Search results for: observer design

Authors: Bououden Soraya

Abstract:

This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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Authors: Mounir Bekaik, Messaoud Ramdani

Abstract:

We present in this work a new technique of stabilization for fault nonlinear systems. The approach we adopt focus on a fuzzy Luenverger observer. The T-S approximation of the nonlinear observer is based on fuzzy C-Means clustering algorithm to find local linear subsystems. The MOESP identification approach was applied to design an empirical model describing the subsystems state variables. The gain of the observer is given by the minimization of the estimation error through Lyapunov-krasovskii functional and LMI approach. We consider a three tank hydraulic system for an illustrative example.

Keywords: nonlinear system, fuzzy, faults, TS, Lyapunov-Krasovskii, observer

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Authors: Joon-Hoon Park

Abstract:

The fundamental concept of observability is important in both theoretical and practical points of modern control systems. In modern control theory, a control system has criteria for determining the design solution exists for the system parameters and design objectives. The idea of observability relates to the condition of observing or estimating the state variables from the output variables that is generally measurable. To design closed-loop control system, the practical problems of implementing the feedback of the state variables must be considered and implementing state feedback control problem has been existed in this case. All the state variables are not available, so it is requisite to design and implement an observer that will estimate the state variables form the output parameters. However sometimes unknown inputs are presented in control systems as practical cases. This paper presents a design method and algorithm for observer of control system with unknown input parameters based on Rationalized Haar transform. The proposed method is more advantageous than the other numerical method.

Keywords: orthogonal functions, rationalized Haar transforms, control system observer, algebraic method

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Authors: Toshiyuki Satoh, Hiroki Hara, Naoki Saito, Jun-ya Nagase, Norihiko Saga

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This paper addresses a control system design for a table drive system based on the disturbance observer (DOB)-based predictive functional critical control (PFCC). To empower the previously developed DOB-based PFC to handle constraints on controlled outputs, we propose to take a critical control approach. To this end, we derive the transfer function representation of the PFC controller, and yield a detailed design procedure. The effectiveness of the proposed method is confirmed through an experimental evaluation.

Keywords: critical control, disturbance observer, mechatronics, motion control, predictive functional control, table drive systems

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

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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: Tomas Menard

Abstract:

The design of control-law for engineering systems has been investigated for many decades. While many results are concerned with continuous systems with continuous output, nowadays, many controlled systems have to transmit their output measurements through network, hence making it discrete-time. But it is well known that the sampling of a system whose control-law is based on the continuous output may render the system unstable, especially when this sampling period is long compared to the system dynamics. The control design then has to be adapted in order to cope with this issue. In this paper, we consider systems which can be modeled as double integrator with uncertainty on the input since many mechanical systems can be put under such form. We present a control scheme based on an observer using only discrete time measurement and which provides continuous time estimation of the state, combined with a continuous control law, which stabilized a system with second-order dynamics even in the presence of uncertainty. It is further shown that arbitrarily long sampling periods can be dealt with properly setting the control scheme parameters.

Keywords: dynamical system, control law design, sampled output, observer design

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

Abstract:

This paper investigates the training of multilayer neural network using the classic approach. Then, for estimation purposes, we suggest the use of a specific neural observer that we study its training algorithm which is the back-propagation one in the case of the disponibility of the state and in the case of an unmeasurable state. A MATLAB simulation example will be studied to highlight the usefulness of this kind of observer.

Keywords: training, estimation purposes, neural observer, back-propagation, unmeasurable state

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Authors: Christian Rathgeber, Franz Winkler, Dirk Odenthal, Steffen Müller

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In this contribution a structure for high level lateral vehicle tracking control based on the disturbance observer is presented. The structure is characterized by stationary compensating side forces disturbances and guaranteeing a cooperative behavior at the same time. Driver inputs are not compensated by the disturbance observer. Moreover the structure is especially useful as it robustly stabilizes the vehicle. Therefore the parameters are selected using the Parameter Space Approach. The implemented algorithms are tested in real world scenarios.

Keywords: disturbance observer, trajectory tracking, robust control, autonomous driving, cooperative driving

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Authors: Mouna Abarkan, Abdelillah Byou, Nacer M'Sirdi, El Hossain Abarkan

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This paper presents the estimation of the state of charge of the battery using two types of observers. The battery model used is the combination of a voltage source, which is the open circuit battery voltage of a strength corresponding to the connection of resistors and electrolyte and a series of parallel RC circuits representing charge transfer phenomena and diffusion. An adaptive observer applied to this model is proposed, this observer to estimate the battery state of charge of the battery is based on EFK and sliding mode that is known for their robustness and simplicity implementation. The results are validated by simulation under MATLAB/Simulink and implemented in Arduino-LabView.

Keywords: model of the battery, adaptive sliding mode observer, the EFK observer, estimation of state of charge, SOC, implementation in Arduino/LabView

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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: Sungsik Jo, Hyeonwoo Kim, Iksu Choi, Hunmo Kim

Abstract:

In the SHP, LVDT sensor is for detecting the length changes of the EHA output, and the thrust of the EHA is controlled by the pressure sensor. Sensor is possible to cause hardware fault by internal problem or external disturbance. The EHA of SHP is able to be uncontrollable due to control by feedback from uncertain information, on this paper; the sliding mode observer algorithm estimates the original sensor output information in permanent sensor fault. The proposed algorithm shows performance to recovery fault of disconnection and short circuit basically, also the algorithm detect various of sensor fault mode.

Keywords: smart hybrid powerpack (SHP), electro hydraulic actuator (EHA), permanent sensor fault tolerance, sliding mode observer (SMO), graphic user interface (GUI)

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Authors: Jin Wang, Chunyi Zhu, Chongjian Li, Dapeng Zheng

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A method based on virtual inertia for suppressing electromechanical torsional vibration of a large-power AC drive system is presented in this paper. The main drive system of the rolling mill is the research object, and a two-inertia elastic model is established to study the mechanism of electromechanical torsional vibration. The improvement is made based on the control of the load observer. The virtual inertia control ratio K is added to the speed forward channel, and the feedback loop adds 1-K to design virtual inertia control. The control method combines the advantages of the positive and negative feedback control of the load observer, can achieve the purpose of controlling the moment of inertia of the motor from the perspective of electrical control, and effectively suppress oscillation.

Keywords: electromechanical torsional vibration, large-power AC drive system, load observer, simulation design

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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: N. Ben Si Ali, N. Benalia, N. Zarzouri

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Speed sensorless systems are intensively studied during recent years; this is mainly due to their economical benefit and fragility of mechanical sensors and also the difficulty of installing this type of sensor in many applications. These systems suffer from instability problems and sensitivity to parameter mismatch at low speed operation. In this paper an analysis of adaptive observer stability with stator resistance estimation is given.

Keywords: motor drive, sensorless control, adaptive observer, stator resistance estimation

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Authors: Jason Sheng-Hong Tsai, Faezeh Ebrahimzadeh, Min-Ching Chung, Shu-Mei Guo, Leang-San Shieh, Tzong-Jiy Tsai, Li Wang

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In this paper, we first construct a new state and disturbance estimator using discrete-time proportional plus integral observer to estimate the system state and the unknown external disturbance for the discrete-time system with an input-to-output direct-feedthrough term. Then, the generalized optimal linear quadratic digital tracker design is applied to construct a proportional plus integral observer-based tracker for the system with an unknown external disturbance to have a desired tracking performance. Finally, a numerical simulation is given to demonstrate the effectiveness of the new application of our proposed approach.

Keywords: non-minimum phase system, optimal linear quadratic tracker, proportional plus integral observer, state and disturbance estimator

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In this paper, a robust fault-tolerant predictive control (FTPC) strategy is proposed for systems with linear parameter varying (LPV) models and input constraints subject to sensor faults. Generally, virtual observers are used for improving the observation precision and reduce the impacts of sensor faults and uncertainties in the system. However, this type of observer lacks certain system measurements which substantially reduce its accuracy. To deal with this issue, a real observer is then designed based on the virtual observer, and consequently a real observer-based robust predictive control is designed for polytopic LPV systems. Moreover, the proposed observer can entirely assure that all system states and sensor faults are estimated. As a result, and based on both observers, a robust fault-tolerant predictive control is then established via the Lyapunov method where sufficient conditions are proposed, for stability analysis and control purposes, in linear matrix inequalities (LMIs) form. Finally, simulation results are given to show the effectiveness of the proposed approach.

Keywords: linear parameter varying systems, fault-tolerant predictive control, observer-based control, sensor faults, input constraints, linear matrix inequalities

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Authors: Seyed Mohammad Hashemi, Shahrokh Barati

Abstract:

The problem of fault-tolerant control (FTC) by accommodation method has been studied in this paper. The fault occurs in any system components such as actuators, sensors or internal structure of the system and leads to loss of performance and instability of the system. When a fault occurs, the purpose of the fault-tolerant control is designate strategy that can keep the control loop stable and system performance as much as possible perform it without shutting down the system. Here, the section of fault detection and isolation (FDI) system has been evaluated with regard to actuator's fault. Designing a fault detection and isolation system for a multi input-multi output (MIMO) is done by an unknown input observer, so the system is divided to several subsystems as the effect of other inputs such as disturbing given system state equations. In this observer design method, the effect of these disturbances will weaken and the only fault is detected on specific input. The results of this approach simulation can confirm the ability of the fault detection and isolation system design. After fault detection and isolation, it is necessary to redesign controller based on a suitable modification. In this regard after the use of unknown input observer theory and obtain residual signal and evaluate it, PID controller parameters redesigned for iterative. Stability of the closed loop system has proved in the presence of this method. Also, In order to soften the volatility caused by Annie variations of the PID controller parameters, modifying Sigma as a way acceptable solution used. Finally, the simulation results of three tank popular example confirm the accuracy of performance.

Keywords: fault tolerant control, fault detection and isolation, actuator fault, unknown input observer

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Authors: Alireza Gholami, Amir H. D. Markazi

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In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.

Keywords: adaptive algorithm, fuzzy systems, membership functions, observer

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Authors: Samir Zeghlache, Abderrahmen Bouguerra, Kamel Kara, Djamel Saigaa

Abstract:

The control of the trirotor helicopter includes nonlinearities, uncertainties and external perturbations that should be considered in the design of control laws. This paper presents a control strategy for an underactuated six degrees of freedom (6 DOF) trirotor helicopter, based on the coupling of the fuzzy logic control and sliding mode control (SMC). The main purpose of this work is to eliminate the chattering phenomenon. To achieve our purpose we have used a fuzzy logic control to generate the hitting control signal, also the non linear observer is then synthesized in order to estimate the unmeasured states. Finally simulation results are included to indicate the trirotor UAV with the proposed controller can greatly alleviate the chattering effect and remain robust to the external disturbances.

Keywords: fuzzy sliding mode control, trirotor helicopter, dynamic modelling, underactuated systems

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Authors: Oluwaseun Simon Adekanle, M'hammed Guisser, Elhassane Abdelmounim, Mohamed Aboulfatah

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In this paper, modeling and control of a grid connected 660KW Doubly-Fed Induction Generator wind turbine is presented. Stator flux orientation is used to realize active-reactive power decoupling to enable independent control of active and reactive power. The recursive Integral Backstepping technique is used to control generator speed to its optimum value and to obtain unity power factor. The controller is combined with High Gain Observer to estimate the mechanical torque of the machine. The most important advantage of this combination of High Gain Observer and the Integral Backstepping controller is the annulation of static error that may occur due to incertitude between the actual value of a parameter and its estimated value by the controller. Simulation results under Matlab/Simulink show the robustness of this control technique in presence of parameter variation.

Keywords: doubly-fed induction generator, field orientation control, high gain observer, integral backstepping control

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Authors: Ali Afaghi, Sehraneh Ghaemi

Abstract:

The coordination of the multi-agent systems has been one of the interesting topic in recent years, because of its potential applications in many branches of science and engineering such as sensor networks, flocking, underwater vehicles and etc. In the most of the related studies, it is assumed that the dynamics of the multi-agent systems are integer-order and linear and the multi-agent systems with the fractional-order nonlinear dynamics are rarely considered. However many phenomena in nature cannot be described within integer-order and linear characteristics. This paper investigates the leader-following consensus problem for a class of nonlinear fractional-order multi-agent systems based on observer-based cooperative control. In the system, the dynamics of each follower and leader are nonlinear. For a multi-agent system with fixed directed topology firstly, an observer-based consensus protocol is proposed based on the relative observer states of neighboring agents. Secondly, based on the property of the stability theory of fractional-order system, some sufficient conditions are presented for the asymptotical stability of the observer-based fractional-order control systems. The proposed method is applied on a five-agent system with the fractional-order nonlinear dynamics and unavailable states. The simulation example shows that the proposed scenario results in the good performance and can be used in many practical applications.

Keywords: fractional-order multi-agent systems, leader-following consensus, nonlinear dynamics, directed graphs

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Authors: I. Gahlouz, A. Chellil

Abstract:

The paper concerns the estimation of system components faults by using an unknown inputs observer. To reach this goal, we used the Bond Graph approach to physical modelling. We showed that this graphical tool is allowing the representation of system components faults as unknown inputs within the state representation of the considered physical system. The study of the causal and structural features of the system (controllability, observability, finite structure, and infinite structure) based on the Bond Graph approach was hence fulfilled in order to design an unknown inputs observer which is used for the system component fault estimation.

Keywords: estimation, bond graph, controllability, observability

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Authors: P.Kiruthika, K. Ramani

Abstract:

This paper presented the design and advancement of a single-phase 27-level Hybrid Multilevel DC-AC Converter interfacing with Photo Voltaic. In this context, the Multicarrier Pulse Width Modulation method can be implemented in 27-level Hybrid Multilevel Inverter for generating a switching pulse. Perturb & Observer algorithm can be used in the Maximum Power Point Tracking method for the Photo Voltaic system. By implementing Maximum Power Point Tracking with three separate solar panels as an input source to the 27-level Hybrid Multilevel Inverter. This proposed method can be simulated by using MATLAB/simulink. The result shown that the proposed method can achieve silky output wave forms, more flexibility in voltage range, and to reduce Total Harmonic Distortion in medium-voltage drives.

Keywords: Multi Carrier Pulse Width Modulation Technique (MCPWM), Multi Level Inverter (MLI), Maximum Power Point Tracking (MPPT), Perturb and Observer (P&O)

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Authors: P. Karimi, A. H. Khedmati Bazkiaei

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The main goal of this study is to test differential neural network as a controller of smart structure and is to enumerate its advantages and disadvantages in comparison with other controllers. In this study, the smart structure has been considered as a Euler Bernoulli cantilever beam and it has been tried that it be under control with the use of vibration neural network resulting from movement. Also, a linear observer has been considered as a reference controller and has been compared its results. The considered vibration charts and the controlled state have been recounted in the final part of this text. The obtained result show that neural observer has better performance in comparison to the implemented linear observer.

Keywords: smart material, on-line differential artificial neural network, active control, finite element method

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Authors: Hashim Ali, Sheheryar Khan

Abstract:

Security for applications is always been a keen issue of concern. In general, security is to allow access of grant to legal user or to deny non-authorized access to the system. Shoulder surfing is an observation technique to hack an account or to enter into a system. When a malicious observer is capturing or recording the fingers of a user while he is entering sensitive inputs (PIN, Passwords etc.) and may be able to observe user’s password credential. It is very rigorous for a novice user to prevent himself from shoulder surfing or unaided observer in a public place while accessing his account. In order to secure the user account, there are five factors of authentication; they are: “(i) something you have, (ii) something you are, (iii) something you know, (iv) somebody you know, (v) something you process”. A technique has been developed of fifth-factor authentication “something you process” to provide novel approach to the user. In this paper, we have applied position based operational code authentication in such a way to more easy and user friendly to the user.

Keywords: shoulder surfing, malicious observer, sensitive inputs, authentication

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Authors: Abderrhamane Jarou, Dominique Sauter, Christophe Aubrun

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Over the past decade, the growing demand for energy efficiency in buildings has attracted the attention of the control community. Failures in HVAC (heating, ventilation and air conditioning) systems in buildings can have a significant impact on the desired and expected energy performance of buildings and on the user's comfort as well. FTC is a recent technology area that studies the adaptation of control algorithms to faulty operating conditions of a system. The application of Fault-Tolerant Control (FTC) in HVAC systems has gained attention in the last two decades. The objective is to maintain the variations in system performance due to faults within an acceptable range with respect to the desired nominal behavior. This paper considers the so-called active approach, which is based on fault and identification scheme combined with a control reconfiguration algorithm that consists in determining a new set of control parameters so that the reconfigured performance is "as close as possible, "in some sense, to the nominal performance. Thermal models of buildings and their HVAC systems are described by non-linear (usually bi-linear) equations. Most of the works carried out so far in FDI (fault diagnosis and isolation) or FTC consider a linearized model of the studied system. However, this model is only valid in a reduced range of variation. This study presents a new fault diagnosis (FD) algorithm based on a bilinear observer for the detection and accurate estimation of the magnitude of the HVAC system failure. The main contribution of the proposed FD algorithm is that instead of using specific linearized models, the algorithm inherits the structure of the actual bilinear model of the building thermal dynamics. As an immediate consequence, the algorithm is applicable to a wide range of unpredictable operating conditions, i.e., weather dynamics, outdoor air temperature, zone occupancy profile. A bilinear fault detection observer is proposed for a bilinear system with unknown inputs. The residual vector in the observer design is decoupled from the unknown inputs and, under certain conditions, is made sensitive to all faults. Sufficient conditions are given for the existence of the observer and results are given for the explicit computation of observer design matrices. Dedicated observer schemes (DOS) are considered for sensor FDI while unknown input bilinear observers are considered for actuator or system components FDI. The proposed strategy for FTC works as follows: At a first level, FDI algorithms are implemented, making it also possible to estimate the magnitude of the fault. Once the fault is detected, the fault estimation is then used to feed the second level and reconfigure the control low so that that expected performances are recovered. This paper is organized as follows. A general structure for fault-tolerant control of buildings is first presented and the building model under consideration is introduced. Then, the observer-based design for Fault Diagnosis of bilinear systems is studied. The FTC approach is developed in Section IV. Finally, a simulation example is given in Section V to illustrate the proposed method.

Keywords: bilinear systems, fault diagnosis, fault-tolerant control, multi-zones building

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Authors: Sarah Odofin, Zhiwei Gao

Abstract:

Operations and maintenance of wind turbine have received much attention by researcher due to rapid expansion of wind farms. This paper explores a novel fault diagnosis that is designed and optimized to be very sensitive to faults and robust to disturbances. The faults considered are the sensor faults of which the augmented observer is considered to enlarge faults and to be robust to disturbance. A qualitative model based analysis is proposed for early fault diagnosis to minimize downtime mostly caused by components breakdown and exploit productivity. Simulation results are computed validating the models provided which demonstrates system performance using practical application of fault type examples. The results demonstrate the effectiveness of the developed techniques investigated in a Matlab/Simulink environment.

Keywords: wind turbine, condition monitoring, genetic algorithm, fault diagnosis, augmented observer, disturbance robustness, fault estimation, sensor monitoring

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Authors: Ahmed Abbou

Abstract:

This paper present a sensorless controller designed by the backstepping approach for the speed control of induction motor. In this strategy of control, we also combined the method Fuzzy MRAS to estimate the rotor speed and the observer type Luenburger to observe Rotor flux. The control model involves a division by the flux variable that may lead to unbounded solutions. Such a risk is avoided by basing the controller design on Lyapunov function that accounts for the model singularity. On the other hand, this mixed method gives better results in Sensorless operation and especially at low speed. The response time at 5% of the flux is 20ms while the error between the speed with sensor and the estimated speed remains in the range of ±0.8 rad/s for the rated functioning and ±1.5 rad/s for low speed.

Keywords: backstepping approach, fuzzy logic, induction motor, luenburger observer, sensorless MRAS

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Authors: Jun-ya Nagase, Toshiyuki Satoh, Norihiko Saga, Koichi Suzumori

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In recent years, Japanese society has been aging, engendering a labour shortage of young workers. Robots are therefore expected to perform tasks such as rehabilitation, nursing elderly people, and day-to-day work support for elderly people. The pneumatic balloon actuator is a rubber artificial muscle developed for use in a robot hand in such environments. This actuator has a long stroke, and a high power-to-weight ratio compared with the present pneumatic artificial muscle. Moreover, the dynamic characteristics of this actuator resemble those of human muscle. This study evaluated characteristics of force control of balloon actuator using a predictive functional control (PFC) system with disturbance observer. The predictive functional control is a model-based predictive control (MPC) scheme that predicts the future outputs of the actual plants over the prediction horizon and computes the control effort over the control horizon at every sampling instance. For this study, a 1-link finger system using a pneumatic balloon actuator is developed. Then experiments of PFC control with disturbance observer are performed. These experiments demonstrate the feasibility of its control of a pneumatic balloon actuator for a robot hand.

Keywords: disturbance observer, pneumatic balloon, predictive functional control, rubber artificial muscle

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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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