PID, LQR, and LQG Controllers to Maintain the Stability of an AVR System at Varied Model Parameters

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

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Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4025896 ◽

2015 ◽

Vol 10 (3) ◽

Cited By ~ 4

Author(s):

Da Yang ◽

Liling Zhu ◽

Yun Pu

Keyword(s):

Traffic Flow ◽

Heterogeneous Traffic ◽

Model Parameters ◽

Optimal Velocity ◽

Stability Functions ◽

Car Following Model ◽

Traffic Wave ◽

The Stability ◽

Different Characteristics ◽

Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

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Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

Journal of Applied Mechanics ◽

10.1115/1.3169122 ◽

1985 ◽

Vol 52 (3) ◽

pp. 686-692 ◽

Cited By ~ 4

Author(s):

L. A. Month ◽

R. H. Rand

Keyword(s):

Angular Velocity ◽

Rigid Body ◽

Classical Problem ◽

Moment Of Inertia ◽

Model Parameters ◽

Stability Chart ◽

The Stability ◽

Transition Curves ◽

Minimum Moment ◽

Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

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A Theoretical Model for the Transmission Dynamics of the Buruli Ulcer with Saturated Treatment

Computational and Mathematical Methods in Medicine ◽

10.1155/2014/576039 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 8

Author(s):

Ebenezer Bonyah ◽

Isaac Dontwi ◽

Farai Nyabadza

Keyword(s):

Human Population ◽

Reproduction Number ◽

Buruli Ulcer ◽

Coupled System ◽

Model Parameters ◽

The Public ◽

Treatment Function ◽

Medical Facilities ◽

The Stability ◽

Saturated Treatment

The management of the Buruli ulcer (BU) in Africa is often accompanied by limited resources, delays in treatment, and macilent capacity in medical facilities. These challenges limit the number of infected individuals that access medical facilities. While most of the mathematical models with treatment assume a treatment function proportional to the number of infected individuals, in settings with such limitations, this assumption may not be valid. To capture these challenges, a mathematical model of the Buruli ulcer with a saturated treatment function is developed and studied. The model is a coupled system of two submodels for the human population and the environment. We examine the stability of the submodels and carry out numerical simulations. The model analysis is carried out in terms of the reproduction number of the submodel of environmental dynamics. The dynamics of the human population submodel, are found to occur at the steady states of the submodel of environmental dynamics. Sensitivity analysis is carried out on the model parameters and it is observed that the BU epidemic is driven by the dynamics of the environment. The model suggests that more effort should be focused on environmental management. The paper is concluded by discussing the public implications of the results.

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Using the LIST model to Estimate the Effects of Contact Tracing on COVID-19 Endemic Equilibria in England and its Regions

10.1101/2020.06.11.20128611 ◽

2020 ◽

Author(s):

Rosalyn J. Moran ◽

Alexander J. Billig ◽

Maell Cullen ◽

Adeel Razi ◽

Jean Daunizeau ◽

...

Keyword(s):

Endemic Equilibrium ◽

Contact Tracing ◽

Model Parameters ◽

Infection Rates ◽

Stable States ◽

Medium Term ◽

The Stability ◽

Lower Death Rate ◽

The Impact ◽

List Model

AbstractGovernments across Europe are preparing for the emergence from lockdown, in phases, to prevent a resurgence in cases of COVID-19. Along with social distancing (SD) measures, contact tracing – find, track, trace and isolate (FTTI) policies are also being implemented. Here, we investigate FTTI policies in terms of their impact on the endemic equilibrium. We used a generative model – the dynamic causal ‘Location’, ‘Infection’, ‘Symptom’ and ‘Testing’ (LIST) model to identify testing, tracing, and quarantine requirements. We optimised LIST model parameters based on time series of daily reported cases and deaths of COVID-19 in England— and based upon reported cases in the nine regions of England and in all 150 upper tier local authorities. Using these optimised parameters, we forecasted infection rates and the impact of FTTI for each area—national, regional, and local. Predicting data from early June 2020, we find that under conditions of medium-term immunity, a ‘40%’ FTTI policy (or greater), could reach a distinct endemic equilibrium that produces a significantly lower death rate and a decrease in ICU occupancy. Considering regions of England in isolation, some regions could substantially reduce death rates with 20% efficacy. We characterise the accompanying endemic equilibria in terms of dynamical stability, observing bifurcation patterns whereby relatively small increases in FTTI efficacy result in stable states with reduced overall morbidity and mortality. These analyses suggest that FTTI will not only save lives, even if only partially effective, and could underwrite the stability of any endemic steady-state we manage to attain.

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Modeling the Vibratory Drilling Process

Volume 7A: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8024 ◽

1999 ◽

Author(s):

Stephen A. Batzer ◽

Alexander M. Gouskov ◽

Sergey A. Voronov

Keyword(s):

Rotational Velocity ◽

Time Lag ◽

Chip Thickness ◽

Cutting Conditions ◽

Model Parameters ◽

Drilling Process ◽

Workpiece Material ◽

Velocity Amplitude ◽

The Stability

Abstract The dynamic behavior of deep-hole vibratory drilling is analyzed. The mathematical model presented allows the determination of axial tool and workpiece displacements and cutting forces for significant dynamic system behavior such as the entrance of the cutting tool into workpiece material and exit. Model parameters include the actual rigidity of the tool and workpiece, time-varying chip thickness, time lag for chip formation due to tool rotation and possible disengagement of drill cutting edges from the workpiece due to tool and/or workpiece axial vibrations. The main features of this model are its nonlinearity and inclusion of time lag differential equations which require numeric solutions. The specific cutting conditions (feed, tool rotational velocity, amplitude and frequency of forced vibrations) necessary to obtain discontinuous chips and reliable removal are determined. The stability conditions of excited vibrations are also investigated. Calculated bifurcation diagrams make it possible to derive the domain of system parameters along with the determination of optimal cutting conditions.

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Optimization models for managing limited resources in logistics

10.12737/1082948 ◽

2021 ◽

Author(s):

Aleksandr Mischenko ◽

Anastasiya Ivanova

Keyword(s):

Stochastic Models ◽

Optimization Models ◽

Limited Resources ◽

Model Parameters ◽

Systems Modeling ◽

Deterministic Models ◽

Logistics Systems ◽

Industrial Enterprises ◽

The Stability ◽

Senior Students

In the proposed monograph, optimization models for managing limited resources in logical systems are considered. Such systems are primarily used by industrial enterprises, transport companies and trade organizations, including those that carry out wholesale activities. As a rule, the efficiency of these objects largely depends on how rational use of limited resources such as: consumer camera business, labor, vehicles, etc. In this paper, various approaches to managing such resources are considered both for deterministic models and for the situation when a number of model parameters are not specified exactly, that is, for stochastic models. In this case, it is proposed to evaluate the stability of models to the occurrence of various types of risk events, both by the structure of the solution and by the functionality. It is addressed to senior students, postgraduates and masters studying in the specialty "Management" and "Logistics", as well as specialists in the field of logistics systems modeling.

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Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model

Journal of Applied Mathematics ◽

10.1155/2019/8465747 ◽

2019 ◽

Vol 2019 ◽

pp. 1-13 ◽

Cited By ~ 10

Author(s):

Hailay Weldegiorgis Berhe ◽

Oluwole Daniel Makinde ◽

David Mwangi Theuri

Keyword(s):

Sensitivity Analysis ◽

Reproduction Number ◽

Transmission Rate ◽

Nonlinear Least Squares ◽

Model Parameters ◽

Nonlinear Least Squares Problem ◽

The Stability ◽

Diarrhea Disease ◽

Effective Transmission ◽

Disease Free

In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease-free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for R0>1. The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is R0=1.1208. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (βh). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.

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Variable Chaplygin gas in Kaluza–Klein framework

Canadian Journal of Physics ◽

10.1139/cjp-2017-0873 ◽

2019 ◽

Vol 97 (2) ◽

pp. 117-124 ◽

Cited By ~ 1

Author(s):

M. Salti ◽

O. Aydogdu ◽

A. Tas ◽

K. Sogut ◽

E.E. Kangal

Keyword(s):

Dark Matter ◽

Dark Energy ◽

Chaplygin Gas ◽

Model Parameters ◽

Energy Scenario ◽

Type Ia ◽

The Stability ◽

Best Fit ◽

Matter Energy ◽

Kaluza Klein

We investigate cosmological features of the variable Chaplygin gas (VCG) describing a unified dark matter–energy scenario in a universe governed by the five dimensional (5D) Kaluza–Klein (KK) gravity. In such a proposal, the VCG evolves from the dust-like phase to the phantom or the quintessence phases. It is concluded that the background evolution for the KK-type VCG definition is equivalent to that for the dark energy interacting with the dark matter. Next, after performing neo-classical tests, we calculated the proper, luminosity, and angular diameter distances. Additionally, we construct a connection between the VCG in the KK universe and a homogenous minimally coupled scalar field by introducing its self-interacting potential and also we confirm the stability of the KK-type VCG model by making use of thermodynamics. Moreover, we use data from type Ia supernova, observational H(z) dataset and Planck-2015 results to place constraints on the model parameters. Subsequently, according to the best-fit values of the model parameters we analyze our results numerically.

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Stable Stationary Solitons of the One-Dimensional Modified Complex Ginzburg-Landau Equation

Zeitschrift für Naturforschung A ◽

10.1515/zna-2007-7-803 ◽

2007 ◽

Vol 62 (7-8) ◽

pp. 368-372

Author(s):

Woo-Pyo Hong

Keyword(s):

Landau Equation ◽

Model Parameters ◽

Ginzburg Landau ◽

One Dimensional ◽

Paraxial Ray Approximation ◽

New Family ◽

Ginzburg Landau Equation ◽

The Stability ◽

The One ◽

Paraxial Ray

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.

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