Steady-state analysis of piecewise-linear dynamic systems

1981 ◽  
Vol 28 (3) ◽  
pp. 234-242 ◽  
Author(s):  
I. Hajj ◽  
S. Skelboe
Keyword(s):  
Steady State ◽  
Dynamic Systems ◽  
Piecewise Linear ◽  
Steady State Analysis ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
State Analysis

scholarly journals STEADY-STATE ANALYSIS OF NONLINEARLY COUPLED CHUA'S CIRCUITS WITH PERIODIC INPUT

2003 ◽  
Vol 13 (11) ◽  
pp. 3395-3407 ◽  
Author(s):  
F. A. SAVACI ◽  
M. E. YALÇIN ◽  
C. GÜZELIŞ
Keyword(s):  
Steady State ◽  
Time Domain ◽  
Transfer Functions ◽  
Piecewise Linear ◽  
Time Domain Analysis ◽  
Steady State Analysis ◽  
Linear Dynamic Systems ◽  
Periodic Input ◽  
The Time Domain ◽  
State Analysis

In this paper, nonlinearly coupled identical Chua's circuits, when driven by sinusoidal signal have been analyzed in the time-domain by using the steady-state analysis techniques of piecewise-linear dynamic systems. With such techniques, it has become possible to obtain analytical expressions for the transfer functions in terms of the circuit parameters. The proposed system under consideration has also been studied by analog simulations of the overall system on a hardware realization using off-the-shelf components as well as by a time-domain analysis of the synchronization error.

Chebyshev Expansion of Linear and Piecewise Linear Dynamic Systems With Time Delay and Periodic Coefficients Under Control Excitations

2003 ◽  
Vol 125 (2) ◽  
pp. 236-243 ◽  
Author(s):  
Haitao Ma ◽  
Eric A. Butcher ◽  
Ed Bueler
Keyword(s):  
Time Delay ◽  
Fundamental Solution ◽  
Dynamic Systems ◽  
Floquet Theory ◽  
Piecewise Linear ◽  
Delay Period ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Fundamental Solution Matrix ◽  
Solution Matrix

In this paper, a new efficient method is proposed to obtain the transient response of linear or piecewise linear dynamic systems with time delay and periodic coefficients under arbitrary control excitations via Chebyshev polynomial expansion. Since the time domain can be divided into intervals with length equal to the delay period, at each such interval the fundamental solution matrix for the corresponding periodic ordinary differential equation (without delay) is constructed in terms of shifted Chebyshev polynomials by using a previous technique that reduces the problem to a set of linear algebraic equations. By employing a convolution integral formula, the solution for each interval can be directly obtained in terms of the fundamental solution matrix. In addition, by combining the properties of the periodic system and Floquet theory, the computational processes are simplified and become very efficient. An alternate version, which does not employ Floquet theory, is also presented. Several examples of time-periodic delay systems, when the excitation period is equal to or larger than the delay period and for linear and piecewise linear systems, are studied. The numerical results obtained via this method are compared with those obtained from Matlab DDE23 software (Shampine, L. F., and Thompson, S., 2001, “Solving DDEs in MATLAB,” Appl. Numer. Math., 37(4), pp. 441–458.) An error bound analysis is also included. It is found that this method efficiently provides accurate results that find general application in areas such as machine tool vibrations and parametric control of robotic systems.

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