Fault-Tolerant Control for Markovian Jump Delay Systems with an Adaptive Observer Approach

This paper investigates the problem of fault estimation and fault-tolerant control for a class of Markovian jump systems with mode-dependent interval time-varying delay and Lipschitz nonlinearities. In this paper, a new adaptive fault observer is designed to solve the problem of fault estimation. The proposed observer can estimate the states and faults simultaneously, whether faults are of time-varying or constant characterization. Based on the fault estimation, a fault-tolerant controller is designed to stabilize the closed-loop system. Sufficient conditions for the existence of the observer gain and fault-tolerant controller gain are got by a set of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the proposed fault-tolerant control method.     

A New Approach to Observer-Based Fault-Tolerant Controller Design for Takagi-Sugeno Fuzzy Systems with State Delay

This paper deals with the problem of active fault-tolerant control (FTC) for time-delay Takagi-Sugeno (T-S) fuzzy systems based on a fuzzy adaptive fault diagnosis observer (AFDO). A novel fuzzy fast adaptive fault estimation (FAFE) algorithm for T-S fuzzy models is proposed to enhance the performance of fault estimation, and sufficient conditions for the existence of the fault estimator are given in terms of linear matrix inequalities (LMIs). Using the obtained on-line fault estimation information, an observer-based fast active fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system. Simulation results of a track trail system and a nonlinear numerical example are presented to illustrate the effectiveness of the proposed method.     

Robust Adaptive Fault Estimation for a Class of Nonlinear Systems Subject to Multiplicative Faults

In this paper, a fault estimation problem for a class of nonlinear systems subject to multiplicative faults and unknown disturbances is investigated. Multiplicative faults usually mixed with system states and inputs can cause additional complexity in the design of fault estimator due to parameter changes within process. Especially for the nonlinear system corrupted with unknown disturbances, it is not an easy work to distinguish the real fault factor from the mixed term. Under the nonlinear Lipschitz condition, the proposed robust adaptive fault estimation approach not only estimates the multiplicative faults and system states simultaneously, but also extracts the real effect of the faults. Meanwhile, the effect of disturbances is restricted to an L ₂ gain performance criteria which can be formulated into the basic feasibility problem of a linear matrix inequality (LMI). In order to reduce the conservatism of the proposed method, a relaxing Lipschitz matrix is introduced. Finally, an illustrative example is applied to verify the efficiency of the proposed robust adaptive estimation scheme.     

Robust Fault Detection of Markovian Jump Systems

This paper deals with the problem of observer-based robust fault detection for both continuous- and discrete-time linear Markovian jump systems with an unknown input. By using a fault detection filter as residual generator and a proposed performance index as objective function, the robust fault detection filter design is formulated as an optimization problem. A sufficient condition to solve this problem is established in terms of the feasibility of certain matrix inequalities, which can be solved via iterative linear matrix inequality (LMI) algorithms. The residual evaluation problem is also considered. A numerical example is given to illustrate the effectiveness of the proposed techniques.     

Incipient Fault Detection Using an Associated Adaptive and Sliding-Mode Observer for Quadrotor Helicopter Attitude Control Systems

An associated adaptive and sliding-mode observer (AASMO) design is proposed to detect and estimate the incipient actuator faults of a quadrotor. The incipient faults considered are physical structure aging and quadrotor leakage. First, disturbances and nonlinear parameters are considered in system formulation for a realistic mathematical model of the quadrotor. Its fault model is also introduced. Second, the decomposed subsystems are obtained through coordinate transformations to separate the incipient faults from the disturbances. For the subsystem with no disturbance, the adaptive observer can estimate the incipient faults. For the subsystem with disturbances, the sliding-mode observer has strong robustness against the disturbances. Dynamic error convergence and system stability can also be guaranteed by Lyapunov stability theory. Finally, the simulation results of quadrotor helicopter attitude systems validate the efficiency of the proposed AASMO-based incipient fault detection algorithm.     

Sensorless Control of Induction Machines by a New Neural Algorithm: The TLS EXIN Neuron

This paper proposes two speed observers for high-performance induction machine drives, both adopting an online adaptation law based on a new total least-squares (TLS) technique: the TLS EXIN neuron. The first is a model reference adaptive system (MRAS) observer with a neural adaptive integrator in the reference model and a neural adaptive model trained online by the TLS EXIN neuron. This observer, presented in a previous article of the authors, has been improved here in two aspects: first, the neural adaptive integrator has been modified to make its learning factor vary according to the reference speed of the drive, second, a neural adaptive model based on the modified Euler integration has been proposed to solve the discretization instability problem in field-weakening. The second observer is a new full-order adaptive one based on the state equations of the induction machine, where the speed is estimated by means of a TLS EXIN adaptation technique. Both these observers have been provided with an inverter nonlinearity compensation algorithm and with techniques for the online estimation of the stator resistance of the machine. Moreover, a thorough theoretical stability analysis has been developed for them both, with particular reference to the field-weakening region behavior for the TLS MRAS observer and to the regenerating mode at low speeds for the TLS adaptive observer. Both speed observers have been verified in numerical simulation and experimentally on a test setup, and have also been compared experimentally with the BPN MRAS observer, the classic adaptive observer and with an open-loop estimator. Results show that both proposed observers outperform all other three observers in every working condition, with the TLS adaptive observer resulting in a better performance than the TLS MRAS observer     

Integral-observer-based chaos synchronization

In this paper, a new scheme based on integral observer approach is designed for a class of chaotic systems to achieve synchronization. Unlike the proportional observer approach, the proposed scheme is demonstrated to be effective under a noisy environment in the transmission channel. Based on the Lyapunov stability theory, a sufficient condition for synchronization is derived in the form of a Lyapunov inequality. This Lyapunov inequality is further transformed into a linear matrix inequality (LMI) form by using the Schur theorem and some matrix operation techniques, which can be easily solved by the LMI toolboxes for the design of suitable control gains. It is demonstrated with the Murali-Lakshmanan-Chua system that a better noise suppression and a faster convergence speed can be achieved for chaos synchronization by using this integral observer scheme, as compared with the traditional proportional observer approach.     

Sensing of the time-varying angular rate for MEMS Z-axis gyroscopes

In this paper, a nonlinear estimation strategy for sensing the time-varying angular rate of a Z-axis MEMS gyroscope is presented. An off-line adaptive least-squares estimation strategy is first developed to accurately estimate the unknown model parameters. Both axes of a Z-axis MEMS gyroscope are then actively controlled utilizing an on-line controller/observer to facilitate time-varying angular rate sensing. The proposed nonlinear estimation strategy is developed based on a Lyapunov-based analysis, which proves that the time-varying angular rate experienced by the device can be estimated accurately. Two cases for angular rate are investigated which are time-varying and constant magnitudes. An adaptive controller/observer was also utilized for sensing the angular rate to investigate the performance of the proposed controller/observer. Representative numerical results are discussed to demonstrate the performance of the proposed nonlinear strategy in accurately sensing the applied angular rate. Overall, the proposed nonlinear controller/observer improves sensing the constant angular rate by 50% and the time-varying angular rate by 90% when compared with an adaptive controller/observer.     

Observer-Based Optimal Fault Detection and Diagnosis Using Conditional Probability Distributions

A new optimal fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (pdf's) of the system. The square-root B-spline functional approximation technique is used to formulate the output pdf's with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. In order to improve FDD performances, two optimization measures, namely guaranteed cost performance and$H_infty$performance, are applied to optimize the observer design. Simulations are given to demonstrate the efficiency of the proposed approach.     

High-Gain Observers With Sliding Mode for State and Unknown Input Estimations

To handle the state estimation of a nonlinear system perturbed by a scalar disturbance distributed by a known nonlinear vector, a sliding-mode term is incorporated into the nonlinear high-gain observer (HGO) to realize a robust HGO. By imposing a structural assumption on the unknown input distribution vector, the observability of the disturbance with respect to the output is safeguarded, and the disturbance can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the nonlinear observers are designed under the structural assumption that the system is observable with respect to any input. In the sliding mode, the disturbance under an equivalent control becomes an increment of Lipschitzian function, and the convergence of the estimation error dynamics can be proven similar to the analysis of HGOs. The proposed technique can be applied for fault detection and isolation. The simulation results for the bioreactor application demonstrate the effectiveness of the proposed method.      

Flux observer with online tuning of stator and rotor resistancesfor induction motors

This paper proposes an adaptive flux observer for induction motors, where stator and rotor resistances are estimated in online environments. The variation of motor parameters during operation degrades the performance of the controller and the flux observer. Among the parameters of induction motors, rotor resistance is a crucial one for flux estimation, and stator resistance also becomes critical in the low-speed region. Under the persistent excitation condition, the proposed method estimates the actual values of stator and rotor resistances simultaneously, which guarantees the exact estimation of the rotor flux. The persistent excitation condition is not satisfied when the electric torque of an induction motor is absent due to the lack of rotor currents. Even in this case, the proposed method achieves the correct estimation of the rotor flux. Simulations and actual experiments show that the rotor flux is estimated in all operating conditions and that both resistances converge to their actual values when the electrical motor torque exists     

Robust Fault Estimation and Accommodation for a Class of T–S Fuzzy Systems with Local Nonlinear Models

This paper focuses on the problems of fault estimation and accommodation for a class of T–S fuzzy systems with local nonlinear models and having an external disturbance and sensor and actuator faults, simultaneously. A fuzzy robust fault estimation observer is designed to estimate the system state and sensor and actuator faults. Compared with existing results, the observer not only is robust to the disturbance but also has a wider application range and more freedom for design. To compensate for the effect of faults and to stabilize the closed-loop system, an observer-based fault-tolerant controller is proposed. The separate design of the observer and controller avoids coupling between them. Finally, a simulation is conducted to demonstrate the effectiveness of the proposed method.     

Robust Delay-Derivative-Dependent Sliding Mode Observer for Fault Reconstruction : A Diesel Engine System Application

In this paper, a new delay-derivative-dependent sliding mode observer (SMO) design for a class of linear uncertain time-varying delay systems is presented. Based on this observer, a robust actuator fault reconstruction method is developed. In the meantime, the considered uncertainty is bounded and the time-delay is varying and affects the state system. Besides, the dynamic properties of the observer are analyzed and the reachability condition is satisfied. Applying the developed SMO, the \(H_\infty \) concept and a delay-derivative-dependent bounded real lemma (BRL), a robust actuator fault reconstruction is obtained wherein the effect of the uncertainty is minimized. Also, both the SMO and the BRL are delay-derivative-dependent which reduces the time-varying delay conservatism on the state estimation and on the fault reconstruction. A diesel engine system is included to illustrate the validity and the applicability of the proposed approaches.     

Integrated MIMO fault detection and disturbance observer-based control

This paper presents a new method of disturbance observer-based control (DOBC) for multi-input-multi-output (MIMO) highly-coupled unstable systems. In contrast to the current input–output approach for stable single-input-single-output (SISO) systems, the Youla parameterization of stabilizing controllers by full order state observer (FOSO) feedback control is shown more appropriate for general MIMO systems, while retaining the intuitive aspects of DOBC design. We propose a general MIMO DOBC expanded from this single FOSO stabilizing control, where a parallel number of FOSOs for fault detection, state estimation, and disturbance observer are integrated to achieve the relevant operational requirements and performance. Within this integrated control system, we propose a MIMO disturbance observer design method by a game-theoretic detection filter (GTDF) design. The DOBC design features GTDF disturbance decoupling followed by H-infinity model matching to establish the desired bandwidth for each channel of the decoupled disturbance observer. The proposed DOBC is applied to an open-loop unstable MIMO Active Magnetic Bearing Spindle (AMBS). Experimental results are presented to demonstrate the design method and control performance.     

Robust-adaptive-observer design based on /spl gamma/-positive real problem for sensorless induction-motor drives

This paper proposes a design of a robust-adaptive full-order observer based on the /spl gamma/-positive real problem for sensorless induction-motor drives. The adaptive full-order observer is known to become unstable in a major part of the regenerating-mode low-speed operation, and this prevents the sensorless vector controller from operating an induction motor successfully. In this paper, a design of the observer gain for both stable speed identification and robust flux phase estimation and an adaptive scheme for stator resistance identification are proposed. First, the error system of the adaptive full-order observer is reconsidered-requirements of this observer with a speed identifier are described, in which a simple robust observer gain design in the sense of H/sub /spl infin// optimization is not useful in reality. Next, in order to satisfy all the requirements of the robust adaptive observer, the design of the observer gain based on the /spl gamma/-positive real problem and the adaptive scheme for stator resistance are described. Finally, several experimental results show the feasibility and effectiveness of the proposed design.     

Fault-tolerant control system of flexible arm for sensor fault by using reaction force observer

In recent years, control system reliability has received much attention with increase of situations where computer-controlled systems such as robot control systems are used. In order to improve reliability, control systems need to have abilities to detect a fault (fault detection) and to maintain the stability and the control performance (fault tolerance). In this paper, we address the vibration suppression control of a one-link flexible arm robot. Vibration suppression is realized by an additional feedback of a strain gauge sensor attached to the arm besides motor position. However, a sensor fault (e.g., disconnection) may degrade the control performance and make the control system unstable at its worst. In this paper, we propose a fault-tolerant control system for strain gauge sensor fault. The proposed control system estimates a strain gauge sensor signal based on the reaction force observer and detects the fault by monitoring the estimation error. After fault detection, the proposed control system exchanges the faulty sensor signal for the estimated one and switches to a fault-mode controller so as to maintain the stability and the control performance. We apply the proposed control system to the vibration suppression control system of a one-link flexible arm robot and confirm the effectiveness of the proposed control system by some experiments.     

基于集员未知输入观测器的风力机桨距执行器故障诊断

风力机一般放置在恶劣的环境中,其桨距执行器极易出现故障。文中针对一类含有未知但有界干扰和噪声的风力机系统的桨距执行器故障问题,设计了集员未知输入观测器对桨距的执行器故障进行检测并分离。采用气动机理和现代辨识原理建立风力机系统模型,通过优化未知输入观测器设计对系统中的干扰解耦,基于中心对称多胞体估计不考虑故障时残差的区间包络,并将其作为残差估计的上下动态阈值,实现状态估计。在上述基础上提出了利用一组集员未知输入观测器进行故障诊断的策略。仿真结果表明,在实验过程中,文中所设计的集员未知输入观测器准确地诊断出了风力机桨距执行器的3阶和5阶线性系统在发生突变故障和缓慢时变故障的时间和位置,证明了所提故障诊断策略的有效性。     

基于反步自适应技术的四旋翼无人机执行器故障问题研究

四旋翼无人机是一个具有多变量、强耦合、强非线性特性的欠驱动非稳定被控对象,快速准确地进行故障诊断对实现无人机安全飞行具有重要意义。基于Newton-Euler运动定理建立四旋翼无人机动力学方程,针对四旋翼无人机执行器故障基于反步法、Lyapunov理论结合自适应技术推导出自适应律,反解出滚转角、俯仰角的期望值,从而进行在线故障估计,取代用于故障重构的观测器,较好地实现执行器容错控制。通过仿真实验验证了本文所提的反步自适应容错控制方法的有效性。     

A hybrid speed estimator of flux observer for induction motor drives

This paper proposes a hybrid speed estimator that gives the synergetic effect between the model- and the saliency-based field orientations for induction motor drives. The model-based field orientation consists of a flux observer with an adaptive speed estimator that has unstable regions at zero frequency and zero speed. Saliency-based flux orientation utilizes magnetic saliencies caused by saturation and high-frequency injection that causes the torque ripples due to the chattering. The chattering is caused by the higher cutoff frequency of the flux-angle estimation to keep its high dynamics. The proposed method compensates both faults and realizes complete speed estimation from zero to high-speed condition including zero stator frequency.