Stabilization of time-varying linear system using ZD and ZG methods respectively with pseudo division-by-Zero phenomenon shown

2017 ◽  
Author(s):  
Yunong Zhang ◽  
Jinjin Guo ◽  
Binbin Qiu ◽  
Jian Li ◽  
Zhi Yang
Keyword(s):  
Linear System ◽  
Time Varying

The Application of the Ritz Averaging Method to Determining the Response of Systems with Time Varying Stiffness to Harmonic Excitation

1980 ◽  
Vol 102 (2) ◽  
pp. 384-390 ◽  
Author(s):  
M. Benton ◽  
A. Seireg
Keyword(s):  
Linear System ◽  
Averaging Method ◽  
Approximate Solutions ◽  
Harmonic Excitation ◽  
Time Varying ◽  
Parametric Vibrations ◽  
Nonlinear Characteristics ◽  
Closed Form Solutions ◽  
Mathieu’S Equation ◽  
Stiffness Variation

Parametric vibrations occur in many mechanical systems such as gears where the stiffness variation and external excitations generally occur at integer multiples of the rotational speed. This paper describes a procedure based on the Ritz Averaging Method for developing closed form solutions for the response of such systems to harmonic excitations. Although the method is illustrated in the paper by the case of a linear system with harmonic stiffness fluctuation (defined by Mathieu’s equation) it can be readily applied to determine approximate solutions for systems with nonlinear characteristics and any periodic variations of parameters.

scholarly journals State Estimation with Reduced-Order Observer and Adaptive-LQR Control of Time Varying Linear System

2020 ◽  
Vol 26 (2) ◽  
pp. 24-31
Author(s):  
Omer Aydogdu ◽  
Mehmet Latif Levent
Keyword(s):  
Optimal Control ◽  
Linear System ◽  
State Estimation ◽  
Servo System ◽  
Variable Load ◽  
Time Varying ◽  
Load Effect ◽  
Reduced Order ◽  
Lqr Control ◽  
Reduced Order Observer

In this study, a new controller design was created to increase the control performance of a variable loaded time varying linear system. For this purpose, a state estimation with reduced order observer and adaptive-LQR (Linear–Quadratic Regulator) control structure was offered. Initially, to estimate the states of the system, a reduced-order observer was designed and used with LQR control method that is one of the optimal control techniques in the servo system with initial load. Subsequently, a Lyapunov-based adaptation mechanism was added to the LQR control to provide optimal control for varying loads as a new approach in design. Thus, it was aimed to eliminate the variable load effects and to increase the stability of the system. In order to demonstrate the effectiveness of the proposed method, a variable loaded rotary servo system was modelled as a time-varying linear system and used in simulations in Matlab-Simulink environment. Based on the simulation results and performance measurements, it was observed that the proposed method increases the system performance and stability by minimizing variable load effect.

Uniform global asymptotic stability for half-linear differential systems with time-varying coefficients

2011 ◽  
Vol 141 (5) ◽  
pp. 1083-1101 ◽  
Author(s):  
Masakazu Onitsuka ◽  
Jitsuro Sugie
Keyword(s):  
Linear System ◽  
Zero Solution ◽  
Integrable Case ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Varying Coefficients ◽  
Linear Differential Systems ◽  
Time Varying Coefficients ◽  
Linear Differential ◽  
Image Position

The present paper deals with the following system:where p and p* are positive numbers satisfying 1/p + 1/p* = 1, and ϕq(z) = |z|q−2z for q = p or q = p*. This system is referred to as a half-linear system. We herein establish conditions on time-varying coefficients e(t), f(t), g(t) and h(t) for the zero solution to be uniformly globally asymptotically stable. If (e(t), f(t)) ≡ (h(t), g(t)), then the half-linear system is integrable. We consider two cases: the integrable case (e(t), f(t)) ≡ (h(t), g(t)) and the non-integrable case (e(t), f(t)) ≢ (h(t), g(t)). Finally, some simple examples are presented to illustrate our results.

scholarly journals On the number of upper Bohl exponents for diagonal discrete time-varying linear system

2015 ◽  
Vol 429 (1) ◽  
pp. 337-353 ◽  
Author(s):  
Artur Babiarz ◽  
Adam Czornik ◽  
Michał Niezabitowski
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Time Varying

Asymptotic trends in time-varying oscillatory period for a dual-staged torsional system

2016 ◽  
Vol 231 (22) ◽  
pp. 4126-4138
Author(s):  
Michael D Krak ◽  
Rajendra Singh
Keyword(s):  
Linear System ◽  
Mechanical System ◽  
Time Domain ◽  
Effective Stiffness ◽  
Step Response ◽  
Analysis Tool ◽  
Time Varying ◽  
Non Linear ◽  
Non Linear System ◽  
Oscillatory Period

The primary goal of this article is to propose a new analysis tool that estimates the asymptotic trends in the time-varying oscillatory period of a non-linear mechanical system. The scope is limited to the step-response of a torsional oscillator containing a dry friction element and dual-staged spring. Prior work on the stochastic linearization techniques is extended and modified for application in time domain. Subsequently, an instantaneous expected value operator and the concept of instantaneous effective stiffness are proposed. The non-linear system is approximated at some instant during the step-response by a linear time-invariant mechanical system that utilizes the instantaneous effective stiffness concept. The oscillatory period of the non-linear step-response at that instant is then approximated by the natural period of the corresponding linear system. The proposed method is rigorously illustrated via two computational example cases (a near backlash and near pre-load non-linearities), and the necessary digital signal processing parameters for time domain analysis are investigated. Finally, the feasibility and applicability of the proposed method is demonstrated by estimating the softening and hardening trends in the time-varying oscillatory period of the measured response for two laboratory experiments that contain clearance elements and multi-staged torsional springs.

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