scholarly journals Stability Analysis of the Mathematical Model on the Control of HIV/AID Pandemic in a Heterogenous Population

2019 ◽  
Vol 56 (2-4) ◽  
pp. 47-53
Author(s):  
David Omale ◽  
Saikat Gochhait
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Heterogenous Population ◽  
The Mathematical Model

Walking Stability Analysis of Multi-Legged Crablike Robot over Slope

2013 ◽  
Vol 572 ◽  
pp. 636-639
Author(s):  
Xi Chen ◽  
Gang Wang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Stability Criterion ◽  
Stability Margin ◽  
Static Stability ◽  
Matlab Simulation ◽  
And Performance ◽  
The Stability ◽  
The Mathematical Model ◽  
The Relationship

This paper deals with the walking stability analysis of a multi-legged crablike robot over slope using normalized energy stability margin (NESM) method in order to develop a common stabilization description method and achieve robust locomotion for the robot over rough terrains. The robot is simplified with its static stability being described by NESM. The mathematical model of static stability margin is built so as to carry out the simulation of walking stability over slope for the crablike robot that walks in double tetrapod gait. As a consequence, the relationship between stability margin and the height of the robots centroid, as well as its inclination relative to the ground is calculated by the stability criterion. The success and performance of the stability criterion proposed is verified through MATLAB simulation and real-world experiments using multi-legged crablike robot.

Stability of Car Trailer Systems With Special Regard to Trailer Design

1974 ◽  
Vol 96 (2) ◽  
pp. 236-243 ◽  
Author(s):  
R. L. Collins ◽  
J. P. Wong
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Moment Of Inertia ◽  
Tire Pressure ◽  
Special Regard ◽  
Articulated Vehicle ◽  
The Mathematical Model ◽  
Solution Techniques

A linear stability analysis is performed on the articulated vehicle to provide information on the effects that various trailer parameters and variations in tire pressure have on the inherent towing stability of the typical car-trailer combination. Although certain portions of the mathematical model and solution techniques are similar to some previous efforts, the results are generalized to include a much larger class of vehicles than previously presented. The results indicate that hitch loading, trailer length, mass and moment of inertia, and fairly small variations in the car tire pressures can influence trailer towing stability.

Modeling and Stability Analysis of Hydraulic System for Wave Simulation

2013 ◽  
Vol 291-294 ◽  
pp. 1934-1939
Author(s):  
Jian Jun Peng ◽  
Yan Jun Liu ◽  
Yu Li ◽  
Ji Bin Liu
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Mathematical Models ◽  
Hydraulic System ◽  
Simulation System ◽  
Displacement Sensor ◽  
Schematic Diagram ◽  
Wave Simulation ◽  
The Stability ◽  
The Mathematical Model

This thesis put forward a hydraulic wave simulation system based on valve-controlled cylinder hydraulic system, which simulated wave movement on the land. The mathematical model of valve-controlled symmetric cylinder was deduced and the mathematical models of servo valve, displacement sensor and servo amplifier were established according to the schematic diagram of the hydraulic system designed, on the basis of which the mathematical model of hydraulic wave simulation system was obtained. Then the stability of the system was analyzed. The results indicated that the system was reliable.

Stability Analysis of a Viscoelastic Ring Subjected to Uniform Pressure

2011 ◽  
Vol 71-78 ◽  
pp. 3695-3701
Author(s):  
M Yang
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Galerkin Method ◽  
Numerical Method ◽  
Evolutionary Trend ◽  
Uniform Pressure ◽  
Free Standing ◽  
Viscoelastic Theory ◽  
The Mathematical Model

Based on Boltzmann’s viscoelastic theory, the mathematical model of a free-standing viscoelastic ring subjected to uniform pressure is established by applying assumed modes method, Galerkin method and numerical method. It is found that, the free-standing viscoelastic ringing has both a stantaneous critic load and a durable critic load under uniform pressure. The influence of structure size and parameters of the material are discussed, The evolutionary trend of the system is also investigated.

scholarly journals Practical Computational Approach for the Stability Analysis of Fuzzy Model-Based Predictive Control of Substrate and Biomass in Activated Sludge Processes

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 531
Author(s):  
Pedro M. Vallejo LLamas ◽  
Pastora Vega
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Activated Sludge ◽  
Predictive Control ◽  
Closed Loop ◽  
Complex Dynamics ◽  
Linear Time ◽  
Fuzzy Model ◽  
The Stability ◽  
The Mathematical Model

This paper presents a procedure for the closed-loop stability analysis of a certain variant of the strategy called Fuzzy Model-Based Predictive Control (FMBPC), with a model of the Takagi-Sugeno type, applied to the wastewater treatment process known as the Activated Sludge Process (ASP), with the aim of simultaneously controlling the substrate concentration in the effluent (one of the main variables that should be limited according to environmental legislations) and the biomass concentration in the reactor. This case study was chosen both for its environmental relevance and for special process characteristics that are of great interest in the field of nonlinear control, such as strong nonlinearity, multivariable nature, and its complex dynamics, a consequence of its biological nature. The stability analysis, both of fuzzy systems (FS) and the very diverse existing strategies of nonlinear predictive control (NLMPC), is in general a mathematically laborious task and difficult to generalize, especially for processes with complex dynamics. To try to minimize these difficulties, in this article, the focus was placed on the mathematical simplification of the problem, both with regard to the mathematical model of the process and the stability analysis procedures. Regarding the mathematical model, a state-space model of discrete linear time-varying (DLTV), equivalent to the starting fuzzy model (previously identified), was chosen as the base model. Furthermore, in a later step, the DLTV model was approximated to a local model of type discrete linear time-invariant (DLTI). As regards the stability analysis itself, a computational method was developed that greatly simplified this difficult task (in a local environment of an operating point), compared to other existing methods in the literature. The use of the proposed method provides useful conclusions for the closed-loop stability analysis of the considered FMBPC strategy, applied to an ASP process; at the same time, the possibility that the method may be useful in a more general way, for similar fuzzy and predictive strategies, and for other complex processes, was observed.

Spread of Tuberculosis Among Smokers

2020 ◽  
pp. 49-73
Author(s):  
Purvi M. Pandya ◽  
Ekta N. Jayswal ◽  
Yash Shah
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Psychological Health ◽  
Matrix Method ◽  
Equilibrium Points ◽  
Research Work ◽  
Linear Ordinary Differential Equations ◽  
Smoking Addiction ◽  
The Mathematical Model

Smoking tobacco has some hazardous implications on an individual's physical, physiological, and psychological health; health of the passive smokers near him or her; and on the surrounding environment. From carcinomas to auto-immune disorders, smoking has a role to play. Therefore, there arises a need to frame a systemic pathway to decipher relationship between smoking and a perilous disease such as tuberculosis. This research work focuses on how drugs or medications can affect individuals who are susceptible to tuberculosis because of smoking habits and also on individuals who have already developed symptoms of tuberculosis due to their smoking addiction. The mathematical model is formulated using non-linear ordinary differential equations, and then threshold is calculated for different equilibrium points using next generation matrix method. Stability analysis along with numerical simulations are carried out to validate the data.

scholarly journals Θ-SEIHRD mathematical model of Covid19-stability analysis using fast-slow decomposition

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e10019
Author(s):  
OPhir Nave ◽  
Israel Hartuv ◽  
Uziel Shemesh
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Nonlinear Differential Equations ◽  
Equilibrium Points ◽  
Asymptotic Methods ◽  
Fast Subsystem ◽  
The Stability ◽  
System Variables ◽  
The Mathematical Model ◽  
Slow Decomposition

In general, a mathematical model that contains many linear/nonlinear differential equations, describing a phenomenon, does not have an explicit hierarchy of system variables. That is, the identification of the fast variables and the slow variables of the system is not explicitly clear. The decomposition of a system into fast and slow subsystems is usually based on intuitive ideas and knowledge of the mathematical model being investigated. In this study, we apply the singular perturbed vector field (SPVF) method to the COVID-19 mathematical model of to expose the hierarchy of the model. This decomposition enables us to rewrite the model in new coordinates in the form of fast and slow subsystems and, hence, to investigate only the fast subsystem with different asymptotic methods. In addition, this decomposition enables us to investigate the stability analysis of the model, which is important in case of COVID-19. We found the stable equilibrium points of the mathematical model and compared the results of the model with those reported by the Chinese authorities and found a fit of approximately 96 percent.

Improving learning experiences using LEGO Mindstorms EV3 robots in control systems course

2020 ◽  
pp. 002072092096587 ◽  
Author(s):  
Meirong Zhang ◽  
Yan Wan
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Transfer Function ◽  
Control Systems ◽  
Experimental Model ◽  
Learning Experiences ◽  
Stability Range ◽  
Lego Mindstorms ◽  
Mindstorms Ev3 ◽  
The Mathematical Model

This paper integrates LEGO Mindstorms EV3 robots into undergraduate control systems course to improve students’ learning experiences using Matlab as a development tool. This platform facilitates the students throughout teaching the course in learning the essential concepts of control systems such as modeling, stability analysis, and skill of designing controllers for the dynamic systems. The participants of the course identify the transfer function of the robot and compare it with the transfer function developed by using laws of physics. The students, then compare the identified model with the mathematical model by using stability analysis techniques, finding out that the stability range is much smaller for the experimental model than the mathematical model. After that, several types of controllers are designed and tested on the experimental model and EV3 robots, which demonstrates that there exists discrepancies between conceptual and practical designs. Finally, a comparison of students’ apprehension of a set of capabilities before and after taking the course shows the value of using EV3 robots on improving students’ learning experiences of control systems course.

scholarly journals Modeling and Stability Analysis of Wedge Clutch System

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jian Yao ◽  
Li Chen ◽  
Chengliang Yin
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Piecewise Linear ◽  
Wedge Angle ◽  
Stable Condition ◽  
System A ◽  
Actuation System ◽  
Linearized System ◽  
The Stability ◽  
The Mathematical Model

A wedge clutch with unique features of self-reinforcement and small actuation force was designed. Its self-reinforcement feature, associated with different factors such as the wedge angle and friction coefficient, brings different dynamics and unstable problem with improper parameters. To analyze this system, a complete mathematical model of the actuation system is built, which includes the DC motor, the wedge mechanism, and the actuated clutch pack. By considering several nonlinear factors, such as the slip-stick friction and the contact or not of the clutch plates, the system is piecewise linear. Through the stability analysis of the linearized system in clutch slipping phase, the stable condition of the designed parameters is obtained asα>arctan⁡(μc). The mathematical model of the actuation system is validated by prototype testing. And with the validated model, the system dynamics in both stable and unstable conditions is investigated and discussed in engineering side.

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