Nonlinear Systems ◽  
Linear Systems ◽  
Mean Square Error ◽  
Random Excitation ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Local Mean ◽  
Non Linear Systems ◽  
Mean Square Error Criterion

The paper presents the analysis of three non-linear systems under random excitation by using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization proposed by Caughey. The obtained results shows that the new technique allows to get much more accurate solutions than .that using Caughey Criterion. The paper leads out some new conclusions which have not been found yet by the previous researches. The new conclusions more clarify the significance of this technique.

scholarly journals On the problem of stability of a motion of essentially nonlinear systems

2021 ◽  
pp. 3-12
Author(s):  
A.A. Martynyuk ◽  
V.O. Chernienko
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Systems Of Equations ◽  
Affine Systems ◽  
The Stability ◽  
Second Order Systems

This article discusses essentially nonlinear systems. Following the approach of applying the pseudolinear inequalitiesdeveloped in a number of works, new estimates for the variation of Lyapunov functions along solutionsof the considered systems of equations are obtained. Based on these estimates, we obtain sufficient conditionsfor the equiboundedness of solutions of second-order systems and sufficient conditions for the stability of anessentially nonlinear system under large initial perturbations. Conditions for the stability of affine systems arealso obtained.

Mean-square composite-rotating consensus of second-order systems with communication noises

2018 ◽  
Vol 27 (7) ◽  
pp. 070504 ◽  
Author(s):  
Li-po Mo ◽  
Shao-yan Guo ◽  
Yong-guang Yu
Keyword(s):  
Second Order ◽  
Mean Square ◽  
Second Order Systems
Sign in / Sign up

Export Citation Format

Share Document