Search results for: Area Control Error

Authors: Kalyan Chatterjee

Abstract:

The optimal design of PI controller for Automatic Generation Control in two area is presented in this paper. The concept of Dual mode control is applied in the PI controller, such that the proportional mode is made active when the rate of change of the error is sufficiently larger than a specified limit otherwise switched to the integral mode. A digital simulation is used in conjunction with the Hooke-Jeeve’s optimization technique to determine the optimum parameters (individual gain of proportional and integral controller) of the PI controller. Integrated Square of the Error (ISE), Integrated Time multiplied by Absolute Error(ITAE) , and Integrated Absolute Error(IAE) performance indices are considered to measure the appropriateness of the designed controller.  The proposed controller are tested for a two area single nonreheat thermal system considering the practical aspect of the problem such as Deadband and Generation Rate Constraint(GRC). Simulation results show that  dual mode with optimized values of the gains improved the control performance than the commonly used Variable Structure .

Keywords: Load Frequency Control, Area Control Error(ACE), Dual Mode PI Controller, Performance Index

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Authors: Fangfang Meng, Shuang Cong

Abstract:

In the closed quantum system, if the control system is strongly regular and all other eigenstates are directly coupled to the target state, the control system can be asymptotically stabilized at the target eigenstate by the Lyapunov control based on the state error. However, if the control system is not strongly regular or as long as there is one eigenstate not directly coupled to the target state, the situations will become complicated. In this paper, we propose an implicit Lyapunov control method based on the state error to solve the convergence problems for these two degenerate cases. And at the same time, we expand the target state from the eigenstate to the arbitrary pure state. Especially, the proposed method is also applicable in the control system with multi-control Hamiltonians. On this basis, the convergence of the control systems is analyzed using the LaSalle invariance principle. Furthermore, the relation between the implicit Lyapunov functions of the state distance and the state error is investigated. Finally, numerical simulations are carried out to verify the effectiveness of the proposed implicit Lyapunov control method. The comparisons of the control effect using the implicit Lyapunov control method based on the state distance with that of the state error are given.

Keywords: Implicit Lyapunov control, state error, degenerate cases, convergence.

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Authors: M. S. Kang, D. H. Kim, J. S. Yoon, B. S. Park, J. K. Lee

Abstract:

Since straightness error of linear motor stage is hardly dependent upon machining accuracy and assembling accuracy, there is limit on maximum realizable accuracy. To cope with this limitation, this paper proposed a servo system to compensate straightness error of a linear motor stage. The servo system is mounted on the slider of the linear motor stage and moves in the direction of the straightness error so as to compensate the error. From position dependency and repeatability of the straightness error of the slider, a feedforward compensation control is applied to the platform servo control. In the consideration of required fine positioning accuracy, a platform driven by an electro-magnetic actuator is suggested and a sliding mode control was applied. The effectiveness of the sliding mode control was verified along with some experimental results.

Keywords: Linear Motor Stage, Straightness Error, Friction, Sliding Mode Control.

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Authors: Rajesh Joseph Abraham, D. Das, Amit Patra

Abstract:

This paper is concerned with the application of small rating Capacitive Energy Storage units for the improvement of Automatic Generation Control of a multiunit multiarea power system. Generation Rate Constraints are also considered in the investigations. Integral Squared Error technique is used to obtain the optimal integral gain settings by minimizing a quadratic performance index. Simulation studies reveal that with CES units, the deviations in area frequencies and inter-area tie-power are considerably improved in terms of peak deviations and settling time as compared to that obtained without CES units.

Keywords: Automatic Generation Control, Capacitive EnergyStorage, Integral Squared Error.

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Authors: R. N. Patel

Abstract:

This paper deals with the tuning of parameters for Automatic Generation Control (AGC). A two area interconnected hydrothermal system with PI controller is considered. Genetic Algorithm (GA) and Particle Swarm optimization (PSO) algorithms have been applied to optimize the controller parameters. Two objective functions namely Integral Square Error (ISE) and Integral of Time-multiplied Absolute value of the Error (ITAE) are considered for optimization. The effectiveness of an objective function is considered based on the variation in tie line power and change in frequency in both the areas. MATLAB/SIMULINK was used as a simulation tool. Simulation results reveal that ITAE is a better objective function than ISE. Performances of optimization algorithms are also compared and it was found that genetic algorithm gives better results than particle swarm optimization algorithm for the problems of AGC.

Keywords: Area control error, Artificial intelligence, Automatic generation control, Genetic Algorithms and modeling, ISE, ITAE, Particle swarm optimization.

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Authors: Mazidah Tajjudin, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

Keywords: Fractional-order PI, Ziegler-Nichols tuning, Oustaloup's Recursive Approximation, steam temperature control.

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Authors: Ahmed Abdolkhalig, Rastko Zivanovic

Abstract:

This paper evaluates the Total Vector Error of an estimated Phasor as define in IEEE C37.118 standard within different medium access in Local Area Networks (LAN). Three different LAN models (CSMA/CD, CSMA/AMP and Switched Ethernet) are evaluated. The Total Vector Error of the estimated Phasor has been evaluated for the effect of Nodes Number under the standardized network Band-width values defined in IEC 61850-9-2 communication standard (i.e. 0.1, 1 and 10 Gbps).

Keywords: Phasor, Local Area Network, Total Vector Error, IEEE C37.118, IEC 61850.

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Authors: Richard W. Longman

Abstract:

Iterative learning control aims to achieve zero tracking error of a specific command. This is accomplished by iteratively adjusting the command given to a feedback control system, based on the tracking error observed in the previous iteration. One would like the iterations to converge to zero tracking error in spite of any error present in the model used to design the learning law. First, this need for stability robustness is discussed, and then the need for robustness of the property that the transients are well behaved. Methods of producing the needed robustness to parameter variations and to singular perturbations are presented. Then a method involving reverse time runs is given that lets the world behavior produce the ILC gains in such a way as to eliminate the need for a mathematical model. Since the real world is producing the gains, there is no issue of model error. Provided the world behaves linearly, the approach gives an ILC law with both stability robustness and good transient robustness, without the need to generate a model.

Keywords: Iterative learning control, stability robustness, monotonic convergence.

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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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Authors: Surya Prakash, Sunil Kumar Sinha

Abstract:

This paper deals with the application of artificial neural network (ANN) and fuzzy based Adaptive Neuro Fuzzy Inference System(ANFIS) approach to Load Frequency Control (LFC) of multi unequal area hydro-thermal interconnected power system. The proposed ANFIS controller combines the advantages of fuzzy controller as well as quick response and adaptability nature of ANN. Area-1 and area-2 consists of thermal reheat power plant whereas area-3 and area-4 consists of hydro power plant with electric governor. Performance evaluation is carried out by using intelligent controller like ANFIS, ANN and Fuzzy controllers and conventional PI and PID control approaches. To enhance the performance of intelligent and conventional controller sliding surface is included. The performances of the controllers are simulated using MATLAB/SIMULINK package. A comparison of ANFIS, ANN, Fuzzy, PI and PID based approaches shows the superiority of proposed ANFIS over ANN & fuzzy, PI and PID controller for 1% step load variation.

Keywords: Load Frequency Control (LFC), ANFIS, ANN & Fuzzy, PI, PID Controllers, Area Control Error (ACE), Tie-line, MATLAB / SIMULINK.

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Authors: Sang-Chul Kim, Sung-Il Chien

Abstract:

The error diffusion method generates worm artifacts, and weakens the edge of the halftone image when the continuous gray scale image is reproduced by a binary image. First, to enhance the edges, we propose the edge-enhancing filter by considering the quantization error information and gradient of the neighboring pixels. Furthermore, to remove worm artifacts often appearing in a halftone image, we add adaptively random noise into the weights of an error filter.

Keywords: Artifact suppression, Edge enhancement, Error diffusion method, Halftone image

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Authors: Mohammad Rakibul Islam

Abstract:

Link reliability and transmitted power are two important design constraints in wireless network design. Error control coding (ECC) is a classic approach used to increase link reliability and to lower the required transmitted power. It provides coding gain, resulting in transmitter energy savings at the cost of added decoder power consumption. But the choice of ECC is very critical in the case of wireless sensor network (WSN). Since the WSNs are energy constraint in nature, both the BER and power consumption has to be taken into count. This paper develops a step by step approach in finding suitable error control codes for WSNs. Several simulations are taken considering different error control codes and the result shows that the RS(31,21) fits both in BER and power consumption criteria.

Keywords: Error correcting code, RS, BCH, wireless sensor networks.

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Authors: N. Z. Azlan, H. Yamaura

Abstract:

The experimental study of position control of a light weight and small size robotic finger during non-contact motion is presented in this paper. The finger possesses fingertip pinching and self adaptive grasping capabilities, and is made of a seven bar linkage mechanism with a slider in the middle phalanx. The control system is tested under the Proportional Integral Derivative (PID) control algorithm and Recursive Least Square (RLS) based Feedback Error Learning (FEL) control scheme to overcome the uncertainties present in the plant. The experiments conducted in Matlab Simulink and xPC Target environments show that the overall control strategy is efficient in controlling the finger movement.

Keywords: Anthropomorphic finger, position control, feedback error learning, experimental study

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Authors: Heesung Lee, Joonkyung Sung, Euntai Kim

Abstract:

This paper proposes a method which reduces power consumption in single-error correcting, double error-detecting checker circuits that perform memory error correction code. Power is minimized with little or no impact on area and delay, using the degrees of freedom in selecting the parity check matrix of the error correcting codes. The genetic algorithm is employed to solve the non linear power optimization problem. The method is applied to two commonly used SEC-DED codes: standard Hamming and odd column weight Hsiao codes. Experiments were performed to show the performance of the proposed method.

Keywords: Error correcting codes, genetic algorithm, non-linearpower optimization, Hamming code, Hsiao code.

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Authors: Kamran Turkoglu, Ugur Ozdemir, Melike Nikbay, Elbrous M. Jafarov

Abstract:

In this paper, an automatic control system design based on Integral Squared Error (ISE) parameter optimization technique has been implemented on longitudinal flight dynamics of an UAV. It has been aimed to minimize the error function between the reference signal and the output of the plant. In the following parts, objective function has been defined with respect to error dynamics. An unconstrained optimization problem has been solved analytically by using necessary and sufficient conditions of optimality, optimum PID parameters have been obtained and implemented in control system dynamics.

Keywords: Optimum Design, KKT Conditions, UAV, Longitudinal Flight Dynamics, ISE Parameter Optimization.

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Authors: Apidet Booranawong, Wiklom Teerapabkajorndet

Abstract:

An enhanced ad-hoc on-demand distance vector routing (E-AODV) protocol for control system applications in wireless sensor and actuator networks (WSANs) is proposed. Our routing algorithm is designed by considering both wireless network communication and the control system aspects. Control system error and network delay are the main selection criteria in our routing protocol. The control and communication performance is evaluated on multi-hop IEEE 802.15.4 networks for building-temperature control systems. The Gilbert-Elliott error model is employed to simulate packet loss in wireless networks. The simulation results demonstrate that the E-AODV routing approach can significantly improve the communication performance better than an original AODV routing under various packet loss rates. However, the control performance result by our approach is not much improved compared with the AODV routing solution.

Keywords: WSANs, building temperature control, AODV routing protocol, control system error, settling time, delay, delivery ratio.

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Authors: Yeonsoo Jang, Dongweon Yoon, Ki Ho Kwon, Jaeyoon Lee, Wooju Lee

Abstract:

Phase error in communications systems degrades error performance. In this paper, we present a simple approximation for the average error probability of the binary phase shift keying (BPSK) in the presence of phase error having a uniform distribution on arbitrary intervals. For the simple approximation, we use symmetry and periodicity of a sinusoidal function. Approximate result for the average error probability is derived, and the performance is verified through comparison with simulation result.

Keywords: Average error probability, Phase shift keying, Phase error

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Authors: Gulshan Sharma

Abstract:

This article presents the design of optimal automatic generation control (AGC) based on full state feedback control for a multi-area interconnected power system. An extra high voltage AC transmission line in parallel with a high voltage DC link is considered as an area interconnection between the areas. The optimal AGC are designed and implemented in the wake of 1% load perturbation in one of the areas and the system dynamic response plots for various system states are obtained to investigate the system dynamic performance. The pattern of closed-loop eigenvalues are also determined to analyze the system stability. From the investigations carried out in the work, it is revealed that the dynamic performance of the system under consideration has an appreciable improvement when a high voltage DC line is paralleled with an extra high voltage AC line as an interconnection between the areas. The investigation of closed-loop eigenvalues reveals that the system stability is ensured in all case studies carried out with the designed optimal AGC.

Keywords: Automatic generation control, area control error, DC link, optimal AGC regulator, closed-loop eigenvalues.

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Authors: M. A. M. El-Bendary, H. Kazimian, A. E. Abo-El-azm, N. A. El-Fishawy, F. El-Samie, F. Shawki

Abstract:

This paper studies a vital issue in wireless communications, which is the transmission of images over Wireless Personal Area Networks (WPANs) through the Bluetooth network. It presents a simple method to improve the efficiency of error control code of old Bluetooth versions over mobile WPANs through Interleaved Error Control Code (IECC) technique. The encoded packets are interleaved by simple block interleaver. Also, the paper presents a chaotic interleaving scheme as a tool against bursts of errors which depends on the chaotic Baker map. Also, the paper proposes using the chaotic interleaver instead of traditional block interleaver with Forward Error Control (FEC) scheme. A comparison study between the proposed and standard techniques for image transmission over a correlated fading channel is presented. Simulation results reveal the superiority of the proposed chaotic interleaving scheme to other schemes. Also, the superiority of FEC with proposed chaotic interleaver to the conventional interleavers with enhancing the security level with chaotic interleaving packetby- packet basis.

Keywords: Mobile Bluetooth terminals, WPANs, Jackes' model, Interleaving technique, chaotic interleaver

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Authors: Shuting Ji, Yueming Zhang, Jing Zhao

Abstract:

The output error of the globoidal cam mechanism can be considered as a relevant indicator of mechanism performance, because it determines kinematic and dynamical behavior of mechanical transmission. Based on the differential geometry and the rigid body transformations, the mathematical model of surface geometry of the globoidal cam is established. Then we present the analytical expression of the output error (including the transmission error and the displacement error along the output axis) by considering different manufacture and assembly errors. The effects of the center distance error, the perpendicular error between input and output axes and the rotational angle error of the globoidal cam on the output error are systematically analyzed. A globoidal cam mechanism which is widely used in automatic tool changer of CNC machines is applied for illustration. Our results show that the perpendicular error and the rotational angle error have little effects on the transmission error but have great effects on the displacement error along the output axis. This study plays an important role in the design, manufacture and assembly of the globoidal cam mechanism.

Keywords: Globoidal cam mechanism, manufacture error, transmission error, automatic tool changer.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

A self tuning PID control strategy using reinforcement learning is proposed in this paper to deal with the control of wind energy conversion systems (WECS). Actor-Critic learning is used to tune PID parameters in an adaptive way by taking advantage of the model-free and on-line learning properties of reinforcement learning effectively. In order to reduce the demand of storage space and to improve the learning efficiency, a single RBF neural network is used to approximate the policy function of Actor and the value function of Critic simultaneously. The inputs of RBF network are the system error, as well as the first and the second-order differences of error. The Actor can realize the mapping from the system state to PID parameters, while the Critic evaluates the outputs of the Actor and produces TD error. Based on TD error performance index and gradient descent method, the updating rules of RBF kernel function and network weights were given. Simulation results show that the proposed controller is efficient for WECS and it is perfectly adaptable and strongly robust, which is better than that of a conventional PID controller.

Keywords: Wind energy conversion systems, reinforcementlearning; Actor-Critic learning; adaptive PID control; RBF network.

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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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Authors: Muhammad Muhsin, Abhishek Mishra, Shreyansh Vishwakarma, K. Dasaratha Babu, Anudevi Samuel

Abstract:

In an interconnected power system, any sudden small load perturbation in any of the interconnected areas causes the deviation of the area frequencies, the tie line power and voltage deviation at the generator terminals. This paper deals with the study of performance of intelligent Fuzzy Logic controllers coupled with Conventional Controllers (PI and PID) for Load Frequency Control. For analysis, an isolated single area and interconnected two area thermal power systems with and without generation rate constraints (GRC) have been considered. The studies have been performed with conventional PI and PID controllers and their performance has been compared with intelligent fuzzy controllers. It can be demonstrated that these controllers can successfully bring back the excursions in area frequencies and tie line powers within acceptable limits in smaller time periods and with lesser transients as compared to the performance of conventional controllers under same load disturbance conditions. The simulations in MATLAB have been used for comparative studies.

Keywords: Area Control Error, Fuzzy Logic, Generation rate constraint, Load Frequency, Tie line Power.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

Abstract:

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: Derjew Ayele Ejigu, Houde Song, Xiaojing Liu

Abstract:

This work presents the particle swarm optimization trained neural network (PSO-NN) supervisory proportional integral derivative (PID) control method to monitor the pressurized water reactor (PWR) core power for safe operation. The proposed control approach is implemented on the transfer function of the PWR core, which is computed from the state-space model. The PWR core state-space model is designed from the neutronics, thermal-hydraulics, and reactivity models using perturbation around the equilibrium value. The proposed control approach computes the control rod speed to maneuver the core power to track the reference in a closed-loop scheme. The particle swarm optimization (PSO) algorithm is used to train the neural network (NN) and to tune the PID simultaneously. The controller performance is examined using integral absolute error, integral time absolute error, integral square error, and integral time square error functions, and the stability of the system is analyzed by using the Bode diagram. The simulation results indicated that the controller shows satisfactory performance to control and track the load power effectively and smoothly as compared to the PSO-PID control technique. This study will give benefit to design a supervisory controller for nuclear engineering research fields for control application.

Keywords: machine learning, neural network, pressurized water reactor, supervisory controller

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

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

Abstract:

This study presents a novel means of designing a simple and effective torque controller for Permanent Magnet Synchronous Motor (PMSM). The overall stability of the system is shown using Lyapunov technique. The Lyapunov functions used contain a term penalizing the integral of the tracking error, enhancing the stability. The tracking error is shown to be globally uniformly bounded. Simulation results are presented to show the effectiveness of the approach.

Keywords: Integral action, Lyapunov Technique, Non Linear Control, Permanent Magnet Synchronous Motors, Torque Control, Stability.

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Authors: Raouf Fareh, Maarouf Saad, Sofiane Khadraoui, Tamer Rabie

Abstract:

This paper presents a tracking control strategy based on Lyapunov approach for nonholonomic wheeled mobile robot. This control strategy consists of two levels. First, a kinematic controller is developed to adjust the right and left wheel velocities. Using this velocity control law, the stability of the tracking error is guaranteed using Lyapunov approach. This kinematic controller cannot be generated directly by the motors. To overcome this problem, the second level of the controllers, dynamic control, is designed. This dynamic control law is developed based on Lyapunov theory in order to track the desired trajectories of the mobile robot. The stability of the tracking error is proved using Lupunov and Barbalat approaches. Simulation results on a nonholonomic wheeled mobile robot are given to demonstrate the feasibility and effectiveness of the presented approach.

Keywords: Mobile robot, trajectory tracking, Lyapunov, stability.

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Authors: K. Kouzi

Abstract:

In order to have stable and high performance of direct torque and flux control (DTFC) of double star induction motor drive (DSIM), proper on-line adaptation of the stator resistance is very important. This is inevitably due to the variation of the stator resistance during operating conditions, which introduces error in estimated flux position and the magnitude of the stator flux. Error in the estimated stator flux deteriorates the performance of the DTFC drive. Also, the effect of error in estimation is very important especially at low speed. Due to this, our aim is to overcome the sensitivity of the DTFC to the stator resistance variation by proposing on-line fuzzy estimation stator resistance. The fuzzy estimation method is based on an on-line stator resistance correction through the variations of the stator current estimation error and its variations. The fuzzy logic controller gives the future stator resistance increment at the output. The main advantage of the suggested algorithm control is to avoid the drive instability that may occur in certain situations and ensure the tracking of the actual stator resistance. The validity of the technique and the improvement of the whole system performance are proved by the results.

Keywords: Direct torque control, dual stator induction motor, fuzzy logic estimation, stator resistance adaptation.

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Authors: Hyun-Gwang Cho, Wan-Seok Yang, Su-Jin Kim, Jeong-Seok Oh, Chun-Hong Park

Abstract:

Machine tools are improved capacity remarkably during the 20th century. Improving the precision of machine tools are related with precision of products and accurate processing is always associated with the subject of interest. There are a lot of the elements that determine the precision of the machine, as guides, motors, structure, control, etc. In this paper we focused on the phenomenon that vertical movement system has worse precision than horizontal movement system even they were made up with same components. The vertical movement system needs to be studied differently from the horizontal movement system to develop its precision. The vertical movement system has load on its transfer direction and it makes the movement system weak in precision than the horizontal one. Some machines have mechanical counter balance, hydraulic or pneumatic counter balance to compensate the weight of the machine head. And there is several type of compensating the weight. It can push the machine head and also can use chain or wire lope to transfer the compensating force from counter balance to machine head. According to the type of compensating, there could be error from friction, pressure error of hydraulic or pressure control error. Also according to what to use for transferring the compensating force, transfer error of compensating force could be occur.

Keywords: Chain chordal action, counter balance, setup error, vertical positioning system.

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