scholarly journals An Approximate Method for Analysis of Stability and Step Response of the Nonlinear Second Order System with a Periodically Time-Varying Restoring-Force Term

1967 ◽  
Vol 3 (4) ◽  
pp. 339-346
Author(s):  
Tsunenori HONDA ◽  
Ryoichi MIURA ◽  
Ryozaburo TAGAWA ◽  
Shoichi KOYAMA
Keyword(s):  
Approximate Method ◽  
Second Order ◽  
Step Response ◽  
Order System ◽  
Time Varying ◽  
Force Term ◽  
Restoring Force ◽  
Analysis Of Stability

scholarly journals Development of FOPDT and SOPDT model from arbitrary process identification data using the properties of orthonormal basis function

2018 ◽  
Vol 7 (2.21) ◽  
pp. 77 ◽  
Author(s):  
Lalu Seban ◽  
Namita Boruah ◽  
Binoy K. Roy
Keyword(s):  
Basis Function ◽  
Delay Time ◽  
Orthonormal Basis ◽  
Control Point ◽  
Second Order ◽  
Step Test ◽  
Step Response ◽  
Order System ◽  
Model Parameters ◽  
First Order

Most of industrial process can be approximately represented as first-order plus delay time (FOPDT) model or second-order plus delay time (FOPDT) model. From a control point of view, it is important to estimate the FOPDT or SOPDT model parameters from arbitrary process input as groomed test like step test is not always feasible. Orthonormal basis function (OBF) are class of model structure having many advantages, and its parameters can be estimated from arbitrary input data. The OBF model filters are functions of poles and hence accuracy of the model depends on the accuracy of the poles. In this paper, a simple and standard particle swarm optimisation technique is first employed to estimate the dominant discrete poles from arbitrary input and corresponding process output. Time constant of first order system or period of oscillation and damping ratio of second order system is calculated from the dominant poles. From the step response of the developed OBF model, time delay and steady state gain are estimated. The parameter accuracy is improved by employing an iterative scheme. Numerical examples are provided to show the accuracy of the proposed method. 

The Step Response: Second-Order System

2018 ◽  
pp. 46-57
Author(s):  
Richard J. Jagacinski ◽  
John M. Flach
Keyword(s):  
Second Order ◽  
Step Response ◽  
Order System

System Identification of a Class of Second-Order Continuous System

2014 ◽  
Vol 651-653 ◽  
pp. 528-533 ◽  
Author(s):  
Zhi Gang Jia ◽  
Xing Xuan Wang
Keyword(s):  
Linear Equations ◽  
Continuous System ◽  
Least Square Method ◽  
Second Order ◽  
Least Square ◽  
Step Response ◽  
Order System ◽  
Simulation Results ◽  
Order Continuous ◽  
Identification Model

An identification method of a class of second-order continuous system is proposed. This method constructs a discrete-time identification model, forms a set of linear equations. The parameters can be obtained by least square method. Simulation results show that the method is effective for a class of second-order system, and is not only for step response but also for square wave signal.

Transient Responses of Second-Order System

2011 ◽  
Vol 55-57 ◽  
pp. 224-228
Author(s):  
Gao Fei Guo ◽  
Shun Xiang Wu ◽  
Da Cao
Keyword(s):  
Damping Ratio ◽  
Time Domain Analysis ◽  
Domain Analysis ◽  
Frequency Domain Analysis ◽  
Second Order ◽  
Step Response ◽  
Order System ◽  
Peak Time ◽  
Root Locus ◽  
The Impact

This paper analyses the transient response of second-order system through time domain analysis, root locus and frequency domain analysis, meanwhile, studies the influence exerted to the system by the second-order system damping ratio and the coefficient ratio as well as the research and damping ratio associated with the relevant parameters, like delay time, rise time, peak time, overshoot, time regulation, basing on the unit step response, and the stability of the system is studied by root locus. Finally, graphics are built through the application of Matlab in order to have an intuitive understanding of the impact on the performance of the system.

Natural Forcing Functions in Nonlinear Systems

1958 ◽  
Vol 25 (3) ◽  
pp. 352-356
Author(s):  
T. J. Harvey
Keyword(s):  
Frequency Response ◽  
Maximum Amplitude ◽  
Second Order ◽  
Point Of View ◽  
Order System ◽  
Nonlinear Frequency ◽  
Restoring Force ◽  
Forcing Function ◽  
Special Cases ◽  
Forcing Functions

Abstract The response of nonlinear, second-order systems is examined from a new point of view which greatly simplifies presentation of the usual frequency-response diagrams. The use of “natural” forcing functions results in a general equation relating the maximum amplitude of the applied force to the maximum amplitude of the restoring force. The relationship is found to be a function of the ratio of the period of free oscillation to the period of the forcing function. The results apply for any second-order system without damping and with a nonlinear (or linear) restoring force. The special cases of a linear system and of Duffing’s equation are considered to illustrate similarities as well as differences between treatment of linear and nonlinear frequency-response problems.

A boundedness theorem for non-linear differential equations of the second order

1951 ◽  
Vol 47 (1) ◽  
pp. 49-54 ◽  
Author(s):  
G. E. H. Reuter
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Damping Factor ◽  
Force Term ◽  
Restoring Force ◽  
Boundedness Theorem ◽  
Linear Differential ◽  
Image Position

1. This paper deals with the differential equation(dots denoting derivatives with respect to t), where for large x the ‘restoring force’ term g(x) has the sign of x and the ‘damping factor’ kf(x) is positive on the average. It will be shown that every solution of (1) ultimately (for sufficiently large t) satisfieswith B independent of k. The conditions on f(x), g(x) and p(t) (stated in §§ 2, 3) are rather milder than those assumed by Cartwright and Littlewood (1, 2) and Newman (3) in proving similar results.

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