Search results for: Pendulum nonlinear dynamics

Authors: Yoichi Ishikawa, Yuichi Masukake, Yoshihisa Ishida

Abstract:

This paper presents a novel control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. The proposed method first identifies the nonlinear part of the chaotic system off-line and then constructs a model-following controller using only the estimated system parameters. Simulation results show the effectiveness of the proposed control scheme.

Keywords: Chaos, nonlinear plant, radial basis function network.

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Authors: Amir Taghavi, kourosh Parand, Hosein Fani

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In this paper we propose, a Lagrangian method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on Modified generalized Laguerre functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also compare this work with some other numerical results. The findings show that the present solution is highly accurate.

Keywords: Unsteady gas equation, Generalized Laguerre functions, Lagrangian method, Nonlinear ODE.

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Authors: Santosh Kr. Choudhary

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In this article, LQR based PID controller design for 3DOF helicopter system is investigated. The 3-DOF helicopter system is a benchmark laboratory model having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. This article first presents the mathematical model of the 3DOF helicopter system and then illustrates the basic idea and technical formulation for controller design. The paper explains the simple approach for the approximation of PID design parameters from the LQR controller gain matrix. The simulation results show that the investigated controller has both static and dynamic performance, therefore the stability and the quick control effect can be obtained simultaneously for the 3DOF helicopter system.

Keywords: 3DOF helicopter system, PID controller, LQR controller, modeling, simulation.

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Authors: Aras Adhami Mirhoseini, Mohammad J. Yazdanpanah

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In this paper, we consider nested sliding mode control of SISO nonlinear systems, perturbed by bounded matched and unmatched uncertainties. The systems are assumed to be in strict-feedback form. A step wise procedure is introduced to obtain the controller. In each step, a continuous sliding mode controller is designed as virtual control law. Then the next step sliding surface is defined by using this virtual controller. These sliding surfaces are selected as nonlinear static functions of the system states. Finally in the last step, smooth static state feedback control law is determined such that the output reaches the desired set-point while the system is forced arbitrary close to the intersection of sliding surfaces and the states remain bounded.

Keywords: Sliding mode control, Strict-feedback form, Unmatched uncertainty, output regulation.

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Authors: An Hong Nguyen, Chatpan Chintanapakdee, Toshiro Hayashikawa

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Presented herein is an assessment of current nonlinear static procedures (NSPs) for seismic evaluation of bucklingrestrained braced frames (BRBFs) which have become a favorable lateral-force resisting system for earthquake resistant buildings. The bias and accuracy of modal, improved modal pushover analysis (MPA, IMPA) and mass proportional pushover (MPP) procedures are comparatively investigated when they are applied to BRBF buildings subjected to two sets of strong ground motions. The assessment is based on a comparison of seismic displacement demands such as target roof displacements, peak floor/roof displacements and inter-story drifts. The NSP estimates are compared to 'exact' results from nonlinear response history analysis (NLRHA). The response statistics presented show that the MPP procedure tends to significantly overestimate seismic demands of lower stories of tall buildings considered in this study while MPA and IMPA procedures provide reasonably accurate results in estimating maximum inter-story drift over all stories of studied BRBF systems.

Keywords: Buckling-restrained braced frames, nonlinearresponse history analysis, nonlinear static procedure, seismicdemands.

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Authors: Gilberto Gonzalez-A

Abstract:

Bond graph models of an electrical transformer including the nonlinear saturation are presented. These models determine the relation between self and mutual inductances, and the leakage and magnetizing inductances of power transformers with two and three windings using the properties of a bond graph. The modelling and analysis using this methodology to three phase power transformers or transformers with internal incipient faults can be extended.

Keywords: Bond graph, electrical transformer, nonlinear saturation

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Authors: Hocine Hammoum, Karima Bouzelha, Lounis Ziani, Lounis Hamitouche

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In this paper, we study a complex structure which is an apartment building surmounted by a reinforced concrete water tank. The tank located on the top floor of the building is a container with capacity of 1000 m³. The building is complex in its design, its calculation and by its behavior under earthquake effect. This structure located in Algiers and aged of 53 years has been subjected to several earthquakes, but the earthquake of May 21^st, 2003 with a magnitude of 6.7 on the Richter scale that struck Boumerdes region at 40 Kms East of Algiers was fatal for it. It was downgraded after an investigation study because the central core sustained serious damage. In this paper, to estimate the degree of its damages, the seismic performance of the structure will be evaluated taking into account the hydrodynamic effect, using a static equivalent nonlinear analysis called pushover.

Keywords: Performance analysis, building, reinforced concrete tank, seismic analysis, nonlinear analysis, hydrodynamic, pushover.

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Authors: Fouad Salha , X. Guillaud

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Directional over current relays (DOCR) are commonly used in power system protection as a primary protection in distribution and sub-transmission electrical systems and as a secondary protection in transmission systems. Coordination of protective relays is necessary to obtain selective tripping. In this paper, an approach for efficiency reduction of DOCRs nonlinear optimum coordination (OC) is proposed. This was achieved by modifying the objective function and relaxing several constraints depending on the four constraints classification, non-valid, redundant, pre-obtained and valid constraints. According to this classification, the far end fault effect on the objective function and constraints, and in consequently on relay operating time, was studied. The study was carried out, firstly by taking into account the near-end and far-end faults in DOCRs coordination problem formulation; and then faults very close to the primary relays (nearend faults). The optimal coordination (OC) was achieved by simultaneously optimizing all variables (TDS and Ip) in nonlinear environment by using of Genetic algorithm nonlinear programming techniques. The results application of the above two approaches on 6-bus and 26-bus system verify that the far-end faults consideration on OC problem formulation don-t lose the optimality.

Keywords: Backup/Primary relay, Coordination time interval (CTI), directional over current relays, Genetic algorithm, time dial setting (TDS), pickup current setting (Ip), nonlinear programming.

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Authors: Attitude Stabilization of Satellites Using Random Dither Quantization

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Recently, the effectiveness of random dither quantization method for linear feedback control systems has been shown in several papers. However, the random dither quantization method has not yet been applied to nonlinear feedback control systems. The objective of this paper is to verify the effectiveness of random dither quantization method for nonlinear feedback control systems. For this purpose, we consider the attitude stabilization problem of satellites using discrete-level actuators. Namely, this paper provides a control method based on the random dither quantization method for stabilizing the attitude of satellites using discrete-level actuators.

Keywords: Quantized control, nonlinear systems, random dither quantization.

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

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Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well known formulas.

Keywords: Conjugate gradient method, conjugate gradient coefficient, global convergence.

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Authors: Ling Liu, Yuan Ye

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In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results.

Keywords: Discrete-time SIR epidemic model, time delay, nonlinear incidence rate, impulse.

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Authors: Soon-Hyun Park, Takami Matsuo

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This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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Authors: S.M. Lee, J.H. Koo, J.H. Park, S.C. Won

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In this paper, we propose synchronization of an array of nonlinear systems with time delays. The array of systems is decomposed into isolated systems to establish appropriate Lyapunov¬Krasovskii functional. Using the Lyapunov-Krasovskii functional, a sufficient condition for the synchronization is derived in terms of LMIs(Linear Matrix Inequalities). Delayed feedback control gains are obtained by solving the sufficient condition. Numerical examples are given to show the validity the proposed method.

Keywords: Synchronization, Delay, Lyapunov method, LMI.

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Authors: Sajid Iqbal, Masood Ahmed, Suhail Aftab Qureshi

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DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.

Keywords: Buck converter, boost converter, period- doubling, chaos, bifurcation, strange attractor.

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Authors: Fooad Karimi Ghaleh Jough, Mohsen Soori

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Today, the occurrence of progressive failure in structures has become a challenging issue, requiring the presentation of suitable solutions for structural resistance to this phenomenon. It is also necessary to evaluate the vulnerability of existing and under-construction buildings to progressive failure. The kind of lateral load-resisting system the building and its connections have is one of the most significant and influential variables in structural resistance to the risk of progressing failure. Using the "Alternative Path" approach suggested by the GSA2003 and UFC2013 recommendations, different configurations of semi-rigid connections against progressive failure are offered in this study. In order to do this, the Opensees program was used to model nine distinct semi-rigid connection configurations on a three-story Special Area of Conservation (SAC) structure, accounting for the impact of connection stiffness. Then, using nonlinear dynamic analysis, the effects of column removal were explored in two scenarios: corner column removal and middle column removal on the first level. Nonlinear static analysis results showed that when a column is removed, structures with semi-rigid connections experience larger displacements, which result in the construction of a plastic hinge. Furthermore, it was clear from the findings of the nonlinear static analysis that the possibility of progressive failure increased with the number of semi-rigid connections in the structure.

Keywords: Semi-rigid, nonlinear static analysis, progressive collapse, alternative path.

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Authors: Etsuo Morishita

Abstract:

This paper presents the project and experiment-based fluid dynamics education in Meisei University, a private institution in Tokyo, Japan. We pay attention not only to the basic engineering courses but also to the practical aspect of engineering experience. So, we prepare courses called the Projects from I to VI. The Projects I and II are designed for the first year, III and IV are designated for the second year, V and VI are prepared for the third year, respectively. Each supervisor is responsible for two of these projects every year. When students take the Project V and VI at the third year, we automatically assume that these students will join the lab of the project for the graduation thesis. We would like to show our experience in the Project I in the summer term, 2016. In this project, we introduce a traction flight vehicle called Cat Flyer. This is a kind of a kite towed by a car for example. This is very similar to parasailing, but flight is possible even on the roads. Experiments in mechanical engineering education are also very important, and we would like to explain our course on centrifugal pump, venture, and orifice. Although these are described in detail in the text books of fluid dynamics, it is still crucial to have practical experiments as a student.

Keywords: Aerodynamics, experiment, fluid dynamics, project.

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Authors: Hasimah Sapiri, Anton Abdulbasah Kamil, Razman Mat Tahar, Hanafi Tumin

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Salary risk and demographic risk have been identified as main risks in analyzing pension expenditure particularly in Defined Benefit pension plan. Therefore, public pension plan in Malaysia is studied to analyze pension expenditure due to salary and demographic risk. Through the literature review and interview session with several officers in public sector, factors affecting pension expenditure are determined. Then, the inter-relationships between these factors are analyzed through causal loop diagram. The System Dynamics model is later developed using iThink software to show how demographic and salary changes affect the pension expenditure. Then, by using actual data, the impact of different policy scenarios on pension expenditure is analyzed. It is shown that dynamics simulation model of pension expenditure is useful to evaluate the impact of changes and policy decisions on risk particularly involving demographic and salary risk.

Keywords: Demographic and Salary risk, Pension Expenditure, Public Policy, System Dynamics.

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Authors: Daniela Elena Marinescu, Ioana Manafi, Dumitru Marin

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We consider a Principal-Agent model with the Principal being a seller who does not know perfectly how much the buyer (the Agent) is willing to pay for the good. The buyer-s preferences are hence his private information. The model corresponds to the nonlinear pricing problem of Maskin and Riley. We assume there are three types of Agents. The model is solved using “informational rents" as variables. In the last section we present the main characteristics of the optimal contracts in asymmetric information and some possible extensions of the model.

Keywords: Adverse selection, asymmetric information, informational rent, nonlinear pricing, optimal contract

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Authors: B. Kiyani, R. H. Amiri, S. H. Hosseini, A. Bourouni, A. Karimi

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Nowadays, offshore's complicated facilities need their own communications requirements. Nevertheless, developing and real-world applications of new communications technology are faced with tremendous problems for new technology users, developers and implementers. Traditional systems engineering cannot be capable to develop a new technology effectively because it does not consider the dynamics of the process. This paper focuses on the design of a holistic model that represents the dynamics of new communication technology development within offshore industry. The model shows the behavior of technology development efforts. Furthermore, implementing this model, results in new and useful insights about the policy option analysis for developing a new communications technology in offshore industry.

Keywords: Technology development, Offshore industry, Systemdynamics, Voice Over IP.

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is reexamined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: Ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness.

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Authors: József Valyon, Gábor Horváth

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In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi

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In this paper a real-time obstacle avoidance approach for both autonomous and non-autonomous dynamical systems (DS) is presented. In this approach the original dynamics of the controller which allow us to determine safety margin can be modulated. Different common types of DS increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle especially when robot moves very fast in changeable complex environments. The method is validated by simulation and influence of different autonomous and non-autonomous DS such as important characteristics of limit cycles and unstable DS. Furthermore, the position of different obstacles in complex environment is explained. Finally, the verification of avoidance trajectories is described through different parameters such as safety factor.

Keywords: Limit cycles, Nonlinear dynamical system, Real time obstacle avoidance.

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Authors: Mahdi Kiani, Hassan Salarieh, Aria Alasty, S. Mahdi Darbandi

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The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.

Keywords: Active magnetic bearing, three pole AMB, hybrid control, Lyapunov function.

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Authors: E. Sobhani-Tehrani, K. Khorasani, N. Meskin

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This paper presents a novel integrated hybrid approach for fault diagnosis (FD) of nonlinear systems. Unlike most FD techniques, the proposed solution simultaneously accomplishes fault detection, isolation, and identification (FDII) within a unified diagnostic module. At the core of this solution is a bank of adaptive neural parameter estimators (NPE) associated with a set of singleparameter fault models. The NPEs continuously estimate unknown fault parameters (FP) that are indicators of faults in the system. Two NPE structures including series-parallel and parallel are developed with their exclusive set of desirable attributes. The parallel scheme is extremely robust to measurement noise and possesses a simpler, yet more solid, fault isolation logic. On the contrary, the series-parallel scheme displays short FD delays and is robust to closed-loop system transients due to changes in control commands. Finally, a fault tolerant observer (FTO) is designed to extend the capability of the NPEs to systems with partial-state measurement.

Keywords: Hybrid fault diagnosis, Dynamic neural networks, Nonlinear systems.

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Authors: Ji Hoon Kim, Hyung Gi Min, Jae Dong Cho, Jae Hoon Jang, Sung-Ha Kwon, Eun Tae Jeung

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Since MEMS gyro sensors measure not angle of rotation but angular rate, an estimator is designed to estimate the angles in many applications. Gyro and accelerometer are used to improve estimating accuracy of the angle. This paper presents a method of finding filter coefficients of the well-known estimator which is to get rotation angles from gyro and accelerometer data. In order to verify the performance of our method, the estimated angle is compared with the encoder output in a rotary pendulum system.

Keywords: gyro, accelerometer, estimator, least square.

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Authors: Nicolò Vaiana, Giorgio Serino

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In this paper, an advanced Nonlinear Exponential Model (NEM), able to simulate the uniaxial dynamic behavior of seismic isolators having a continuously decreasing tangent stiffness with increasing displacement in the relatively large displacements range and a hardening or softening behavior at large displacements, is presented. The mathematical model is validated by comparing the experimental force-displacement hysteresis loops obtained during cyclic tests, conducted on a helical wire rope isolator and a recycled rubber-fiber reinforced bearing, with those predicted analytically. Good agreement between the experimental and simulated results shows that the proposed model can be an effective numerical tool to predict the force-displacement relationship of seismic isolation devices within the large displacements range. Compared to the widely used Bouc-Wen model, unable to simulate the response of seismic isolators at large displacements, the proposed one allows to avoid the numerical solution of a first order nonlinear ordinary differential equation for each time step of a nonlinear time history analysis, thus reducing the computation effort. Furthermore, the proposed model can simulate the smooth transition of the hysteresis loops from small to large displacements by adopting only one set of five parameters determined from the experimental hysteresis loops having the largest amplitude.

Keywords: Base isolation, hardening behavior, nonlinear exponential model, seismic isolators, softening behavior.

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Authors: Omid Heydarnia, Akbar Allahverdizadeh, Behnam Dadashzadeh, M. R. Sayyed Noorani

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Underactuated biped robots control is one of the interesting topics in robotics. The main difficulties are its highly nonlinear dynamics, open-loop instability, and discrete event at the end of the gait. One of the methods to control underactuated systems is the partial feedback linearization, but it is not robust against uncertainties and disturbances that restrict its performance to control biped walking and running. In this paper, fuzzy partial feedback linearization is presented to overcome its drawback. Numerical simulations verify the effectiveness of the proposed method to generate stable and robust biped walking and running gaits.

Keywords: Underactuated system, biped robot, fuzzy control, partial feedback linearization.

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Authors: Randhir Singh Baghel, Joydip Dhar, Renu Jain

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In this paper, for the understanding of the phytoplankton dynamics in marine ecosystem, a susceptible and an infected class of phytoplankton population is considered in spatiotemporal domain. Here, the susceptible phytoplankton is growing logistically and the growth of infected phytoplankton is due to the instantaneous Holling type-II infection response function. The dynamics are studied in terms of the local and global stabilities for the system and further explore the possibility of Hopf -bifurcation, taking the half saturation period as (i.e., ) the bifurcation parameter in temporal domain. It is also observe that the reaction diffusion system exhibits spatiotemporal chaos and pattern formation in phytoplankton dynamics, which is particularly important role play for the spatially extended phytoplankton system. Also the effect of the diffusion coefficient on the spatial system for both one and two dimensional case is obtained. Furthermore, we explore the higher-order stability analysis of the spatial phytoplankton system for both linear and no-linear system. Finally, few numerical simulations are carried out for pattern formation.

Keywords: Phytoplankton dynamics, Reaction-diffusion system, Local stability, Hopf-bifurcation, Global stability, Chaos, Pattern Formation, Higher-order stability analysis.

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Authors: Jaipong Kasemsuwan

Abstract:

This paper presents the finite difference scheme and the numerical simulation of suspended string. The vibration solutions when the various external forces are taken into account are obtained and compared with the solutions without external force. In addition, we also investigate how the external forces and their powers and coefficients affect the amplitude of vibration.

Keywords: Nonlinear external forces, Numerical simulation, Suspended string equation.

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Authors: Delfim Soares Jr., Webe J. Mansur

Abstract:

The Time-Domain Boundary Element Method (TDBEM) is a well known numerical technique that handles quite properly dynamic analyses considering infinite dimension media. However, when these analyses are also related to nonlinear behavior, very complex numerical procedures arise considering the TD-BEM, which may turn its application prohibitive. In order to avoid this drawback and model nonlinear infinite media, the present work couples two BEM formulations, aiming to achieve the best of two worlds. In this context, the regions expected to behave nonlinearly are discretized by the Domain Boundary Element Method (D-BEM), which has a simpler mathematical formulation but is unable to deal with infinite domain analyses; the TD-BEM is employed as in the sense of an effective non-reflexive boundary. An iterative procedure is considered for the coupling of the TD-BEM and D-BEM, which is based on a relaxed renew of the variables at the common interfaces. Elastoplastic models are focused and different time-steps are allowed to be considered by each BEM formulation in the coupled analysis.

Keywords: Boundary Element Method, Dynamic Elastoplastic Analysis, Iterative Coupling, Multiple Time-Steps.

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