Search results for: Adaptive beam forming
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1461

Search results for: Adaptive beam forming

1401 Cognitive Emotion Regulation in Children Is Attributable to Parenting Style, Not to Family Type and Child’s Gender

Authors: AKM Rezaul Karim, Tania Sharafat, Abu Yusuf Mahmud

Abstract:

The study aimed to investigate whether cognitive emotion regulation in children varies with parenting style, family type and gender. Toward this end, cognitive emotion regulation and perceived parenting style of 206 school children were measured. Standard regression analyses of data revealed that the models were significant and explained 17.3% of the variance in adaptive emotion regulation (Adjusted =0.173; F=9.579, p<.001), and 7.1% of the variance in less adaptive emotion regulation (Adjusted =.071, F=4.135, p=.001). Results showed that children’s cognitive emotion regulation is functionally associated with parenting style, but not with family type and their gender. Amongst three types of parenting, authoritative parenting was the strongest predictor of the overall adaptive emotion regulation while authoritarian parenting was the strongest predictor of the overall less adaptive emotion regulation. Permissive parenting has impact neither on adaptive nor on less adaptive emotion regulation. The findings would have important implications for parents, caregivers, child psychologists, and other professionals working with children or adolescents.

Keywords: Cognitive Emotion Regulation, Adaptive, Less Adaptive, Parenting Style, Family Type.

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1400 Texture Characterization Based on a Chandrasekhar Fast Adaptive Filter

Authors: Mounir Sayadi, Farhat Fnaiech

Abstract:

In the framework of adaptive parametric modelling of images, we propose in this paper a new technique based on the Chandrasekhar fast adaptive filter for texture characterization. An Auto-Regressive (AR) linear model of texture is obtained by scanning the image row by row and modelling this data with an adaptive Chandrasekhar linear filter. The characterization efficiency of the obtained model is compared with the model adapted with the Least Mean Square (LMS) 2-D adaptive algorithm and with the cooccurrence method features. The comparison criteria is based on the computation of a characterization degree using the ratio of "betweenclass" variances with respect to "within-class" variances of the estimated coefficients. Extensive experiments show that the coefficients estimated by the use of Chandrasekhar adaptive filter give better results in texture discrimination than those estimated by other algorithms, even in a noisy context.

Keywords: Texture analysis, statistical features, adaptive filters, Chandrasekhar algorithm.

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1399 Forced Vibration of a Fiber Metal Laminated Beam Containing a Delamination

Authors: Sh. Mirhosseini, Y. Haghighatfar, M. Sedighi

Abstract:

Forced vibration problem of a delaminated beam made of fiber metal laminates is studied in this paper. Firstly, a delamination is considered to divide the beam into four sections. The classic beam theory is assumed to dominate each section. The layers on two sides of the delamination are constrained to have the same deflection. This hypothesis approves the conditions of compatibility as well. Consequently, dynamic response of the beam is obtained by the means of differential transform method (DTM). In order to verify the correctness of the results, a model is constructed using commercial software ABAQUS 6.14. A linear spring with constant stiffness takes the effect of contact between delaminated layers into account. The attained semi-analytical outcomes are in great agreement with finite element analysis.

Keywords: Delamination, forced vibration, finite element modelling, natural frequency.

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1398 Vibration Analysis of Functionally Graded Engesser- Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation

Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Functionally Graded Beam, Free Vibration, Elastic Foundation, Engesser-Timoshenko Beam Theory.

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1397 Experimental Study of Specific Cross Beam Types Appropriate for Modular Bridges

Authors: Seung-Kyung Kye, Young-Hyo Son, Jin-Woong Choi, Dooyong Cho, Sun-Kyu Park

Abstract:

Recently in the field of bridges that are newly built or repaired, fast construction is required more than ever. For these reasons, precast prefabricated bridge that enables rapid construction is actively discussed and studied today. In South Korea, it is called modular bridge. Cross beam is an integral component of modular bridge. It functions for load distribution, reduction of bending moment, resistance of horizontal strength on lateral upper structure. In this study, the structural characteristics of domestic and foreign cross beam types were compared. Based on this, alternative cross beam connection types suitable for modular bridge were selected. And bulb-T girder specimens were fabricated with each type of connection. The behavior of each specimen was analyzed under static loading, and cross beam connection type which is expected to be best suited to modular bridge proposed.

Keywords: Bulb-T girder, Cross beam, Modular bridge.

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1396 Sub-Impact Phenomenon of Elasto-Plastic Free-Free Beam during a Strike

Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

Abstract:

Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

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1395 Experimental Investigation of Natural Frequency and Forced Vibration of Euler-Bernoulli Beam under Displacement of Concentrated Mass and Load

Authors: Aref Aasi, Sadegh Mehdi Aghaei, Balaji Panchapakesan

Abstract:

This work aims to evaluate the free and forced vibration of a beam with two end joints subjected to a concentrated moving mass and a load using the Euler-Bernoulli method. The natural frequency is calculated for different locations of the concentrated mass and load on the beam. The analytical results are verified by the experimental data. The variations of natural frequency as a function of the location of the mass, the effect of the forced frequency on the vibrational amplitude, and the displacement amplitude versus time are investigated. It is discovered that as the concentrated mass moves toward the center of the beam, the natural frequency of the beam and the relative error between experimental and analytical data decreases. There is a close resemblance between analytical data and experimental observations.

Keywords: Euler-Bernoulli beam, natural frequency, forced vibration, experimental setup.

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1394 Fractional Order Feedback Control of a Ball and Beam System

Authors: Santosh Kr. Choudhary

Abstract:

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

Keywords: Fractional order calculus, fractional order controller, fractional order system, ball and beam system, PIλDμ controller, modelling, simulation.

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1393 Gas Detonation Forming by a Mixture of H2+O2 Detonation

Authors: Morteza Khaleghi Meybodi, Hossein Bisadi

Abstract:

Explosive forming is one of the unconventional techniques in which, most commonly, the water is used as the pressure transmission medium. One of the newest methods in explosive forming is gas detonation forming which uses a normal shock wave derived of gas detonation, to form sheet metals. For this purpose a detonation is developed from the reaction of H2+O2 mixture in a long cylindrical detonation tube. The detonation wave goes through the detonation tube and acts as a blast load on the steel blank and forms it. Experimental results are compared with a finite element model; and the comparison of the experimental and numerical results obtained from strain, thickness variation and deformed geometry is carried out. Numerical and experimental results showed approximately 75 – 90 % similarity in formability of desired shape. Also optimum percent of gas mixture obtained when we mix 68% H2 with 32% O2.

Keywords: Explosive forming, High strain rate, Gas detonation, Finite element analysis.

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1392 Experimental and Simulation Stress Strain Comparison of Hot Single Point Incremental Forming

Authors: Amar Al-Obaidi, Verena Kräusel, Dirk Landgrebe

Abstract:

Induction assisted single point incremental forming (IASPIF) is a flexible method and can be simply utilized to form a high strength alloys. Due to the interaction between the mechanical and thermal properties during IASPIF an evaluation for the process is necessary to be performed analytically. Therefore, a numerical simulation was carried out in this paper. The numerical analysis was operated at both room and elevated temperatures then compared with experimental results. Fully coupled dynamic temperature displacement explicit analysis was used to simulated the hot single point incremental forming. The numerical analysis was indicating that during hot single point incremental forming were a combination between complicated compression, tension and shear stresses. As a result, the equivalent plastic strain was increased excessively by rising both the formed part depth and the heating temperature during forming. Whereas, the forming forces were decreased from 5 kN at room temperature to 0.95 kN at elevated temperature. The simulation shows that the maximum true strain was occurred in the stretching zone which was the same as in experiment.

Keywords: Induction heating, single point incremental forming, FE modeling, advanced high strength steel.

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1391 Determination of Measurement Uncertainty in Extracting of Forming Limit Diagrams

Authors: M. Mahboubkhah, H. Fayazfar

Abstract:

In this research, Forming Limit Diagrams for supertension sheet metals which are using in automobile industry have been obtained. The exerted strains to sheet metals have been measured with four different methods and the errors of each method have also been represented. These methods have been compared with together and the most efficient and economic way of extracting of the exerted strains to sheet metals has been introduced. In this paper total error and uncertainty of FLD extraction procedures have been derived. Determination of the measurement uncertainty in extracting of FLD has a great importance in design and analysis of the sheet metal forming process.

Keywords: Forming Limit Diagram, Major and Minor Strain, Measurement Uncertainty.

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1390 Impulsive Noise-Resilient Subband Adaptive Filter

Authors: Young-Seok Choi

Abstract:

We present a new subband adaptive filter (R-SAF) which is robust against impulsive noise in system identification. To address the vulnerability of adaptive filters based on the L2-norm optimization criterion against impulsive noise, the R-SAF comes from the L1-norm optimization criterion with a constraint on the energy of the weight update. Minimizing L1-norm of the a posteriori error in each subband with a constraint on minimum disturbance gives rise to the robustness against the impulsive noise and the capable convergence performance. Experimental results clearly demonstrate that the proposed R-SAF outperforms the classical adaptive filtering algorithms when impulsive noise as well as background noise exist.

Keywords: Subband adaptive filter, L1-norm, system identification, robustness, impulsive interference.

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1389 Mechanical Buckling of Engesser-Timoshenko Beams with a Pair of Piezoelectric Layers

Authors: A. R. Nezamabadi, M. Karami Khorramabadi

Abstract:

This paper presents the elastic buckling of homogeneous beams with a pair of piezoelectric layers surface bonded on both sides of the beams. The displacement field of beam is assumed based on the Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of applied voltage, dimensionless geometrical parameter and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Mechanical Buckling, Engesser-Timoshenko beam theory - Piezoelectric layer.

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1388 Adaptive Thermal Comfort Model for Air-Conditioned Lecture Halls in Malaysia

Authors: B. T. Chew, S. N. Kazi, A. Amiri

Abstract:

This paper presents an adaptive thermal comfort model study in the tropical country of Malaysia. A number of researchers have been interested in applying the adaptive thermal comfort model to different climates throughout the world, but so far no study has been performed in Malaysia. For the use as a thermal comfort model, which better applies to hot and humid climates, the adaptive thermal comfort model was developed as part of this research by using the collected results from a large field study in six lecture halls with 178 students. The relationship between the operative temperature and behavioral adaptations was determined. In the developed adaptive model, the acceptable indoor neutral temperatures lay within the range of 23.9-26.0C, with outdoor temperatures ranging between 27.0-34.6C. The most comfortable temperature for students in lecture hall was 25.7C.

Keywords: Hot and humid, Lecture halls, Neutral temperature, Adaptive thermal comfort model.

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1387 Designing Intelligent Adaptive Controller for Nonlinear Pendulum Dynamical System

Authors: R. Ghasemi, M. R. Rahimi Khoygani

Abstract:

This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: Adaptive Neural Controller, Nonlinear Dynamical, Neural Network, RBF, Driven Pendulum, Position Control.

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1386 Design of Adaptive Sliding Mode Controller for Robotic Manipulators Tracking Control

Authors: T. C. Kuo, Y. J. Huang, B. W. Hong

Abstract:

This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.

Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.

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1385 Investigating the Capacity of Ultimate Torsion of Concrete Prismatic Beams with Transverse Spiral Bars

Authors: Hadi Barghlame, M. A. Lotfollahi-Yaghin

Abstract:

In this paper, the torsion capacity of ultimate point on rectangular beams with spiral reinforcements in the torsion direction and its anti-direction are investigated. Therefore, models of above-mentioned beams have been numerically analyzed under various loads using ANSYS software. It was observed that, spirallyreinforced prismatic beam and beam with spiral links, show lower torsion capacity than beam with normal links also in anti-direction. The result is that the concrete regulations are violated in this case.

Keywords: RC beam, ultimate torsion, finite element, prismatic beams, spirally tie.

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1384 A Type-2 Fuzzy Adaptive Controller of a Class of Nonlinear System

Authors: A. El Ougli, I. Lagrat, I. Boumhidi

Abstract:

In this paper we propose a robust adaptive fuzzy controller for a class of nonlinear system with unknown dynamic. The method is based on type-2 fuzzy logic system to approximate unknown non-linear function. The design of the on-line adaptive scheme of the proposed controller is based on Lyapunov technique. Simulation results are given to illustrate the effectiveness of the proposed approach.

Keywords: Fuzzy set type-2, Adaptive fuzzy control, Nonlinear system.

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1383 Numerical Analysis of End Plate Bolted Connection with Corrugated Beam

Authors: M. A. Sadeghian, J. Yang, Q. F. Liu

Abstract:

Steel extended end plate bolted connections are recommended to be widely utilized in special moment-resisting frame subjected to monotonic loading. Improper design of steel beam to column connection can lead to the collapse and fatality of structures. Therefore comprehensive research studies of beam to column connection design should be carried out. Also the performance and effect of corrugated on the strength of beam column end plate connection up to failure under monotonic loading in horizontal direction is presented in this paper. The non-linear elastic–plastic behavior has been considered through a finite element analysis using the multi-purpose software package LUSAS. The effect of vertically and horizontally types of corrugated web was also investigated.

Keywords: Corrugated beam, monotonic loading, finite element analysis, end plate connection.

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1382 Toward a Measure of Appropriateness of User Interfaces Adaptations Solutions

Authors: A. Siam, R. Maamri, Z. Sahnoun

Abstract:

The development of adaptive user interfaces (UI) presents for a long time an important research area in which researcher attempt to call upon the full resources and skills of several disciplines, The adaptive UI community holds a thorough knowledge regarding the adaptation of UIs with users and with contexts of use. Several solutions, models, formalisms, techniques and mechanisms were proposed to develop adaptive UI. In this paper, we propose an approach based on the fuzzy set theory for modeling the concept of the appropriateness of different solutions of UI adaptation with different situations for which interactive systems have to adapt their UIs.

Keywords: Adaptive user interfaces, adaptation solution’s appropriateness, fuzzy sets.

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1381 An Adaptive Approach to Synchronization of Two Chua's Circuits

Authors: Majid Reza Naseh, Mohammad Haeri

Abstract:

This paper introduces an adaptive control scheme to synchronize two identical Chua's systems. Introductory part of the paper is presented in the first part of the paper and then in the second part, a new theorem is proposed based on which an adaptive control scheme is developed to synchronize two identical modified Chua's circuit. Finally, numerical simulations are included to verify the effectiveness of the proposed control method.

Keywords: Chaos synchronization, adaptive control, Chua's circuits.

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1380 SystemC Modeling of Adaptive Least Mean Square Filter

Authors: Kyu Han Kim, Soon Kyu Kwon, Heung Sun Yoon, Jong Tae Kim

Abstract:

In this paper, we demonstrate the adaptive least-mean-square (LMS) filter modeling using SystemC. SystemC is a modeling language that allows designer to model both hardware and software component and makes it possible to design from high level system of abstraction to low level system of abstraction. We produced five adaptive least-mean-square filter models that are classed as five abstraction levels using SystemC proceeding from the abstract model to the more concrete model.

Keywords: Adaptive Filter, Least-Mean-Square Algorithm, SystemC, Transversal Fir Filter.

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1379 Studies on Ti/Al Sheet Joint Using Laser Beam Welding – A Review

Authors: K. Kalaiselvan, A. Elango, N. M. Nagarajan, N. Mathiyazagan

Abstract:

Laser beam welding has wide acceptability due to least welding distortion, low labour costs and convenient operation. However, laser welding for dissimilar titanium and aluminium alloys is a new area which is having wider applications in aerospace, aircraft, automotive, electronics and other industries. The present study is concerned with welding parameters namely laser power, welding speed, focusing distance and type of shielding gas and thereby evaluate welding performance of titanium and aluminium alloy thin sheets. This paper reviews the basic concepts associated with different parameters of Ti/Al sheet joint using Laser beam welding.

Keywords: Laser Beam Welding (LBW), Dissimilar joining Titanium and Aluminum sheets.

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1378 A Novel Adaptive E-Learning Model Based on Developed Learner's Styles

Authors: Hazem M. El-Bakry, Ahmed A. Saleh, Taghreed T. Asfour

Abstract:

Adaptive e-learning today gives the student a central role in his own learning process. It allows learners to try things out, participate in courses like never before, and get more out of learning than before. In this paper, an adaptive e-learning model for logic design, simplification of Boolean functions and related fields is presented. Such model presents suitable courses for each student in a dynamic and adaptive manner using existing database and workflow technologies. The main objective of this research work is to provide an adaptive e-learning model based learners' personality using explicit and implicit feedback. To recognize the learner-s, we develop dimensions to decide each individual learning style in order to accommodate different abilities of the users and to develop vital skills. Thus, the proposed model becomes more powerful, user friendly and easy to use and interpret. Finally, it suggests a learning strategy and appropriate electronic media that match the learner-s preference.

Keywords: Adaptive learning, Learning styles, Teaching strategies.

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1377 Chua’s Circuit Regulation Using a Nonlinear Adaptive Feedback Technique

Authors: Abolhassan Razminia, Mohammad-Ali Sadrnia

Abstract:

Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.

Keywords: Chaos, adaptive control, nonlinear control, Chua's circuit.

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1376 Nonlinear Finite Element Modeling of Deep Beam Resting on Linear and Nonlinear Random Soil

Authors: M. Seguini, D. Nedjar

Abstract:

An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.

Keywords: Finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability.

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1375 Adaptive Integral Backstepping Motion Control for Inverted Pendulum

Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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1374 Design of Adaptive Controller Based On Lyapunov Stability for a CSTR

Authors: S. Anbu, N. Jaya

Abstract:

Nonlinearity is the inherent characteristics of all the industrial processes. The Classical control approach used for a generation often fails to show better results particularly for non-linear systems and in the systems, whose parameters changes over a period of time for a variety of reasons. Alternatively, adaptive control strategies provide very good performance. The Model Reference Adaptive Control based on Lyapunov stability analysis and classical PI control strategies are designed and evaluated for Continuous Stirred Tank Reactor, which shows appreciable dynamic nonlinear characteristics.

Keywords: Adaptive Control, CSTR, Lyapunov stability, MRAS, PID.

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1373 Forced Vibration of a Planar Curved Beam on Pasternak Foundation

Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

Abstract:

The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: Curved beam, dynamic analysis, elastic foundation, finite element method.

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1372 Free Vibration Analysis of Functionally Graded Beams

Authors: Gholam Reza Koochaki

Abstract:

This work presents the highly accurate numerical calculation of the natural frequencies for functionally graded beams with simply supported boundary conditions. The Timoshenko first order shear deformation beam theory and the higher order shear deformation beam theory of Reddy have been applied to the functionally graded beams analysis. The material property gradient is assumed to be in the thickness direction. The Hamilton-s principle is utilized to obtain the dynamic equations of functionally graded beams. The influences of the volume fraction index and thickness-to-length ratio on the fundamental frequencies are discussed. Comparison of the numerical results for the homogeneous beam with Euler-Bernoulli beam theory results show that the derived model is satisfactory.

Keywords: Functionally graded beam, Free vibration, Hamilton's principle.

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