An empirical approach for delayed oscillator stability and parametric identification

2006 ◽  
Vol 462 (2071) ◽  
pp. 2145-2160 ◽  
Author(s):  
Brian P Mann ◽  
Keith A Young
Keyword(s):  
Numerical Data ◽  
Parametric Identification ◽  
Empirical Approach ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Machining Processes ◽  
Feedback Control Systems ◽  
Reconstructed Time Series ◽  
The Stability ◽  
Characteristic Multipliers

This paper investigates a semi-empirical approach for determining the stability of systems that can be modelled by ordinary differential equations with a time delay. This type of model is relevant to biological oscillators, machining processes, feedback control systems and models for wave propagation and reflection, where the motion of the waves themselves is considered to be outside the system model. A primary aim is to investigate the extension of empirical Floquet theory to experimental or numerical data obtained from time-delayed oscillators. More specifically, the reconstructed time series from a numerical example and an experimental milling system are examined to obtain a finite number of characteristic multipliers from the reduced order dynamics. A secondary goal of this work is to demonstrate a benefit of empirical characteristic multiplier estimation by performing system identification on a delayed oscillator. The principal results from this study are the accurate estimation of delayed oscillator characteristic multipliers and the utilization the empirical results for parametric identification of model parameters. Combining these results with previous research on an experimental milling system provides a particularly relevant result—the first approach for identifying all model parameters for stability prediction directly from the cutting process vibration history.

Experimental Parameter Identification of a Time Delayed Oscillator

2005 ◽  
Author(s):  
Brian P. Mann ◽  
Keith A. Young ◽  
Amy M. Helvey ◽  
Raul E. Zapata
Keyword(s):  
Parameter Identification ◽  
Experimental Parameter ◽  
Parametric Identification ◽  
Model Parameters ◽  
Element Analysis ◽  
Delayed Systems ◽  
Infinite Dimensional ◽  
Novel Approach ◽  
Dimensional Phase Space ◽  
The Stability

This paper departs from the more traditional focus of systems with time delays — the loss of stability — to examine an intrinsic benefit of time-delayed systems and a novel approach for parametric identification. For instance, it is well-known that the presence of a time delay will result in an infinite dimensional phase space and can compromise the stability characteristics of a dynamical system. This paper explores the utilization the system higher dimensional transients to provide benefit to the common problem of system identification. Observations are first made about which experimental milling tests can be utilized for parameter identification. A model for the milling experiment is then introduced and a temporal finite element analysis is performed to transform the original delay equations into the form of a dynamic map. Experimental data is then examined with empirical Floquet theory and principal orthogonal decomposition to estimate the reduced order dynamics, or truncated state space dimension, and to identify the empirical Floquet multipliers of the system. Parametric identification is performed through the optimization of model parameters that satisfy the characteristic equation.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

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.

scholarly journals Adaptive State-of-Charge Estimation for Lithium-Ion Batteries by Considering Capacity Degradation

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 122
Author(s):  
Peipei Xu ◽  
Junqiu Li ◽  
Chao Sun ◽  
Guodong Yang ◽  
Fengchun Sun
Keyword(s):  
Equivalent Circuit Model ◽  
Lithium Ion ◽  
Maximum Error ◽  
State Of Charge ◽  
Recursive Least Squares ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Soc Estimation ◽  
Capacity Degradation ◽  
Battery Capacity

The accurate estimation of a lithium-ion battery’s state of charge (SOC) plays an important role in the operational safety and driving mileage improvement of electrical vehicles (EVs). The Adaptive Extended Kalman filter (AEKF) estimator is commonly used to estimate SOC; however, this method relies on the precise estimation of the battery’s model parameters and capacity. Furthermore, the actual capacity and battery parameters change in real time with the aging of the batteries. Therefore, to eliminate the influence of above-mentioned factors on SOC estimation, the main contributions of this paper are as follows: (1) the equivalent circuit model (ECM) is presented, and the parameter identification of ECM is performed by using the forgetting-factor recursive-least-squares (FFRLS) method; (2) the sensitivity of battery SOC estimation to capacity degradation is analyzed to prove the importance of considering capacity degradation in SOC estimation; and (3) the capacity degradation model is proposed to perform the battery capacity prediction online. Furthermore, an online adaptive SOC estimator based on capacity degradation is proposed to improve the robustness of the AEKF algorithm. Experimental results show that the maximum error of SOC estimation is less than 1.3%.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
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.

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

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
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.

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

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.

scholarly journals Battery state of charge estimation and online wheel slip ratio control for autonomous wheeled mobile robot

2021 ◽  
Author(s):  
Maral Partovibakhsh
Keyword(s):  
Kalman Filter ◽  
Power Consumption ◽  
Mobile Robot ◽  
Unscented Kalman Filter ◽  
Longitudinal Velocity ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Slip Ratio ◽  
Soc Estimation ◽  
Increasing Function

For autonomous mobile robots moving in unknown environment, accurate estimation of available power along with the robot power demand for each mission is paramount to successful completion of that mission. Regarding the power consumption, the control unit deals with two tasks simultaneously: 1) it has to monitor the power supply (batteries) state of charge (SoC) constantly. This leads to estimation of robot current available power. Besides, batteries are sensitive to deep discharge or overcharge. The battery SoC is an essential factor in power management of a mobile robot. Accurate estimation of the battery SoC can improve power management, optimize the performance, extend the lifetime, and prevent permanent damage to the batteries. 2) The dynamic characteristics of the terrain the robot traverse requires rapid online modifications in its behaviour. The power required for driving a wheel is an increasing function of its slip ratio. For a wheeled robot moving for driving a wheel is an increasing function of its slip ratio. For a wheeled robot moving on different terrains, slip of the wheels should be checked and compensated for to keep the robot moving with less power consumption. To reduce the power consumption, the target robot moving with less power consumption. To reduce the power consumption, the target of the control system is to keep the slip ratio of the driving wheels around the desired value of the control system is to keep the slip ratio of the driving wheels around the desired value. To fulfill the above mentioned tasks, in this thesis, to increase model validity of lithium-ion battery in various charge/discharge scenarios during the mobile robot operation, the battery capacity fade and internal resistance change are modeled by adding them as state variables to a state space model. Using the output measured data, adaptive unscented Kalman Filter (AUKF) is employed for online model parameters identification of the equivalent circuit model at each sampling time. Subsequently, based on the updated model parameters, SoC estimation is conducted using AUKF. The effectiveness of the proposed method is verified through experiments under different power duties in the lab environment through experiments under different power duties in the lab environment. Better results are obtained both in battery model parameters estimation and the battery SoC estimation in comparison with other Kalman filter extensions. Furthermore, for effective control of the slip ratio, a model-based approach to estimating the longitudinal velocity of the mobile robot is presented. The AUKF is developed to estimate the vehicle longitudinal velocity and the wheel angular velocity using measurements from wheel encoders. Based on the estimated slip ratio, a sliding mode controller is designed for slip control of the uncertain nonlinear dynamical system in the presence of model uncertainties, parameter variations, and disturbances. Experiments are carried out in real time on a four-wheel mobile robot to verify the effectiveness of the estimation algorithm and the controller. It is shown that the controller is able to control the slip ratio of the mobile robot on different terrains while adaptive concept of AUKF leads to better results than the unscented Kalman filter in estimating the vehicle velocity which is difficult to measure in actual practice.

Modeling the Vibratory Drilling Process

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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