Abstract: This paper addresses the mathematical model of wind energy system useful for designing fault tolerant control. To serve the demand of power, large capacity wind energy systems are vital. These systems are installed offshore where non planned service is very costly. Whenever there is a fault in between two planned services, the system may stop working abruptly. This might even lead to the complete failure of the system. To enhance the reliability, the availability and reduce the cost of maintenance of wind turbines, the fault tolerant control systems are very essential. For designing any control system, an appropriate mathematical model is always needed. In this paper, the two-mass model is modified by considering the frequent mechanical faults like misalignments in the drive train, gears and bearings faults. These faults are subject to a wear process and cause frictional losses. This paper addresses these faults in the mathematics of the wind energy system. Further, the work is extended to study the variations of the parameters namely generator inertia constant, spring constant, viscous friction coefficient and gear ratio; on the pole-zero plot which is related with the physical design of the wind turbine. Behavior of the wind turbine during drive train faults are simulated and briefly discussed.
Abstract: This paper revisits the free vibration problem of delaminated composite beams. It is shown that during the vibration of composite beams the delaminated parts are subjected to the parametric excitation. This can lead to the dynamic buckling during the motion of the structure. The equation of motion includes time-dependent stiffness and so it leads to a system of Mathieu-Hill differential equations. The free vibration analysis of beams is carried out in the usual way by using beam finite elements. The dynamic buckling problem is investigated locally, and the critical buckling forces are determined by the modified harmonic balance method by using an imposed time function of the motion. The stability diagrams are created, and the numerical predictions are compared to experimental results. The most important findings are the critical amplitudes at which delamination buckling takes place, the stability diagrams representing the instability of the system, and the realistic mode shape prediction in contrast with the unrealistic results of models available in the literature.
Abstract: Slope stability analyses are largely carried out by deterministic methods and evaluated through a single security factor. Although it is known that the geotechnical parameters can present great dispersal, such analyses are considered fixed and known. The probabilistic methods, in turn, incorporate the variability of input key parameters (random variables), resulting in a range of values of safety factors, thus enabling the determination of the probability of failure, which is an essential parameter in the calculation of the risk (probability multiplied by the consequence of the event). Among the probabilistic methods, there are three frequently used methods in geotechnical society: FOSM (First-Order, Second-Moment), Rosenblueth (Point Estimates) and Monte Carlo. This paper presents a comparison between the results from deterministic and probabilistic analyses (FOSM method, Monte Carlo and Rosenblueth) applied to a hypothetical slope. The end was held to evaluate the behavior of the slope and consequent risk analysis, which is used to calculate the risk and analyze their mitigation and control solutions. It can be observed that the results obtained by the three probabilistic methods were quite close. It should be noticed that the calculation of the risk makes it possible to list the priority to the implementation of mitigation measures. Therefore, it is recommended to do a good assessment of the geological-geotechnical model incorporating the uncertainty in viability, design, construction, operation and closure by means of risk management.
Abstract: This paper expounds on the direct-driven PMSG wind power system control strategy, and analyses the stability conditions of the system. The direct-driven PMSG wind power system may generate the intense mechanical vibration, when wind speed changes dramatically. This paper proposes a new type of torque control strategy, which increases the system damping effectively, mitigates mechanical vibration of the system, and enhances the stability conditions of the system. The simulation results verify the reliability of the new torque control strategy.
Abstract: Increasing our ability to solve complex engineering problems is directly related to the processing capacity of computers. By means of such equipments, one is able to fast and accurately run numerical algorithms. Besides the increasing interest in numerical simulations, probabilistic approaches are also of great importance. This way, statistical tools have shown their relevance to the modelling of practical engineering problems. In general, statistical approaches to such problems consider that the random variables involved follow a normal distribution. This assumption tends to provide incorrect results when skew data is present since normal distributions are symmetric about their means. Thus, in order to visualize and quantify this aspect, 9 statistical distributions (symmetric and skew) have been considered to model a hypothetical slope stability problem. The data modeled is the friction angle of a superficial soil in Brasilia, Brazil. Despite the apparent universality, the normal distribution did not qualify as the best fit. In the present effort, data obtained in consolidated-drained triaxial tests and saturated direct shear tests have been modeled and used to analytically derive the probability density function (PDF) of the safety factor of a hypothetical slope based on Mohr-Coulomb rupture criterion. Therefore, based on this analysis, it is possible to explicitly derive the failure probability considering the friction angle as a random variable. Furthermore, it is possible to compare the stability analysis when the friction angle is modelled as a Dagum distribution (distribution that presented the best fit to the histogram) and as a Normal distribution. This comparison leads to relevant differences when analyzed in light of the risk management.
Abstract: By GEO5 FEM program with four rockfill slope
modeling and stability analysis was performed for S1, S2, S3 and
S4 slopes where landslides of the shalefills were limited. Effective
angle of internal friction (φ'°) 17°-22.5°, the effective cohesion (c')
from 0.5 to 1.8 kPa, saturated unit weight 1.78-2.43 g/cm3, natural
unit weight 1.9-2.35 g/cm3, dry unit weight 1.97-2.40 g/cm3, the
permeability coefficient of 1x10-4 - 6.5x10-4 cm/s. In cross-sections
of the slope, GEO 5 FEM program possible critical surface tension
was examined. Rockfill dump design was made to prevent sliding
slopes. Bulk material designated geotechnical properties using also
GEO5 programs FEM and stability program via a safety factor
determined and calculated according to the values S3 and S4 No.
slopes are stable S1 and S2 No. slopes were close to stable state
that has been found to be risk. GEO5 programs with limestone rock
fill dump through FEM program was found to exhibit stability.
Abstract: Cholera is a disease that is predominately common in
developing countries due to poor sanitation and overcrowding
population. In this paper, a deterministic model for the dynamics of
cholera is developed and control measures such as health educational
message, therapeutic treatment, and vaccination are incorporated in
the model. The effective reproduction number is computed in terms
of the model parameters. The existence and stability of the
equilibrium states, disease free and endemic equilibrium states are
established and showed to be locally and globally asymptotically
stable when R0 < 1 and R0 > 1 respectively. The existence of
backward bifurcation of the model is investigated. Furthermore,
numerical simulation of the model developed is carried out to show
the impact of the control measures and the result indicates that
combined control measures will help to reduce the spread of cholera
in the population.
Abstract: This paper studies a mathematical model based on the
integral equations for dynamic analyzes numerical investigations of a
non-uniform or multi-material composite beam. The beam is
subjected to a sub-tangential follower force and elastic foundation.
The boundary conditions are represented by generalized
parameterized fixations by the linear and rotary springs. A
mathematical formula based on Euler-Bernoulli beam theory is
presented for beams with variable cross-sections. The non-uniform
section introduces non-uniformity in the rigidity and inertia of beams
and consequently, more complicated equilibrium who governs the
equation. Using the boundary element method and radial basis
functions, the equation of motion is reduced to an algebro-differential
system related to internal and boundary unknowns. A generalized
formula for the deflection, the slope, the moment and the shear force
are presented. The free vibration of non-uniform loaded beams is
formulated in a compact matrix form and all needed matrices are
explicitly given. The dynamic stability analysis of slender beam is
illustrated numerically based on the coalescence criterion. A realistic
case related to an industrial chimney is investigated.
Abstract: Linear stability analysis of double diffusive convection
in a horizontal porous layer saturated with fluid is examined by
considering the effects of viscous dissipation, concentration based
internal heat source and vertical throughflow. The basic steady
state solution for Governing equations is derived. Linear stability
analysis has been implemented numerically by using shooting
and Runge-kutta methods. Critical thermal Rayleigh number Rac
is obtained for various values of solutal Rayleigh number Sa,
vertical Peclet number Pe, Gebhart number Ge, Lewis number
Le and measure of concentration based internal heat source
γ. It is observed that Ge has destabilizing effect for upward
throughflow and stabilizing effect for downward throughflow. And
γ has considerable destabilizing effect for upward throughflow and
insignificant destabilizing effect for downward throughflow.
Abstract: An investigation has been presented to analyze the
effect of internal heat source on the onset of Hadley-Prats flow in
a horizontal fluid saturated porous medium. We examine a better
understanding of the combined influence of the heat source and mass
flow effect by using linear stability analysis. The resultant eigenvalue
problem is solved by using shooting and Runga-Kutta methods for
evaluate critical thermal Rayleigh number with respect to various
flow governing parameters. It is identified that the flow is switch from
stabilizing to destabilizing as the horizontal thermal Rayleigh number
is enhanced. The heat source and mass flow increases resulting a
stronger destabilizing effect.
Abstract: Tuberculosis (TB) remains a leading cause of
infectious mortality. It is primarily transmitted by the respiratory
route, individuals with active disease may infect others through
airborne particles which releases when they cough, talk, or sing and
subsequently inhale by others. In order to study the effect of the
Bacilli Calmette-Guerin (BCG) vaccine after vaccination of TB
patient, a Vaccinated Susceptible Infected and Recovered (VSIR)
mathematical model is being developed to achieve the desired
objectives. The mathematical model, so developed, shall be used to
quantify the effect of BCG Vaccine to protect the immigrant young
adult person. Moreover, equations are to be established for the
disease endemic and free equilibrium states and subsequently utilized
in disease stability analysis. The stability analysis will give a
complete picture of disease annihilation from the total population if
the total removal rate from the infectious group should be greater
than total number of dormant infections produced throughout
infectious period.
Abstract: Bio-composites derived from plant fiber and/or bioderived
polymer, are likely more ecofriendly and demonstrate
competitive performance with petroleum based composites. In this
research, the bio phenol-formaldehyde (bio-PF) was used as a matrix
and oil palm empty fruit bunch fiber (EFB) as reinforcement. The
matrix was synthesized via liquefaction and condensation to enhance
the combination of phenol and formaldehyde, during the process.
Then, the bio-PF was mixed with different percentage of EFB (5%,
10%, 15% and 20%) and molded at 180oC. The samples that viewed
under scanning electron microscopy (SEM) showed an excellent
wettability and interaction between EFB and matrix. Samples of 10%
EFB gave the optimum properties of impact and hardness meanwhile
sample 15% of EFB gave the highest reading of flexural modulus
(MOE) and flexural strength (MOR). For thermal stability analysis, it
was found that the weight loss and the activation energy (Ea) of the
bio-composites samples were decreased as the filler content
increased.
Abstract: This paper describes a novel application of Fiber
Braggs Grating (FBG) sensors in the assessment of human postural
stability and balance on an unstable platform. In this work, FBG
sensor Stability Analyzing Device (FBGSAD) is developed for
measurement of plantar strain to assess the postural stability of
subjects on unstable platforms during different stances in eyes open
and eyes closed conditions on a rocker board. The studies are
validated by comparing the Centre of Gravity (CG) variations
measured on the lumbar vertebra of subjects using a commercial
accelerometer. The results obtained from the developed FBGSAD
depict qualitative similarities with the data recorded by commercial
accelerometer. The advantage of the FBGSAD is that it measures
simultaneously plantar strain distribution and postural stability of the
subject along with its inherent benefits like non-requirement of
energizing voltage to the sensor, electromagnetic immunity and
simple design which suits its applicability in biomechanical
applications. The developed FBGSAD can serve as a tool/yardstick to
mitigate space motion sickness, identify individuals who are
susceptible to falls and to qualify subjects for balance and stability,
which are important factors in the selection of certain unique
professionals such as aircraft pilots, astronauts, cosmonauts etc.
Abstract: At present, the evaluation of voltage stability
assessment experiences sizeable anxiety in the safe operation of
power systems. This is due to the complications of a strain power
system. With the snowballing of power demand by the consumers
and also the restricted amount of power sources, therefore, the system
has to perform at its maximum proficiency. Consequently, the
noteworthy to discover the maximum ability boundary prior to
voltage collapse should be undertaken. A preliminary warning can be
perceived to evade the interruption of power system’s capacity. The
effectiveness of line voltage stability indices (LVSI) is differentiated
in this paper. The main purpose of the indices used is to predict the
proximity of voltage instability of the electric power system. On the
other hand, the indices are also able to decide the weakest load buses
which are close to voltage collapse in the power system. The line
stability indices are assessed using the IEEE 14 bus test system to
validate its practicability. Results demonstrated that the implemented
indices are practically relevant in predicting the manifestation of
voltage collapse in the system. Therefore, essential actions can be
taken to dodge the incident from arising.
Abstract: In this paper, the dynamic characteristics of a threelobe
journal bearing lubricated with micropolar fluids are determined
by the linear stability theory. Lubricating oil containing additives and
contaminants is modelled as micropolar fluid. The modified
Reynolds equation is obtained using the micropolar lubrication theory
.The finite difference technique has been used to determine the
solution of the modified Reynolds equation. The dynamic
characteristics in terms of stiffness, damping coefficients, the critical
mass and whirl ratio are determined for various values of size of
material characteristic length and the coupling number. The
computed results show that the three-lobe bearing lubricated with
micropolar fluid exhibits better stability compared with that
lubricated with Newtonian fluid. According to the results obtained,
the effect of the parameter micropolar fluid is remarkable on the
dynamic characteristics and stability of the three-lobe bearing.
Abstract: The generalized wave equation models various
problems in sciences and engineering. In this paper, a new three-time
level implicit approach based on cubic trigonometric B-spline for the
approximate solution of wave equation is developed. The usual finite
difference approach is used to discretize the time derivative while
cubic trigonometric B-spline is applied as an interpolating function in
the space dimension. Von Neumann stability analysis is used to
analyze the proposed method. Two problems are discussed to exhibit
the feasibility and capability of the method. The absolute errors and
maximum error are computed to assess the performance of the
proposed method. The results were found to be in good agreement
with known solutions and with existing schemes in literature.
Abstract: The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.
Abstract: This paper deals with the problem of delay-dependent
stability for neural networks with distributed delays. Some new
sufficient condition are derived by constructing a novel
Lyapunov-Krasovskii functional approach. The criteria are
formulated in terms of a set of linear matrix inequalities, this is
convenient for numerically checking the system stability using the
powerful MATLAB LMI Toolbox. Moreover, in order to show the
stability condition in this paper gives much less conservative results
than those in the literature, numerical examples are considered.
Abstract: In this paper, a sliding mode control method based on the passivity approach is proposed to control the position of surface-mounted permanent magnet synchronous motors (PMSMs). Firstly, the dynamics of a PMSM was proved to be strictly passive. The position controller with an adaptive law was used to estimate the load torque to eliminate the chattering effects associated with the conventional sliding mode controller. The stability analysis of the overall position control system was carried out by adopting the passivity theorem instead of Lyapunov-type arguments. Finally, experimental results were provided to show that the good position tracking can be obtained, and exhibit robustness in the variations of the motor parameters and load torque disturbances.
Abstract: In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.