Search results for: Configuration Controller
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1274

Search results for: Configuration Controller

884 Nonlinear Control of a Continuous Bioreactor Based on Cell Population Model

Authors: Mahdi Sharifian, Mohammad Ali Fanaei

Abstract:

Saccharomyces cerevisiae (baker-s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance models can be used to capture the dynamic behavior of such cultures. In this paper an unstructured, segregated model is used which is based on population balance equation(PBE) and then in order to simulation, the 4th order Rung-Kutta is used for time dimension and three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used for discretization of the cell mass domain. The results indicate that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results show that although the PI controller has simpler structure, the GLC has better performance.

Keywords: Bioreactor, cell population balance, finite difference, orthogonal collocation on finite elements, Galerkin finite element, feedback linearization, PI controller.

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883 Bright–Dark Pulses in Nonlinear Polarisation Rotation Based Erbium-Doped Fiber Laser

Authors: R. Z. R. R. Rosdin, N. M. Ali, S. W. Harun, H. Arof

Abstract:

We have experimentally demonstrated bright-dark pulses in a nonlinear polarization rotation (NPR) based mode-locked Erbium-doped fiber laser (EDFL) with a long cavity configuration. Bright–dark pulses could be achieved when the laser works in the passively mode-locking regime and the net group velocity dispersion is quite anomalous. The EDFL starts to generate a bright pulse train with degenerated dark pulse at the mode-locking threshold pump power of 35.09 mW by manipulating the polarization states of the laser oscillation modes using a polarization controller (PC). A split bright–dark pulse is generated when further increasing the pump power up to 37.95 mW. Stable bright pulses with no obvious evidence of a dark pulse can also be generated when further adjusting PC and increasing the pump power up to 52.19 mW. At higher pump power of 54.96 mW, a new form of bright-dark pulse emission was successfully identified with the repetition rate of 29 kHz. The bright and dark pulses have a duration of 795.5 ns and 640 ns, respectively.

Keywords: Erbium-doped fiber laser, Nonlinear polarization rotation, bright-dark pulse.

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882 Thermal Performance of a Pair of Synthetic Jets Equipped in Microchannel

Authors: J. Mohammadpour, G. E. Lau, S. Cheng, A. Lee

Abstract:

Numerical study was conducted using two synthetic jet actuators attached underneath a micro-channel. By fixing the oscillating frequency and diaphragm amplitude, the effects on the heat transfer within the micro-channel were investigated with two synthetic jets being in-phase and 180° out-of-phase at different orifice spacing. There was a significant benefit identified with two jets being 180° out-of-phase with each other at the orifice spacing of 2 mm. By having this configuration, there was a distinct pattern of vortex forming which disrupts the main channel flow as well as promoting thermal mixing at high velocity within the channel. Therefore, this configuration achieved higher cooling performance compared to the other cases studied in terms of the reduction in the maximum temperature and cooling uniformity in the silicon wafer.

Keywords: Synthetic jets, microchannel, electronic cooling, computational fluid dynamics.

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881 Parallel Particle Swarm Optimization Optimized LDI Controller with Lyapunov Stability Criterion for Nonlinear Structural Systems

Authors: P.-W. Tsai, W.-L. Hong, C.-W. Chen, C.-Y. Chen

Abstract:

In this paper, we present a neural-network (NN) based approach to represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov Stability, Parallel Particle Swarm Optimization, Linear Differential Inclusion, Artificial Intelligence.

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880 Artificial Intelligence Techniques for Controlling Spacecraft Power System

Authors: Hanaa T. El-Madany, Faten H. Fahmy, Ninet M. A. El-Rahman, Hassen T. Dorrah

Abstract:

Advancements in the field of artificial intelligence (AI) made during this decade have forever changed the way we look at automating spacecraft subsystems including the electrical power system. AI have been used to solve complicated practical problems in various areas and are becoming more and more popular nowadays. In this paper, a mathematical modeling and MATLAB–SIMULINK model for the different components of the spacecraft power system is presented. Also, a control system, which includes either the Neural Network Controller (NNC) or the Fuzzy Logic Controller (FLC) is developed for achieving the coordination between the components of spacecraft power system as well as control the energy flows. The performance of the spacecraft power system is evaluated by comparing two control systems using the NNC and the FLC.

Keywords: Spacecraft, Neural network, Fuzzy logic control, Photovoltaic array.

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879 Self-Tuning Robot Control Based on Subspace Identification

Authors: Mathias Marquardt, Peter Dünow, Sandra Baßler

Abstract:

The paper describes the use of subspace based identification methods for auto tuning of a state space control system. The plant is an unstable but self balancing transport robot. Because of the unstable character of the process it has to be identified from closed loop input-output data. Based on the identified model a state space controller combined with an observer is calculated. The subspace identification algorithm and the controller design procedure is combined to a auto tuning method. The capability of the approach was verified in a simulation experiments under different process conditions.

Keywords: Auto tuning, balanced robot, closed loop identification, subspace identification.

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878 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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877 Adaptive Impedance Control for Unknown Non-Flat Environment

Authors: Norsinnira Zainul Azlan, Hiroshi Yamaura

Abstract:

This paper presents a new adaptive impedance control strategy, based on Function Approximation Technique (FAT) to compensate for unknown non-flat environment shape or time-varying environment location. The target impedance in the force controllable direction is modified by incorporating adaptive compensators and the uncertainties are represented by FAT, allowing the update law to be derived easily. The force error feedback is utilized in the estimation and the accurate knowledge of the environment parameters are not required by the algorithm. It is shown mathematically that the stability of the controller is guaranteed based on Lyapunov theory. Simulation results presented to demonstrate the validity of the proposed controller.

Keywords: Adaptive impedance control, Function Approximation Technique (FAT), impedance control, unknown environment position.

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876 A Robust Approach to the Load Frequency Control Problem with Speed Regulation Uncertainty

Authors: S. Z. Sayed Hassen

Abstract:

The load frequency control problem of power systems has attracted a lot of attention from engineers and researchers over the years. Increasing and quickly changing load demand, coupled with the inclusion of more generators with high variability (solar and wind power generators) on the network are making power systems more difficult to regulate. Frequency changes are unavoidable but regulatory authorities require that these changes remain within a certain bound. Engineers are required to perform the tricky task of adjusting the control system to maintain the frequency within tolerated bounds. It is well known that to minimize frequency variations, a large proportional feedback gain (speed regulation constant) is desirable. However, this improvement in performance using proportional feedback comes about at the expense of a reduced stability margin and also allows some steady-state error. A conventional PI controller is then included as a secondary control loop to drive the steadystate error to zero. In this paper, we propose a robust controller to replace the conventional PI controller which guarantees performance and stability of the power system over the range of variation of the speed regulation constant. Simulation results are shown to validate the superiority of the proposed approach on a simple single-area power system model.

Keywords: Robust control, power system, integral action, minimax LQG control.

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875 Helicopter Adaptive Control with Parameter Estimation Based on Feedback Linearization

Authors: A. R. Nemati, M. Haddad Zarif, M. M. Fateh

Abstract:

This paper presents an adaptive feedback linearization approach to derive helicopter. Ideal feedback linearization is defined for the cases when the system model is known. Adaptive feedback linearization is employed to get asymptotically exact cancellation for the inherent uncertainty in the knowledge of the given parameters of system. The control algorithm is implemented using the feedback linearization technique and adaptive method. The controller parameters are unknown where an adaptive control law aims to drive them towards their ideal values for providing perfect model matching between the reference model and the closed-loop plant model. The converged parameters of controller would then provide good estimates for the unknown plant parameters.

Keywords: Adaptive control, helicopter, feedback linearization, nonlinear control.

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874 Optimal Digital Pitch Aircraft Control

Authors: N. Popovich, P. Yan

Abstract:

In this paper a controller for the pitch angle of an aircraft regarding to the elevator deflection angle is designed. The way how the elevator angle affects pitching motion of the aircraft is pointed out, as well as, how a pitch controller can be applied for the aircraft to reach certain pitch angle. In this digital optimal system, the elevator deflection angle and pitching angle of the plane are considered to be input and output respectively. A single input single output (SISO) system is presented. A digital pitch aircraft control is demonstrated. A simulation for the whole system has been performed. The optimal control weighting vectors, Q and R have been determined.

Keywords: Aircraft, control, digital, optimal, Q and Rmatrices.

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873 State of Charge Estimator Based On High-Gain Observer for Lithium-Ion Batteries

Authors: Jaeho Han, Moonjung Kim, Won-Ho Kim, Chang-Ho Hyun

Abstract:

This paper introduces a high-gain observer based state of charge(SOC) estimator for lithium-Ion batteries. The proposed SOC estimator has a high-gain observer(HGO) structure. The HGO scheme enhances the transient response speed and diminishes the effect of uncertainties. Furthermore, it guarantees that the output feedback controller recovers the performance of the state feedback controller when the observer gain is sufficiently high. In order to show the effectiveness of the proposed method, the linear RC battery model in ADVISOR is used. The performance of the proposed method is compared with that of the conventional linear observer(CLO) and some simulation result is given.

Keywords: SOC, high-gain, observer, uncertainties, robust

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872 Optimal Resource Configuration and Allocation Planning Problem for Bottleneck Machines and Auxiliary Tools

Authors: Yin-Yann Chen, Tzu-Ling Chen

Abstract:

This study presents the case of an actual Taiwanese semiconductor assembly and testing manufacturer. Three major bottleneck manufacturing processes, namely, die bond, wire bond, and molding, are analyzed to determine how to use finite resources to achieve the optimal capacity allocation. A medium-term capacity allocation planning model is developed by considering the optimal total profit to satisfy the promised volume demanded by customers and to obtain the best migration decision among production lines for machines and tools. Finally, sensitivity analysis based on the actual case is provided to explore the effect of various parameter levels.

Keywords: Capacity planning, capacity allocation, machine migration, resource configuration.

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871 Introducing Fast Robot Roller Hemming Process in Automotive Industry

Authors: Babak Saboori, Behzad Saboori, Johan S. Carlson, Rikard Söderberg

Abstract:

As product life cycle becomes less and less every day, having flexible manufacturing processes for any companies seems more demanding. In the assembling of closures, i.e. opening parts in car body, hemming process is the one which needs more attention. This paper focused on the robot roller hemming process and how to reduce its cycle time by introducing a fast roller hemming process. A robot roller hemming process of a tailgate of Saab 93 SportCombi model is investigated as a case study in this paper. By applying task separation, robot coordination, and robot cell configuration principles in the roller hemming process, three alternatives are proposed, developed, and remarkable reduction in cycle times achieved [1].

Keywords: Cell configuration, cycle time, robot coordination, roller hemming.

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870 Research on Spatial Morphology and Protection of Traditional Rural Settlements Based on Space Syntax: Taking Xiazhuang Village and Shijia Village in Huzhou as Example

Authors: Shenpu Liu

Abstract:

Space syntax, a paradigm of the urban research, which manifests people’s intuitive and abstract perception of a material space with a solid mathematical way, explores how space represents its social characteristics. Taking Xiazhuang village and Shijia Village in Huzhou as an example and focusing on inward structure and street space, this article recognizes the connotative significance of the settlement with the aid of space syntax theory and quantitative analysis method from the perspective of spatial configuration to present relevant suggestions for its future planning and provides references for traditional rural settlement protection.

Keywords: Shijia village, space configuration, space syntax, traditional rural settlement, Xiazhuang village.

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869 Conduction Model Compatible for Multi-Physical Domain Dynamic Investigations: Bond Graph Approach

Authors: A. Zanj, F. He

Abstract:

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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868 Fuzzy Separation Bearing Control for Mobile Robots Formation

Authors: A. Bazoula, H. Maaref

Abstract:

In this article we address the problem of mobile robot formation control. Indeed, the most work, in this domain, have studied extensively classical control for keeping a formation of mobile robots. In this work, we design an FLC (Fuzzy logic Controller) controller for separation and bearing control (SBC). Indeed, the leader mobile robot is controlled to follow an arbitrary reference path, and the follower mobile robot use the FSBC (Fuzzy Separation and Bearing Control) to keep constant relative distance and constant angle to the leader robot. The efficiency and simplicity of this control law has been proven by simulation on different situation.

Keywords: Autonomous mobile robot, Formation control, Fuzzy logic control, Multiple robots, Leader-Follower.

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867 Control Technology for a Daily Load-following Operation in a Nuclear Power Plant

Authors: Keuk Jong Yu, Sang Hee Kang, Sung Chang You

Abstract:

In Korea, the technology of a load fo nuclear power plant has been being developed. automatic controller which is able to control temperature and axial power distribution was developed. identification algorithm and a model predictive contact former transforms the nuclear reactor status into numerically. And the latter uses them and ge manipulated values such as two kinds of control ro this automatic controller, the performance of a coperation was evaluated. As a result, the automatic generated model parameters of a nuclear react to nuclear reactor average temperature and axial power the desired targets during a daily load follow.

Keywords: axial power distribution, model reactor temperature, system identification

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866 Autonomous Control of a Mobile Manipulator

Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper considers the design of a motion planner that will simultaneously accomplish control and motion planning of a n-link nonholonomic mobile manipulator, wherein, a n-link holonomic manipulator is coupled with a nonholonomic mobile platform, within an obstacle-ridden environment. This planner, derived from the Lyapunov-based control scheme, generates collision-free trajectories from an initial configuration to a final configuration in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulator with results through computer simulations of an interesting scenario.

Keywords: Artificial potential fields, Lyapunov-based control scheme, Lyapunov stability, nonholonomic manipulator, minimum distance technique, kinodynamic constraints.

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865 Robotic Arm Control with Neural Networks Using Genetic Algorithm Optimization Approach

Authors: A. Pajaziti, H. Cana

Abstract:

In this paper, the structural genetic algorithm is used to optimize the neural network to control the joint movements of robotic arm. The robotic arm has also been modeled in 3D and simulated in real-time in MATLAB. It is found that Neural Networks provide a simple and effective way to control the robot tasks. Computer simulation examples are given to illustrate the significance of this method. By combining Genetic Algorithm optimization method and Neural Networks for the given robotic arm with 5 D.O.F. the obtained the results shown that the base joint movements overshooting time without controller was about 0.5 seconds, while with Neural Network controller (optimized with Genetic Algorithm) was about 0.2 seconds, and the population size of 150 gave best results.

Keywords: Robotic Arm, Neural Network, Genetic Algorithm, Optimization.

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864 Hand Motion and Gesture Control of Laboratory Test Equipment Using the Leap Motion Controller

Authors: Ian A. Grout

Abstract:

In this paper, the design and development of a system to provide hand motion and gesture control of laboratory test equipment is considered and discussed. The Leap Motion controller is used to provide an input to control a laboratory power supply as part of an electronic circuit experiment. By suitable hand motions and gestures, control of the power supply is provided remotely and without the need to physically touch the equipment used. As such, it provides an alternative manner in which to control electronic equipment via a PC and is considered here within the field of human computer interaction (HCI).

Keywords: Control, hand gesture, human computer interaction, test equipment.

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863 Energy Management System in HEV Using PI Controller

Authors: S. Saravanan, G. Sugumaran

Abstract:

Nowadays the use of Hybrid Electric Vehicles (HEV) is increasing dramatically. The HEV is mainly dependent on electricity and there is always a need for storage of charge. Fuel Cell (FC), Batteries and Ultra Capacitor are being used for the proposed HEV as an electric power source or as an energy storage unit. The aim of developing an energy management technique is to utilize the sources according to the requirement of the vehicle with help of controller. This increases the efficiency of hybrid electric vehicle to reduce the fuel consumption and unwanted emission. The Maximum Power Point Tracking (MPPT) in FC is done using (Perturb & Observe) algorithm. In this paper, the control of automobiles at variable speed is achieved effectively.

Keywords: Batteries, Energy Management System (EMS), Fuel Cell (FC), Hybrid Electric Vehicles (HEVs), Maximum Power Point Tracking (MPPT).

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862 Comparative Study of Some Adaptive Fuzzy Algorithms for Manipulator Control

Authors: Sudeept Mohan, Surekha Bhanot

Abstract:

The problem of manipulator control is a highly complex problem of controlling a system which is multi-input, multioutput, non-linear and time variant. In this paper some adaptive fuzzy, and a new hybrid fuzzy control algorithm have been comparatively evaluated through simulations, for manipulator control. The adaptive fuzzy controllers consist of self-organizing, self-tuning, and coarse/fine adaptive fuzzy schemes. These controllers are tested for different trajectories and for varying manipulator parameters through simulations. Various performance indices like the RMS error, steady state error and maximum error are used for comparison. It is observed that the self-organizing fuzzy controller gives the best performance. The proposed hybrid fuzzy plus integral error controller also performs remarkably well, given its simple structure.

Keywords: Hybrid fuzzy, Self-organizing, Self-tuning, Trajectory tracking.

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861 Using Fuzzy Controller in Induction Motor Speed Control with Constant Flux

Authors: Hassan Baghgar Bostan Abad, Ali Yazdian Varjani, Taheri Asghar

Abstract:

Variable speed drives are growing and varying. Drives expanse depend on progress in different part of science like power system, microelectronic, control methods, and so on. Artificial intelligent contains hard computation and soft computation. Artificial intelligent has found high application in most nonlinear systems same as motors drive. Because it has intelligence like human but there are no sentimental against human like angriness and.... Artificial intelligent is used for various points like approximation, control, and monitoring. Because artificial intelligent techniques can use as controller for any system without requirement to system mathematical model, it has been used in electrical drive control. With this manner, efficiency and reliability of drives increase and volume, weight and cost of them decrease.

Keywords: Artificial intelligent, electrical motor, intelligent drive and control,

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860 A New Nonlinear Excitation Controller for Transient Stability Enhancement in Power Systems

Authors: M. Ouassaid, A. Nejmi, M. Cherkaoui, M. Maaroufi

Abstract:

The very nonlinear nature of the generator and system behaviour following a severe disturbance precludes the use of classical linear control technique. In this paper, a new approach of nonlinear control is proposed for transient and steady state stability analysis of a synchronous generator. The control law of the generator excitation is derived from the basis of Lyapunov stability criterion. The overall stability of the system is shown using Lyapunov technique. The application of the proposed controller to simulated generator excitation control under a large sudden fault and wide range of operating conditions demonstrates that the new control strategy is superior to conventional automatic voltage regulator (AVR), and show very promising results.

Keywords: Excitation control, Lyapunov technique, non linearcontrol, synchronous generator, transient stability, voltage regulation.

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859 Modeling and Control of a 4DoF Robotic Assistive Device for Hand Rehabilitation

Authors: Christopher Spiewak, M. R. Islam, Mohammad Arifur Rahaman, Mohammad H. Rahman, Roger Smith, Maarouf Saad

Abstract:

For those who have lost the ability to move their hand, going through repetitious motions with the assistance of a therapist is the main method of recovery. We have been developed a robotic assistive device to rehabilitate the hand motions in place of the traditional therapy. The developed assistive device (RAD-HR) is comprised of four degrees of freedom enabling basic movements, hand function, and assists in supporting the hand during rehabilitation. We used a nonlinear computed torque control technique to control the RAD-HR. The accuracy of the controller was evaluated in simulations (MATLAB/Simulink environment). To see the robustness of the controller external disturbance as modelling uncertainty (±10% of joint torques) were added in each joints.

Keywords: Biorobotics, rehabilitation, nonlinear control, robotic assistive device, exoskeleton.

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858 Adaptive PID Control of Wind Energy Conversion Systems Using RASP1 Mother Wavelet Basis Function Networks

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

In this paper a PID control strategy using neural network adaptive RASP1 wavelet for WECS-s control is proposed. It is based on single layer feedforward neural networks with hidden nodes of adaptive RASP1 wavelet functions controller and an infinite impulse response (IIR) recurrent structure. The IIR is combined by cascading to the network to provide double local structure resulting in improving speed of learning. This particular neuro PID controller assumes a certain model structure to approximately identify the system dynamics of the unknown plant (WECS-s) and generate the control signal. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution.

Keywords: Adaptive PID Control, RASP1 Wavelets, WindEnergy Conversion Systems.

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857 Modeling and Design of MPPT Controller Using Stepped P&O Algorithm in Solar Photovoltaic System

Authors: R. Prakash, B. Meenakshipriya, R. Kumaravelan

Abstract:

This paper presents modeling and simulation of Grid Connected Photovoltaic (PV) system by using improved mathematical model. The model is used to study different parameter variations and effects on the PV array including operating temperature and solar irradiation level. In this paper stepped P&O algorithm is proposed for MPPT control. This algorithm will identify the suitable duty ratio in which the DC-DC converter should be operated to maximize the power output. Photo voltaic array with proposed stepped P&O-MPPT controller can operate in the maximum power point for the whole range of solar data (irradiance and temperature).

Keywords: Photovoltaic (PV), Maximum Power Point Tracking (MPPT), Boost converter, Stepped Perturb & Observe method (Stepped P&O).

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856 Neural Network Controller for Mobile Robot Motion Control

Authors: Jasmin Velagic, Nedim Osmic, Bakir Lacevic

Abstract:

In this paper the neural network-based controller is designed for motion control of a mobile robot. This paper treats the problems of trajectory following and posture stabilization of the mobile robot with nonholonomic constraints. For this purpose the recurrent neural network with one hidden layer is used. It learns relationship between linear velocities and error positions of the mobile robot. This neural network is trained on-line using the backpropagation optimization algorithm with an adaptive learning rate. The optimization algorithm is performed at each sample time to compute the optimal control inputs. The performance of the proposed system is investigated using a kinematic model of the mobile robot.

Keywords: Mobile robot, kinematic model, neural network, motion control, adaptive learning rate.

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855 Wind Fragility of Window Glass in 10-Story Apartment with Two Different Window Models

Authors: Viriyavudh Sim, WooYoung Jung

Abstract:

Damage due to high wind is not limited to load resistance components such as beam and column. The majority of damage is due to breach in the building envelope such as broken roof, window, and door. In this paper, wind fragility of window glass in residential apartment was determined to compare the difference between two window configuration models. Monte Carlo Simulation method had been used to derive damage data and analytical fragilities were constructed. Fragility of window system showed that window located in leeward wall had higher probability of failure, especially those close to the edge of structure. Between the two window models, Model 2 had higher probability of failure, this was due to the number of panel in this configuration.

Keywords: Wind fragility, glass window, high rise apartment, Monte Carlo Simulation method.

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