scholarly journals The Well-Posedness and Stability Analysis of a Computer Series System

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xing Qiao ◽  
Dan Ma ◽  
Fu Zheng ◽  
Guangtian Zhu
Keyword(s):  
Nonnegative Solution ◽  
Semigroup Theory ◽  
Steady State Solution ◽  
System Model ◽  
Transient Solution ◽  
Reliability Indices ◽  
Unique Existence ◽  
System Operator ◽  
In Series ◽  
The Stability

A repairable computer system model which consists of hardware and software in series is established in this paper. This study is devoted to discussing the unique existence of the solution and the stability of the studied system. In view ofc0semigroup theory, we prove the existence of a unique nonnegative solution of the system. Then by analyzing the spectra distribution of the system operator, we deduce that the transient solution of the system strongly converges to the nonnegative steady-state solution which is the eigenvector corresponding to eigenvalue 0 of the system operator. Finally, some reliability indices of the system are provided at the end of the paper with a new method.

scholarly journals Exponential Stability and Availability Analysis of a Complex Standby System

2014 ◽  
Vol 2 (3) ◽  
pp. 279-288 ◽  
Author(s):  
Chunli Wang ◽  
Mingyan Teng ◽  
Fu Zheng
Keyword(s):  
Exponential Stability ◽  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Well Posedness ◽  
Redundant System ◽  
Bounded Linear ◽  
Reliability Indices ◽  
Availability Analysis ◽  
System Operator

Abstract In this paper, we first investigate the solution of the two correlated units redundant system with two types of failure. By using the method of functional analysis, especially, the c0 semigroup theory of bounded linear operators on Banach space, we prove the well-posedness and the existence of positive solution of the system. By analyzing the spectra distribution of the system operator, we prove that the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Furthermore, we discuss the exponential stability of the system. Finally, we analyze the reliability the system with the help of our main results and present some reliability indices of the system at the end of the paper.

Stability of the Redundant System with Two Correlated Units

2012 ◽  
Vol 198-199 ◽  
pp. 973-977 ◽  
Author(s):  
Xing Qiao ◽  
Ming Fang
Keyword(s):  
Banach Space ◽  
Functional Analysis ◽  
Steady State ◽  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Well Posedness ◽  
Redundant System ◽  
Bounded Linear ◽  
System Operator

In this paper the qualitative behaviors of the two correlated units redundant system with two types of failure were discussed. By using the method of functional analysis, especially, the semigroup theory of bounded linear operators on Banach space, the well-posedness and the existence of positive solution of the system was obtained. By analyzing the spectra distribution of the system operator, the dynamic solution of the system asymptotically converges to the nonnegative steady-state solution which is the eigenfunction corresponding to eigenvalue 0 of the system operator was proved.

scholarly journals Well-posedness and Stability of the Repairable System with Three Units and Vacation

2014 ◽  
Vol 2 (1) ◽  
pp. 54-76
Author(s):  
Xiaoshuang Han ◽  
Mingyan Teng ◽  
Ming Fang
Keyword(s):  
Steady State ◽  
Abstract Cauchy Problem ◽  
Steady State Solution ◽  
State Solution ◽  
Repairable System ◽  
Dynamic Solution ◽  
System Operator ◽  
Mean Ergodicity ◽  
System Equations ◽  
The Stability

AbstractThe stability of the repairable system with three units and vacation was investigated by two different methods in this note. The repairable system is described by a set of ordinary differential equation coupled with partial differential equations with initial values and integral boundaries. To apply the theory of positive operator semigroups to discuss the repairable system, the system equations were transformed into an abstract Cauchy problem on some Banach lattice. The system equations have a unique non-negative dynamic solution and positive steady-state solution and dynamic solution strongly converges to steady-state solution were shown on the basis of the detailed spectral analysis of the system operator. Furthermore, the Cesáro mean ergodicity of the semigroupT(t) generated by the system operator was also shown through the irreducibility of the semigroup.

scholarly journals A Simple Repairable System with Warning Device

2015 ◽  
Vol 2015 ◽  
pp. 1-18
Author(s):  
Xiao Zhang ◽  
Lina Guo
Keyword(s):  
Continuous Semigroup ◽  
Semigroup Theory ◽  
Good Condition ◽  
Markov Renewal Process ◽  
Repairable System ◽  
Analysis Method ◽  
Numerical Examples ◽  
Reliability Indices ◽  
Unique Existence ◽  
Warning Device

This paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described into a group of integrodifferential equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory orC0semigroup theory and the spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes and profit of systems with and without warning device) as well as numerical examples are presented at the end of the paper.

scholarly journals A Bio-Inspired Compliance Planning and Implementation Method for Hydraulically Actuated Quadruped Robots with Consideration of Ground Stiffness

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2838
Author(s):  
Xiaoxing Zhang ◽  
Haoyuan Yi ◽  
Junjun Liu ◽  
Qi Li ◽  
Xin Luo
Keyword(s):  
Harmonic Oscillation ◽  
Ground Surface ◽  
Legged Locomotion ◽  
Soft Ground ◽  
Quadruped Robots ◽  
In Series ◽  
Reaction Forces ◽  
Implementation Method ◽  
The Stability ◽  
Natural Dynamics

There has been a rising interest in compliant legged locomotion to improve the adaptability and energy efficiency of robots. However, few approaches can be generalized to soft ground due to the lack of consideration of the ground surface. When a robot locomotes on soft ground, the elastic robot legs and compressible ground surface are connected in series. The combined compliance of the leg and surface determines the natural dynamics of the whole system and affects the stability and efficiency of the robot. This paper proposes a bio-inspired leg compliance planning and implementation method with consideration of the ground surface. The ground stiffness is estimated based on analysis of ground reaction forces in the frequency domain, and the leg compliance is actively regulated during locomotion, adapting them to achieve harmonic oscillation. The leg compliance is planned on the condition of resonant movement which agrees with natural dynamics and facilitates rhythmicity and efficiency. The proposed method has been implemented on a hydraulic quadruped robot. The simulations and experimental results verified the effectiveness of our method.

scholarly journals Smooth enlargement of human standing sway by instability due to weak reaction floor and noise

2016 ◽  
Vol 3 (1) ◽  
pp. 150570 ◽  
Author(s):  
Tetsuro Funato ◽  
Shinya Aoi ◽  
Nozomi Tomita ◽  
Kazuo Tsuchiya
Keyword(s):  
Nonlinear Control ◽  
Neurological Disorders ◽  
System Model ◽  
Quiet Standing ◽  
Body Sway ◽  
Intermittent Control ◽  
Dynamic Reaction ◽  
Weak Reaction ◽  
Integral Control ◽  
The Stability

Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predicted to exhibit bifurcation. The presence of stability-dependent transition enables dynamic reaction that depends on the stability of the environment, and can explain the change in sway characteristics that accompanies some neurological disorders. This research analyses the characteristics of a system model that induces transition, and discusses whether human standing reflects such a mechanism. In mathematical analysis of system models, (intermittent control-like) nonlinear control with integral control is shown to exhibit Hopf bifurcation. Moreover, from the analytical solution of the system model with noise, noise is shown to work to smooth the enlargement of sway around the bifurcation point. This solution is compared with measured human standing sway on floors with different stabilities. By quantitatively comparing the control parameters between human observation and model prediction, enlargement of sway is shown to appear as predicted by the model analysis.

Dynamical properties about ultrasonic vibration assisted drilling of TiBw/TC4 composite

2020 ◽  
pp. 095440542096843
Author(s):  
Yong Feng ◽  
Haoxiang Wang ◽  
Min Zhang ◽  
Zihao Zhu ◽  
Xiaoyu Wang ◽  
...  
Keyword(s):  
Ultrasonic Vibration ◽  
Cutting Tools ◽  
System Model ◽  
Force Model ◽  
Drilling Process ◽  
Drilling Force ◽  
Dry Cutting ◽  
Analysis System ◽  
The Stability ◽  
Three Degree Of Freedom

TiBw / TC4 composite material was used as the machining object of Ultrasonic vibration assisted drilling (UVAD), the single directional three-degree-of-freedom dynamical system model was established. The dynamic signal test and analysis system was used for modal experiment to identify the parameters in the model. Under the condition of dry cutting, the drilling axial force and tool vibration in the drilling process are studied. The results showed that the maximum values of the predicted and measured axial drilling force were 412.5N and 439.6N respectively, and the error rate was 6.165%, which verified the reliability of the predicted axial drilling force model. For cutting tools, the average amplitudes of simulated vibration and measured vibration were 0.1124mm and 0.1151mm respectively, with a difference of 2.402%, and the overall trends were the same, which verifies the reliability of the dynamical model. Finally, the stability of drilling process was analyzed, and the frequency and amplitude of ultrasonic vibration were analyzed. The results show that in order to expand the unconditional stability region, it is more efficient to increase the amplitude than to increase the frequency.

Multiple Harmonic Balance Method for Aperiodic Vibration of a Piecewise-Linear System

1998 ◽  
Vol 120 (1) ◽  
pp. 181-187 ◽  
Author(s):  
Y. B. Kim
Keyword(s):  
Linear System ◽  
Harmonic Balance ◽  
Piecewise Linear ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Balance Method ◽  
Piecewise Linear System ◽  
Higher Dimensional ◽  
Computational Procedures ◽  
The Stability

A multiple harmonic balance method is presented in this paper for obtaining the aperiodic steady-state solution of a piecewise-linear system. As the method utilizes general and systematic computational procedures, it can be applied to analyze the multi-tone or combination-tone responses for the higher dimensional nonlinear systems such as rotors. Moreover, it is capable of informing the stability of the obtained solution using Floquet theory. To demonstrate the systematic approach of the new method, the almost periodic forced vibration of an articulated loading platform (ALP) with a piecewise-linear stiffness is computed as an example.

scholarly journals Semigroup Methods for the M/G/1 Queueing Model with Working Vacation and Vacation Interruption

2016 ◽  
Vol 8 (5) ◽  
pp. 56 ◽  
Author(s):  
Ehmet Kasim
Keyword(s):  
Semigroup Theory ◽  
Steady State Solution ◽  
Linear Operators ◽  
Time Dependent ◽  
Queueing Model ◽  
Working Vacation ◽  
Positive Time ◽  
Vacation Interruption ◽  
Vacation Period ◽  
Time Dependent Solution

By using the strong continuous semigroup theory of linear operators we prove that the M/G/1 queueing model with working vacation and vacation interruption has a unique positive time dependent solution which satisfies probability conditions. When the both service completion rate in a working vacation period and in a regular busy period are constant, by investigating the spectral properties of an operator corresponding to the model we obtain that the time-dependent solution of the model strongly converges to its steady-state solution.

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