Search results for: output feedback sliding mode control

Authors: Pankaj Negi

Abstract:

Nowadays the demand for receiving the high quality electrical energy is being increasing as consumer wants not only reliable but also quality power. Custom power instruments are of the most well-known compensators of power quality in distributed network. This paper present a comprehensive review of compensating custom power devices mainly DSTATCOM (distribution static compensator),DVR (dynamic voltage restorer), and UPQC (unified power quality compensator) and also deals with sliding mode control and its applications to custom power devices. The sliding mode control strategy provides robustness to custom power device and enhances the dynamic response for compensating voltage sag, swell, voltage flicker, and voltage harmonics. The aim of this paper is to provide a broad perspective on the status of compensating devices in electric power distribution system and sliding mode control strategies to researchers and application engineers who are dealing with power quality and stability issues.

Keywords: active power filters(APF), custom power device(CPD), DSTATCOM, DVR, UPQC, sliding mode control (SMC), power quality

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Authors: Zine Souhila Rached, Mazari Benyounes Bouzid, Mohamed Amine, Allaoui Tayeb

Abstract:

Wind energy has many advantages, it does not pollute and it is an inexhaustible source. However, its high cost is a major constraint, especially on the less windy sites. The purpose of wind energy systems is to maximize energy efficiency, and extract maximum power from the wind speed. In other words, having a power coefficient is maximum and therefore the maximum power point tracking. In this case, the MPPT control becomes important.To realize this control, strategy conventional proportional and integral (PI) controller is usually used. However, this strategy cannot achieve better performance. This paper proposes a robust control of a turbine which optimizes its production, that is improve the quality and energy efficiency, namely, a strategy of sliding mode control. The proposed sliding mode control strategy presents attractive features such as robustness to parametric uncertainties of the turbine; the proposed sliding mode control approach has been simulated on three-blade wind turbine. The simulation result under Matlab\Simulink has validated the performance of the proposed MPPT strategy.

Keywords: wind turbine, maximum power point tracking, sliding mode, energy conversion systems

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Authors: Aziz Sezgin, Yuksel Hacioglu, Nurkan Yagiz

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Sliding mode controller for a vehicle active suspension system is designed in this study. The widely used quarter car model is preferred and it is aimed to improve the ride comfort of the passengers. The effect of the actuator time delay, which may arise due to the information processing, sensors or actuator dynamics, is also taken into account during the design of the controller. A sliding mode controller was designed that has taken into account the actuator time delay by using Smith predictor. The successful performance of the designed controller is confirmed via numerical results.

Keywords: sliding mode control, active suspension system, actuator, time delay, vehicle

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Authors: Jenn-Yih Chen, Bean-Yin Lee, Yuan-Chuan Hsu, Jui-Cheng Lin, Kuang-Chyi Lee

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In this paper, a sliding mode control method based on the passivity approach is proposed to control the position of surface-mounted permanent magnet synchronous motors (PMSMs). Firstly, the dynamics of a PMSM was proved to be strictly passive. The position controller with an adaptive law was used to estimate the load torque to eliminate the chattering effects associated with the conventional sliding mode controller. The stability analysis of the overall position control system was carried out by adopting the passivity theorem instead of Lyapunov-type arguments. Finally, experimental results were provided to show that the good position tracking can be obtained, and exhibit robustness in the variations of the motor parameters and load torque disturbances.

Keywords: adaptive law, passivity theorem, permanent magnet synchronous motor, sliding mode control

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Authors: N. Tadrisi Parsa, A. R. Vali, R. Ghasemi

Abstract:

Diabetes is a growing health problem in worldwide. Especially, the patients with Type 1 diabetes need strict glycemic control because they have deficiency of insulin production. This paper attempts to control blood glucose based on body mathematical body model. The Bergman minimal mathematical model is used to develop the nonlinear controller. A novel back-stepping based sliding mode control (B-SMC) strategy is proposed as a solution that guarantees practical tracking of a desired glucose concentration. In order to show the performance of the proposed design, it is compared with conventional linear and fuzzy controllers which have been done in previous researches. The numerical simulation result shows the advantages of sliding mode back stepping controller design to linear and fuzzy controllers.

Keywords: bergman model, nonlinear control, back stepping, sliding mode control

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Authors: R. Loukil, M. Chtourou, T. Damak

Abstract:

In this work, we use the Fault detection and isolation and the Fault tolerant control based on sliding mode observer in order to introduce the well diagnosis of a nonlinear system. The robustness of the proposed observer for the two techniques is tested through a physical example. The results in this paper show the interaction between the Fault tolerant control and the Diagnosis procedure.

Keywords: fault detection and isolation FDI, fault tolerant control FTC, sliding mode observer, nonlinear system, robustness, stability

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Authors: Chaouch Souad, Abdou Latifa, Larbi Chrifi Alaoui

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This paper deals with sensorless backstepping control of induction motor using MRAS technique associated to sliding mode approach. A high order genetic algorithm structure is used to approximate a control law designed by the Backstepping technique, and to find the best parameters globally optimized. However, the Backstepping control approach is unsuitable for high performance applications because the need of a speed sensor for increased accuracy and the absence of any error decay mechanism. In this paper a nonlinear observer, obtained by combining sliding mode structure and model reference adaptive system (MRAS), is designed for the rotor flux and rotor speed estimations. To validate the proposed method, the results are presented for showing the improved drive characteristics and performances.

Keywords: Backstepping Control, Induction Motor, Genetic Algorithm, Sliding Mode observer

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

Abstract:

In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: autonomous vehicles, convoy, non-linear control, non-linear observer, sliding mode

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Authors: Shabnam Pashaei, Mohammadali Badamchizadeh

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This paper presents a new fractional-order terminal sliding mode control for synchronization of two different fractional-order chaotic systems with uncertainty and external disturbances. A fractional-order integral type nonlinear switching surface is presented. Then, using the Lyapunov stability theory and sliding mode theory, a fractional-order control law is designed to synchronize two different fractional-order chaotic systems. Finally, a simulation example is presented to illustrate the performance and applicability of the proposed method. Based on numerical results, the proposed controller ensures that the states of the controlled fractional-order chaotic response system are asymptotically synchronized with the states of the drive system.

Keywords: terminal sliding mode control, fractional-order calculus, chaotic systems, synchronization

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Authors: Hong Lu, Wei Fan, Yongquan Zhang, Junbo Zhang

Abstract:

A cross coupling sliding synchronization control strategy is proposed for the dual-driving feed system. This technology will minimize the position error oscillation and achieve the precise synchronization performance in the high speed and high precision drive system, especially some high speed and high precision machine. Moreover, a cross coupling compensation matrix is provided to offset the mismatched disturbance and the disturbance observer is established to eliminate the chattering phenomenon. Performance comparisons of proposed dual-driving cross coupling sliding mode control (CCSMC), normal cross coupling control （CCC） strategy with PID control, and electronic virtual main shaft control (EVMSC) strategy with SMC control are investigated by simulation and a dual-driving control system; the results show the effectiveness of the proposed control scheme.

Keywords: cross coupling matrix, dual motors, synchronization control, sliding mode control

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Authors: Ahmad Forouzantabar, Mohammad Azadi, Alireza Alesaadi

Abstract:

This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.

Keywords: lyapunov stability, autonomous underwater vehicle, sliding mode controller, electronics engineering

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Authors: Shun Horikoshi, Tohru Kawabe

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This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis

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Authors: Sana Bembli, Nahla Khraief Haddad, Safya Belghith

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This paper deals with a robust model free terminal sliding mode with gravity compensation approach used to control an exoskeleton-upper limb system. The considered system is a 2-DoF robot in interaction with an upper limb used for rehabilitation. The aim of this paper is to control the flexion/extension movement of the shoulder and the elbow joints in presence of matched disturbances. In the first part, we present the exoskeleton-upper limb system modeling. Then, we controlled the considered system by the model free terminal sliding mode with gravity compensation. A stability study is realized. To prove the controller performance, a robustness analysis was needed. Simulation results are provided to confirm the robustness of the gravity compensation combined with to the Model free terminal sliding mode in presence of uncertainties.

Keywords: exoskeleton- upper limb system, model free terminal sliding mode, gravity compensation, robustness analysis

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Authors: Roya Khajepour, Alireza B. Novinzadeh

Abstract:

A major issue with spherical robot is it surface shape, which is not always predictable. This means that given only the dynamic model of the robot, it is not possible to control the robot. Due to the fact that in certain conditions it is not possible to measure surface friction, control methods must be prepared for these conditions. Moreover, although spherical robot never becomes unstable or topples thanks to its special shape, since it moves by rolling it has a non-holonomic constraint at point of contact and therefore it is considered a non-holonomic system. Existence of such a point leads to complexity and non-linearity of robot's kinematic equations and makes the control problem difficult. Due to the non-linear dynamics and presence of uncertainty, the sliding-mode control is employed. The proposed method is based on Lyapunov Theory and guarantees system stability. This controller is insusceptible to external disturbances and un-modeled dynamics.

Keywords: sliding mode, spherical robot, non-holomonic constraint, system stability

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Authors: Abdellah Boualouch, Ahmed Essadki, Tamou Nasser, Ali Boukhriss, Abdellatif Frigui

Abstract:

This paper presents a power control for a Doubly Fed Induction Generator (DFIG) using in Wind Energy Conversion System (WECS) connected to the grid. The proposed control strategy employs two nonlinear controllers, Backstipping (BSC) and sliding-mode controller (SMC) scheme to directly calculate the required rotor control voltage so as to eliminate the instantaneous errors of active and reactive powers. In this paper the advantages of BSC and SMC are presented, the performance and robustness of this two controller’s strategy are compared between them. First, we present a model of wind turbine and DFIG machine, then a synthesis of the controllers and their application in the DFIG power control. Simulation results on a 1.5MW grid-connected DFIG system are provided by MATLAB/Simulink.

Keywords: backstipping, DFIG, power control, sliding-mode, WESC

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Authors: Rihab Hamdi, Amel Hadri Hamida, Fatiha Khelili, Sakina Zerouali, Ouafae Bennis

Abstract:

This paper features a comparative study performance of sliding mode controller (SMC) for closed-loop voltage control of direct current to direct current (DC-DC) three-cells buck converter connected in parallel, operating in continuous conduction mode (CCM), based on pulse-width modulation (PWM) with SMC based on hysteresis modulation (HM) where an adaptive feedforward technique is adopted. On one hand, for the PWM-based SM, the approach is to incorporate a fixed-frequency PWM scheme which is effectively a variant of SM control. On the other hand, for the HM-based SM, oncoming an adaptive feedforward control that makes the hysteresis band variable in the hysteresis modulator of the SM controller in the aim to restrict the switching frequency variation in the case of any change of the line input voltage or output load variation are introduced. The results obtained under load change, input change and reference change clearly demonstrates a similar dynamic response of both proposed techniques, their effectiveness is fast and smooth tracking of the desired output voltage. The PWM-based SM technique has greatly improved the dynamic behavior with a bit advantageous compared to the HM-based SM technique, as well as provide stability in any operating conditions. Simulation studies in MATLAB/Simulink environment have been performed to verify the concept.

Keywords: DC-DC converter, hysteresis modulation, parallel multi-cells converter, pulse-width modulation, robustness, sliding mode control

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Authors: Tomas Menard

Abstract:

The synthesis of output-feedback control law has been investigated by many researchers since the last century. While many results exist for the case of Linear Time Invariant systems whose measurements are continuously available, nowadays, control laws are usually implemented on micro-controller, then the measurements are discrete-time by nature. This fact has to be taken into account explicitly in order to obtain a satisfactory behavior of the closed-loop system. One considers here a general class of systems corresponding to an observability normal form and which is subject to uncertainties in the dynamics and sampling of the output. Indeed, in practice, the modeling of the system is never perfect, this results in unknown uncertainties in the dynamics of the model. We propose here an output feedback algorithm which is based on a linear state feedback and a continuous-discrete time observer. The main feature of the proposed control law is that only discrete-time measurements of the output are needed. Furthermore, it is formally proven that the state of the closed loop system exponentially converges toward the origin despite the unknown uncertainties. Finally, the performances of this control scheme are illustrated with simulations.

Keywords: dynamical systems, output feedback control law, sampling, uncertain systems

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Authors: I. Khabbazi, R. Ghasemi

Abstract:

This paper presents a combination of both robust nonlinear controller and nonlinear controller for a class of nonlinear 4Y Octorotor UAV using Back-stepping and sliding mode controller. The robustness against internal and external disturbance and decoupling control are the merits of the proposed paper. The proposed controller decouples the Octorotor dynamical system. The controller is then applied to a 4Y Octorotor UAV and its feature will be shown.

Keywords: sliding mode, backstepping, decoupling, octorotor UAV

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Authors: Dong Sang Yoo

Abstract:

The problem of finding control laws for underactuated systems has attracted growing attention since these systems are characterized by the fact that they have fewer actuators than the degrees of freedom to be controlled. The acrobot, which is a planar two-link robotic arm in the vertical plane with an actuator at the elbow but no actuator at the shoulder, is a representative of underactuated systems. In this paper, the dynamic model of the acrobot is implemented using Mathworks’ Simscape. And the sliding mode control is constructed using MATLAB and Simulink.

Keywords: acrobot, MATLAB and simulink, sliding mode control, underactuated system

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Authors: Xuezhang Hou

Abstract:

In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: M. Doumi, K. Tahir, A. Miloudi, A. G. Aissaoui, C. Belfedal, S. Tahir

Abstract:

This paper presents a three-phase grid-connected photovoltaic generation system with unity power factor for any situation of solar radiation based on voltage-oriented control (VOC). An input voltage clamping technique is proposed to control the power between the grid and photovoltaic system, where it is intended to achieve the maximum power point operation. This method uses a Perturb and Observe (P&O) controller. The main objective of this work is to compare the energy production unit performances by the use of two types of controllers (namely, classical PI and Sliding Mode (SM) Controllers) for the grid inverter control. The proposed control has a hierarchical structure with a grid side control level to regulate the power (PQ) and the current injected to the grid and to obtain a common DC voltage constant. To show the effectiveness of both control methods performances analysis of the system are analyzed and compared by simulation and results included in this paper.

Keywords: grid connected photovoltaic, MPPT, inverter control, classical PI, sliding mode, DC voltage constant, voltage-oriented control, VOC

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Authors: Yu-Sheng Lu, Chung-Hsin Cheng, Shuen-Shing Jan

Abstract:

This paper presents the design and implementation of a sliding-mod controller for tracking servo of optical disk drives. The tracking servo is majorly subject to two disturbance sources: radial run-out and shock. The lateral run-out disturbance is mostly repeatable, and a model of such disturbance is incorporated into the controller design to effectively compensate for it. Meanwhile, as a shock disturbance is usually non-repeatable and unpredictable, the sliding-mode controller is employed for its robustness to abrupt perturbations. As a result, a sliding-mode controller design based on the internal model principle is tailored for tracking servo of optical disk drives in order to deal with these two major disturbances. Experimental comparative studies are conducted to investigate the effectiveness of the specially designed controller.

Keywords: mechatronics, optical disk drive, sliding-mode control, servo systems

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Authors: Kessal Abdelhalim, Zebiri Fouad, Rahmani Lazhar

Abstract:

This paper presents an analysis by which the dynamic performances of a permanent magnet brushless DC (PMBLDC) motor is controlled through a hysteresis current loop and an outer speed loop with different controllers. The dynamics of the photovoltaic pumping drive system with sliding mode speed controllers are presented. The proposed structure is constituted of photovoltaic generator associated to DC-DC converter controlled by fuzzy logic to ensure the maximum power point tracking. The PWM signals are generated by the interaction of the motor speed closed-loop system and the current hysteresis. The motor reference current is compared with the motor speed feedback signal. The considered model has been implemented in Matlab/Simpower environment. The results show the effectiveness of the proposed method to increase the performance of the water pumping system.

Keywords: photovoltaic, permanent magnet brushless DC (PMBLDC) motor, MPPT, speed control, fuzzy, sliding mode

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

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

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

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Authors: Abbas Anser, Ahmad Irfan

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The main purpose of the VAV (Variable Air Volume) in Heating, Ventilation, and Air Conditioning (HVAC) system is to reduce energy consumption and make the buildings comfortable for the occupants. For better performance of the air conditioning system, different control techniques have been developed. In this paper, an Improved Sliding Mode Control (ISMC), based on Power Rate Exponential Reaching Law (PRERL), has been implemented on a VAV air conditioning system. Through the proposed technique, fast response and robustness have been achieved. To verify the efficacy of ISMC, a comparison of the suggested control technique has been made with Exponential Reaching Law (ERL) based SMC. And secondly, chattering, which is unfavorable as it deteriorates the mechanical parts of the air conditioning system by the continuous movement of the mechanical parts and consequently it increases the energy loss in the air conditioning system, has been alleviated. MATLAB/SIMULINK results show the effectiveness of the utilized scheme, which ensures the enhancement of the energy efficiency of the VAV air conditioning system.

Keywords: PID, SMC, HVAC, PRERL, feedback linearization, VAV, chattering

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Authors: Iftikhar Ahmad, A. Benallegue, A. El Hadri

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In this paper, we have proposed an observer for the reconstruction and a control law for the rejection application of unknown bounded external disturbance in a dynamical system. The strategy of both the observer and the controller is designed like a second order sliding mode with a proportional-integral (PI) term. Lyapunov theory is used to prove the exponential convergence and stability. Simulations results are given to show the performance of this method.

Keywords: non-linear systems, sliding mode observer, disturbance rejection, nonlinear control

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Authors: Soheil Arash Moghadam, Abdol R. Kashani Nia, Ali Akrami Zade

Abstract:

Considering numerous applications of Autonomous Underwater Vehicles in various industries, there has been plenty of researches and studies on the motion control of such vehicles. One of the useful aspects for studying is the guidance of these vehicles. In this paper, while presenting motion equations with six degrees of freedom for Autonomous Underwater Vehicles, Proportional Navigation Guidance Law and the first order sliding mode control for TAIPAN AUV was used to address its guidance for the purpose of collision with a moving target.

Keywords: Autonomous Underwater Vehicle (AUV), degree of freedom (DOF), hydrodynamic, line of sight(LOS), proportional navigation guidance(PNG), sliding mode control(SMC)

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Authors: Jung-Min Yang

Abstract:

Fault diagnosis of composite asynchronous sequential machines with parallel composition is addressed in this paper. An adversarial input can infiltrate one of two submachines comprising the composite asynchronous machine, causing an unauthorized state transition. The objective is to characterize the condition under which the controller can diagnose any fault occurrence. Two control configurations, state feedback and output feedback, are considered in this paper. In the case of output feedback, the exact estimation of the state is impossible since the current state is inaccessible and the output feedback is given as the form of burst. A simple example is provided to demonstrate the proposed methodology.

Keywords: asynchronous sequential machines, parallel composition, fault diagnosis, corrective control

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Authors: J. Ritonja, R. Brezovnik, M. Petrun, B. Polajžer

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Many modern synchronous generators in power systems are extremely weakly damped. The reasons are cost optimization of the machine building and introduction of the additional control equipment into power systems. Oscillations of the synchronous generators and related stability problems of the power systems are harmful and can lead to failures in operation and to damages. The only useful solution to increase damping of the unwanted oscillations represents the implementation of the power system stabilizers. Power system stabilizers generate the additional control signal which changes synchronous generator field excitation voltage. Modern power system stabilizers are integrated into static excitation systems of the synchronous generators. Available commercial power system stabilizers are based on linear control theory. Due to the nonlinear dynamics of the synchronous generator, current stabilizers do not assure optimal damping of the synchronous generator’s oscillations in the entire operating range. For that reason the use of the robust power system stabilizers which are convenient for the entire operating range is reasonable. There are numerous robust techniques applicable for the power system stabilizers. In this paper the use of sliding mode control for synchronous generator stability improvement is studied. On the basis of the sliding mode theory, the robust power system stabilizer was developed. The main advantages of the sliding mode controller are simple realization of the control algorithm, robustness to parameter variations and elimination of disturbances. The advantage of the proposed sliding mode controller against conventional linear controller was tested for damping of the synchronous generator oscillations in the entire operating range. Obtained results show the improved damping in the entire operating range of the synchronous generator and the increase of the power system stability. The proposed study contributes to the progress in the development of the advanced stabilizer, which will replace conventional linear stabilizers and improve damping of the synchronous generators.

Keywords: control theory, power system stabilizer, robust control, sliding mode control, stability, synchronous generator

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

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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm

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