Search results for: nonlinear exponential model

Authors: Jin-Wei Liang, Hung-Yi Chen, Lung Lin

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In this paper feedforward controller is designed to eliminate nonlinear hysteresis behaviors of a piezoelectric stack actuator (PSA) driven system. The control design is based on inverse Prandtl-Ishlinskii (P-I) hysteresis model identified using particle swarm optimization (PSO) technique. Based on the identified P-I model, both the inverse P-I hysteresis model and feedforward controller can be determined. Experimental results obtained using the inverse P-I feedforward control are compared with their counterparts using hysteresis estimates obtained from the identified Bouc-Wen model. Effectiveness of the proposed feedforward control scheme is demonstrated. To improve control performance feedback compensation using traditional PID scheme is adopted to integrate with the feedforward controller.

Keywords: the Bouc-Wen hysteresis model, particle swarm optimization, Prandtl-Ishlinskii model, automation engineering

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

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In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Chun-Qing Li, Guoyang Fu, Wei Yang

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A significant portion of current water networks is made of cast iron pipes. Due to aging and deterioration with corrosion being the most predominant mechanism, the failure rate of cast iron pipes is very high. Although considerable research has been carried out in the past few decades, most are on the effect of corrosion on the structural capacity of pipes using strength theory as the failure criterion. This paper presents a reliability-based methodology for the assessment of corrosion affected cast iron pipe cracking failures. A nonlinear limit state function taking into account all three fracture modes is proposed for brittle metal pipes with mixed mode fracture. A stochastic model of the load effect is developed, and time-dependent reliability method is employed to quantify the probability of failure and predict the remaining service life. A case study is carried out using the proposed methodology, followed by sensitivity analysis to investigate the effects of the random variables on the probability of failure. It has been found that the larger the inclination angle or the Mode I fracture toughness is, the smaller the probability of pipe failure is. It has also been found that the multiplying and exponential coefficients k and n in the power law corrosion model and the internal pressure have the most influence on the probability of failure for cast iron pipes. The methodology presented in this paper can assist pipe engineers and asset managers in developing a risk-informed and cost-effective strategy for better management of corrosion-affected pipelines.

Keywords: corrosion, inclined surface cracks, pressurized cast iron pipes, stress intensity

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Abdulrahman Abdulrahman

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A side weir is a hydraulic structure set into the side of a channel. This structure is used for water level control in channels, to divert flow from a main channel into a side channel when the water level in the main channel exceeds a specific limit and as storm overflows from urban sewerage system. Computation of water surface over the side weirs is essential to determine the flow rate of the side weir. Analytical solutions for water surface profile along rectangular side weir are available only for the special cases of rectangular and trapezoidal channels considering constant specific energy. In this paper, a rectangular side weir located in a combined (trapezoidal with exponential) channel was considered. Expanding binominal series of integer and fraction powers and the using of reduction formula of cosine function integrals, a general analytical formula was obtained for water surface profile along a side weir in a combined (trapezoidal with exponential) channel. Since triangular, rectangular, trapezoidal and parabolic cross-sections are special cases of the combined cross section, the derived formula, is applicable to triangular, rectangular, trapezoidal cross-sections as analytical solution and semi-analytical solution to parabolic cross-section with maximum relative error smaller than 0.76%. The proposed solution should be a useful engineering tool for the evaluation and design of side weirs in open channel.

Keywords: analytical solution, combined channel, exponential channel, side weirs, trapezoidal channel, water surface profile

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Authors: Blair D. Macdonald

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After nearly one hundred years of its origin, foundational quantum mechanics remains one of the greatest unexplained mysteries in physicists today. Within this time, chaos theory and its geometry, the fractal, has developed. In this paper, the propagation behaviour with an iteration of a simple fractal, the Koch Snowflake, was described and analysed. From an arbitrary observation point within the fractal set, the fractal propagates forward by oscillation—the focus of this study and retrospectively behind by exponential growth from a point beginning. It propagates a potentially infinite exponential oscillating sinusoidal wave of discrete triangle bits sharing many characteristics of light and quantum entities. The model's wave speed is potentially constant, offering insights into the perception and a direction of time where, to an observer, when travelling at the frontier of propagation, time may slow to a stop. In isolation, the fractal is a superposition of component bits where position and scale present a problem of location. In reality, this problem is experienced within fractal landscapes or fields where 'position' is only 'known' by the addition of information or markers. The quantum' measurement problem', 'uncertainty principle,' 'entanglement,' and the classical-quantum interface are addressed; these are a problem of scale invariance associated with isolated fractality. Dual forward and retrospective perspectives of the fractal model offer the opportunity for unification between quantum mechanics and cosmological mathematics, observations, and conjectures. Quantum and cosmological problems may be different aspects of the one fractal geometry.

Keywords: measurement problem, observer, entanglement, unification

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Authors: Eva L. Sanjuán, Jacinto Martín, M. Isabel Parra, Mario M. Pizarro

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In Extreme Value Theory, inference estimation for the parameters of the distribution is made employing a small part of the observation values. When block maxima values are taken, many data are discarded. We developed a new Bayesian inference model to seize all the information provided by the data, introducing informative priors and using the relations between baseline and limit parameters. Firstly, we studied the accuracy of the new model for three baseline distributions that lead to a Gumbel extreme distribution: Exponential, Normal and Gumbel. Secondly, we considered mixtures of Normal variables, to simulate practical situations when data do not adjust to pure distributions, because of perturbations (noise).

Keywords: bayesian inference, extreme value theory, Gumbel distribution, highly informative prior

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Jun Tian, Yu Yang, Liping Zhang, Qianhua Kan

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Experimental results show that SA 508-3 steel exhibits temperature dependent cyclic softening characteristic and obvious ratcheting behaviors, and dynamic strain age was observed at temperature range of 200 ºC to 350 ºC. Based on these observations, a temperature dependent cyclic plastic constitutive model was proposed by introducing the nonlinear cyclic softening and kinematic hardening rules, and the dynamic strain age was also considered into the constitutive model. Comparisons between experiments and simulations were carried out to validate the proposed model at elevated temperature.

Keywords: constitutive model, elevated temperature, ratcheting, SA 508-3

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Authors: Alireza Toloei, Ahmad R. Saffary, Reza Ghasemi

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Due to the growing need for energy and limited fossil resources, the use of renewable energy, particularly wind is strongly favored. We all wind energy can’t be saved. Betz law, 59% of the total kinetic energy of the wind turbine is extracting. Therefore turbine control to achieve maximum performance and maintain stable conditions seem necessary. In this article, we plan for a horizontal axis wind turbine variable-speed variable-pitch nonlinear controller to obtain maximum output power. The model presented in this article, including a wide range of wind turbines are horizontal axis. However, the parameters used in this model is from Vestas V29 225 kW wind turbine. We designed second order sliding mode controller, which was robust in the face of changes in wind speed and it eliminated chattering by using of super twisting algorithm. Finally, using MATLAB software to simulate the results we considered the accuracy of the simulation results.

Keywords: non linear controller, robust, sliding mode, kinetic energy

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Authors: Morteza Shayan Arani, Mohammadamin Esmailzadehazimi, Mohammadreza Moeini, Mohammad Toorani, Aouni A. Lakis

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This paper investigates the nonlinear response of thin, incompressible, hyperelastic cylindrical shells in the presence of a time-varying temperature field while considering initial geometric imperfections. The governing equations of motion are derived using an improved Donnell's shallow shell theory. The hyperelastic material is modeled using the Mooney-Rivlin model with two parameters, incorporating temperature-dependent terms. The Lagrangian method is applied to obtain the equation of motion. The resulting governing equation is addressed through the Lindstedt-Poincaré and Multiple Scale methods. The linear and nonlinear models presented in this study are verified against existing open literature, demonstrating the accuracy and reliability of the presented model. The study focuses on understanding the influence of temperature variations and geometrical imperfections on the natural frequency and amplitude-frequency response of the systems. Notably, the investigation reveals the coexistence of hardening and softening peaks in the amplitude-frequency response, which vary in magnitude depending on these parameters. Additionally, resonance peaks exhibit changes as a result of temperature and geometric imperfections.

Keywords: hyperelastic material, cylindrical shell, geometrical nonlinearity, material naolinearity, initial geometric imperfection, temperature gradient, hardening and softening

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Mohamed Khiatine, Ramdane Bahar

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The research performed during the last years has revealed that the seismic response of the soilis significantly non linear and hysteresis to the deformationsitundergoes during earthquakes and notably during violent shaking. This nonlinear behavior of soils can be characterized by curves showing the evolution of shearmodulus and damping versus distortion. Also, in this context, geotechnical seismic engineering problems often require the characterization of dynamic soil properties over a wide range of deformation. This determination of dynamic soil properties is key to predict the seismic response of soils for important civil engineering structures. This communication discusses a numerical analysis method for evaluating the nonlinear dynamic properties of soils in Algeriausing the FLAC2D software and the database resulting from geophysical and geotechnical studies when laboratory dynamic tests are not available. The nonlinear model proposed by Ramberg-Osgood and limited by the Mohr-coulomb criterion is used.

Keywords: degradation, shear modulus, damping, ramberg-osgood, numerical analysis.

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Authors: Abdelkader Merah, Kada Hartani

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A reference model based control approach for improving behavior following car is proposed in this paper. The reference model is nonlinear and provides dynamic solutions consistent with safety constraints and comfort specifications. a robust fuzzy logic based control strategy is further proposed in this paper. A set of simulation results showing the suitability of the proposed technique for various demanding cenarios is also included in this paper.

Keywords: reference model, longitudinal control, fuzzy logic, design of car

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Authors: Johnson Audu, Faisal Fairag

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In a bounded subset of R^d, d=2 or 3, we consider the Darcy-Forchheimer power model with the exponent 1 < m ≤ 2 for a single-phase strong-inertia fluid flow in a porous medium. Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence and uniqueness of solution (u, p) in L^(m+1 ) (Ω)^d X (W^(1,(m+1)/m) (Ω)^d ⋂L_0^2 (Ω)^d) and its stability.

Keywords: porous media, power law, strong inertia, nonlinear, monotone type

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Authors: Xiang Zhang, David Rey, S. Travis Waller

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Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Keywords: parameter calibration, sequential quadratic programming, stochastic user equilibrium, traffic assignment, transportation planning

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Authors: Fang Li, Xie-Yuan Yin, Xie-Zhen Yin

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Instability and breakup of electrified viscoelastic liquid jets are involved in various applications such as inkjet printing, fuel atomization, the pharmaceutical industry, electrospraying, and electrospinning. Studying on the instability of electrified viscoelastic liquid jets is of theoretical and practical significance. We built a one-dimensional electrified viscoelastic model to study the nonlinear instability behavior of a perfecting conducting, slightly viscoelastic liquid jet under a radial electric field. The model is solved numerically by using an implicit finite difference scheme together with a boundary element method. It is found that under a radial electric field a viscoelastic liquid jet still evolves into a beads-on-string structure with a thin filament connecting two adjacent droplets as in the absence of an electric field. A radial electric field exhibits limited influence on the decay of the filament thickness in the nonlinear evolution process of a viscoelastic jet, in contrast to its great enhancing effect on the linear instability of the jet. On the other hand, a radial electric field can induce axial non-uniformity of the first normal stress difference within the filament. Particularly, the magnitude of the first normal stress difference near the midpoint of the filament can be greatly decreased by a radial electric field. Decreasing the extensional stress by a radial electric field may found applications in spraying, spinning, liquid bridges and others. In addition, the effect of a radial electric field on the formation of satellite droplets is investigated on the parametric plane of the dimensionless wave number and the electrical Bond number. It is found that satellite droplets may be formed for a larger axial wave number at a larger radial electric field. The present study helps us gain insight into the nonlinear instability characteristics of electrified viscoelastic liquid jets.

Keywords: non linear instability, one-dimensional models, radial electric fields, viscoelastic liquid jets

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Authors: Aliasghar Arab

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Autonomous robots interacting with humans, as safety-critical nonlinear control systems, are complex closed-loop cyber-physical dynamical machines. Keeping these intelligent yet complicated systems safe and smooth during their operations is challenging. The aim of the safe predictive output feedback linearization control synthesis is to design a novel controller for smooth trajectory following while unsafe situations must be avoided. The controller design should obtain a linearized output for smoothness and invariance to a safety subset. Inspired by finite-horizon nonlinear model predictive control, the problem is formulated as constrained nonlinear dynamic programming. The safety constraints can be defined as control barrier functions. Avoiding unsafe maneuvers and performing smooth motions increases the predictability of the robot’s movement for humans when robots and people are working together. Our results demonstrate the proposed output linearization method obeys the safety constraints and, compared to existing safety-guaranteed methods, is smoother and performs better.

Keywords: robotics, collaborative robots, safety, autonomous robots

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Authors: E. Feulefack Songong, A. Zingoni

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A vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Although vibrations can be linear or nonlinear depending on the basic components of the system, the interest is mostly pointed towards nonlinear vibrations. This is because most structures around us are to some extent nonlinear and also because we need more accurate values in an analysis. The goal of this research is the integration of nonlinearities in the development and validation of structural models and to ameliorate the resistance of structures when subjected to loads. Although there exist many types of nonlinearities, this thesis will mostly focus on the vibration of free and undamped systems incorporating nonlinearity due to stiffness. Nonlinear stiffness has been a concern to many engineers in general and Civil engineers in particular because it is an important factor that can bring a good modification and amelioration to the response of structures when subjected to loads. The analysis of systems will be done analytically and then numerically to validate the analytical results. We will first show the benefit and importance of stiffness nonlinearity when it is implemented in the structure. Secondly, We will show how its integration in the structure can improve not only the structure’s performance but also its response when subjected to loads. The results of this study will be valuable to practicing engineers as well as industry practitioners in developing better designs and tools for their structures and mechanical devices. They will also serve to engineers to design lighter and stronger structures and to give good predictions as for the behavior of structures when subjected to external loads.

Keywords: elastic foundation, nonlinear, plates, stiffness, structures, vibration

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Authors: S. A. Al-Qallaf, S. A. Al-Mawsawi, A. Haider

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In order to evaluate the performance of a unified power flow controller (UPFC), mathematical models for steady state and dynamic analysis are to be developed. The steady state model is mainly concerned with the incorporation of the UPFC in load flow studies. Several load flow models for UPFC have been introduced in literature, and one of the most reliable models is the decoupled UPFC model. In spite of UPFC decoupled load flow model simplicity, it is more robust compared to other UPFC load flow models and it contains unique capabilities. Some shortcoming such as additional set of nonlinear equations are to be solved separately after the load flow solution is obtained. The aim of this study is to investigate the different control strategies that can be realized in the decoupled load flow model (individual control and combined control), and the impact of the location of the UPFC in the network on its control parameters.

Keywords: UPFC, decoupled model, load flow, control parameters

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Authors: H. Taylan Selamlar, I. Yavuz, G. Yapar

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It is difficult to make predictions especially about the future and making accurate predictions is not always easy. However, better predictions remain the foundation of all science therefore the development of accurate, robust and reliable forecasting methods is very important. Numerous number of forecasting methods have been proposed and studied in the literature. There are still two dominant major forecasting methods: Box-Jenkins ARIMA and Exponential Smoothing (ES), and still new methods are derived or inspired from them. After more than 50 years of widespread use, exponential smoothing is still one of the most practically relevant forecasting methods available due to their simplicity, robustness and accuracy as automatic forecasting procedures especially in the famous M-Competitions. Despite its success and widespread use in many areas, ES models have some shortcomings that negatively affect the accuracy of forecasts. Therefore, a new forecasting method in this study will be proposed to cope with these shortcomings and it will be called ATA method. This new method is obtained from traditional ES models by modifying the smoothing parameters therefore both methods have similar structural forms and ATA can be easily adapted to all of the individual ES models however ATA has many advantages due to its innovative new weighting scheme. In this paper, the focus is on modeling the trend component and handling seasonality patterns by utilizing classical decomposition. Therefore, ATA method is expanded to higher order ES methods for additive, multiplicative, additive damped and multiplicative damped trend components. The proposed models are called ATA trended models and their predictive performances are compared to their counter ES models on the M3 competition data set since it is still the most recent and comprehensive time-series data collection available. It is shown that the models outperform their counters on almost all settings and when a model selection is carried out amongst these trended models ATA outperforms all of the competitors in the M3- competition for both short term and long term forecasting horizons when the models’ forecasting accuracies are compared based on popular error metrics.

Keywords: accuracy, exponential smoothing, forecasting, initial value

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Authors: Alakija Temitope Olufunmilayo, Akinyemi, Yagba Joy

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Hepatitis is the inflammation of the liver tissue that can cause whiteness of the eyes (Jaundice), lack of appetite, vomiting, tiredness, abdominal pain, diarrhea. Hepatitis is acute if it resolves within 6 months and chronic if it last longer than 6 months. Acute hepatitis can resolve on its own, lead to chronic hepatitis or rarely result in acute liver failure. Chronic hepatitis may lead to scarring of the liver (Cirrhosis), liver failure and liver cancer. Modelling Hepatitis B may become necessary in order to reduce its spread. So, dynamic SIR model can be used. This model consists of a system of three coupled non-linear ordinary differential equation which does not have an explicit formula solution. It is an epidemiological model used to predict the dynamics of infectious disease by categorizing the population into three possible compartments. In this study, a five-compartment dynamic model of Hepatitis B disease was proposed and developed by adding control measure of sensitizing the public called awareness. All the mathematical and statistical formulation of the model, especially the general equilibrium of the model, was derived, including the nonlinear least square estimators. The initial parameters of the model were derived using nonlinear least square embedded in R code. The result study shows that the proportion of Hepatitis B patient in the study population is 1.4 per 1,000,000 populations. The estimated Hepatitis B induced death rate is 0.0108, meaning that 1.08% of the infected individuals die of the disease. The reproduction number of Hepatitis B diseases in Nigeria is 6.0, meaning that one individual can infect more than 6.0 people. The effect of sensitizing the public on the basic reproduction number is significant as the reproduction number is reduced. The study therefore recommends that programme should be designed by government and non-governmental organization to sensitize the entire Nigeria population in order to reduce cases of Hepatitis B disease among the citizens.

Keywords: hepatitis B, modelling, non-linear ordinary differential equation, sihar model, sensitization

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Authors: Ali Afaghi, Sehraneh Ghaemi

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The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.

Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs

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Authors: A. Zanj, F. He

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In the current paper, a domain independent conduction model compatible for multi-physical system dynamic investigations is suggested. By means of a port-based approach, a classical nonlinear conduction model containing physical states is first represented. A compatible discrete configuration of the thermal domain in line with the elastic domain is then generated through the enhancement of the configuration of the conventional thermal element. The presented simulation results of a sample structure indicate that the suggested conductive model can cover a wide range of dynamic behavior of the thermal domain.

Keywords: multi-physical domain, conduction model, port based modeling, dynamic interaction, physical modeling

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Authors: Ali Ballouch, Nourelhouda Choukri, Zouhair Soufiani, Mohamed El Jouad, Mohamed Addou

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For several years, significant research has been developed in the areas of applications of semiconductor wide bandgap such as ZnO in optoelectronics. This oxide has the advantage of having a large exciton energy (60 meV) three times higher than that of GaN (21 meV) or ZnS (20 meV). This energy makes zinc oxide resistant for laser irradiations and very interesting for the near UV-visible optic, as well as for studying physical microcavities. A high-energy direct gap at room temperature (Eg > 1 eV) which makes it a potential candidate for emitting devices in the near UV and visible. Our work is to study the nonlinear optical properties, mainly the nonlinear third-order susceptibility of europium doped Zinc oxide thin films. The samples were prepared by chemical vapor spray method (Spray), XRD, SEM technique, THG were used for characterization. In this context, the influence of europium doping on the nonlinear optical response of the Zinc oxide was investigated. The nonlinear third-order properties depend on the physico-chemical parameters (crystallinity, strain, and surface roughness), the nature and the level of doping, temperature.

Keywords: ZnO, characterization, non-linear optical properties, optoelectronics

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Authors: Ce Liu, Wei Huo

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A nonlinear trajectory tracking controller for quadrotor helicopter based on controlled Lagrangian (CL) method is proposed in this paper. A Lagrangian system with virtual angles as generated coordinates rather than Euler angles is developed. Based on the model, the matching conditions presented by nonlinear partial differential equations are simplified and explicitly solved. Smooth tracking control laws and the range of control parameters are deduced based on the controlled energy of closed-loop system. Besides, a constraint condition for reference accelerations is deduced to identify the trackable reference trajectories by the proposed controller and to ensure the stability of the closed-loop system. The proposed method in this paper does not rely on the division of the quadrotor system, and the design of the control torques does not depend on the thrust as in backstepping or hierarchical control method. Simulations for a quadrotor model demonstrate the feasibility and efficiency of the theoretical results.

Keywords: quadrotor, trajectory tracking control, controlled lagrangians, underactuated system

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Authors: Zahir Bakiri, Saci Nacefa

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In this paper a comparison in made between two models, with and without dispersion term, and focused on the characterization of the movement of the sludge blanket in the secondary sedimentation tank using the solid flux theory and the velocity settling. This allowed us develop a one-dimensional models, with and without dispersion based on a thorough experimental study carried out in situ and the application of online data which are the mass load flow, transfer concentration, and influent characteristic. On the other hand, in the proposed model, the new settling velocity law (double-exponential function) used is based on the Vesilind function.

Keywords: wastewater, activated sludge, sedimentation, settling velocity, settling models

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza khalili, Sara Akbari, Davood Domiri Ganji

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In this symposium, our aims are accuracy, capabilities and power at solving of the complicate non-linear differential at the reaction chemical in the catalyst reactor (heterogeneous reaction). Our purpose is to enhance the ability of solving the mentioned nonlinear differential equations at chemical engineering and similar issues with a simple and innovative approach which entitled ‘’Akbari-Ganji's Method’’ or ‘’AGM’’. In this paper we solve many examples of nonlinear differential equations of chemical reactions and its investigate. The chemical reactor with the energy changing (non-isotherm) in two reactors of mixed and plug are separately studied and the nonlinear differential equations obtained from the reaction behavior in these systems are solved by a new method. Practically, the reactions with the energy changing (heat or cold) have an important effect on designing and function of the reactors. This means that possibility of reaching the optimal conditions of operation for the maximum conversion depending on nonlinear nature of the reaction velocity toward temperature, results in the complexity of the operation in the reactor. In this case, the differential equation set which governs the reactors can be obtained simultaneous solution of mass equilibrium and energy and temperature changing at concentration.

Keywords: new method (AGM), nonlinear differential equation, tubular and mixed reactors, catalyst bed

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Authors: El Amine Nebbat

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A void is a dust-free region in dusty plasma, a medium formed of electrons, ions, and charged dust (grain). This structure appears in multiple experimental works. Several researchers have developed models to understand it. Recently, Nebbat and Annou proposed a nonlinear model that describes the void in non-viscos plasma, where the particles of the dusty plasma are treated as a fluid. In fact, the void appears even in dense dusty plasma where viscosity exists through the strong interaction between grains, so in this work, we augment the nonlinear model of Nebbat and Annou by introducing viscosity into the fluid equations. The analysis of the data of the numerical resolution confirms the important effect of this parameter (viscosity). The study revealed that the viscosity increases the dimension of the void for certain dimensions of the grains, and its effect on the value of the density of the grains at the boundary of the void is inversely proportional to their radii, i.e., this density increase for submicron grains and decrease for others. Finally, this parameter reduces the rings of dust density which surround the void.

Keywords: voids, dusty plasmas, variable charge, density, viscosity

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Authors: Y. T. Tsai, Jin H. Huang

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The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method

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