Adaptive fault tolerant control for a class of uncertain fractional‐order systems based on disturbance observer

In this paper, a class of fractional‐order nonlinear systems are considered in the presence of actuator faults. A novel fault tolerant control scheme based on disturbance observer has been presented, where the actuator faults are considered as the system disturbance and can be approximated by the proposed disturbance observer. The developed fault tolerant control guarantees the convergence of the closed‐loop system and the output tracking performance. Finally, a simulation example is presented to verify the effectiveness of the new method.     

Robust control of wind turbines based on fractional nonlinear disturbance observer

In order to assure maximum energy conversion, the angular velocity of the wind turbine rotor tracks a nominal profile depending on the wind speed. However, conventionally, wind flows present non‐differentiable components due to turbulence and gust winds, which affect the wind energy management. Thus, a fast and robust controller is required to induce such nominal regime for maximum energy transfer. A fractional‐order nonlinear disturbance‐observer (FNDOB) is proposed in this paper to cancel the non‐differentiable components of the wind speed, as well as dynamic uncertainties and other aerodynamic disturbances. The proposed FNDOB is based on continuous fractional sliding modes, assuring that disturbances and uncertainties are exactly compensated in finite‐time. A representative simulation study for a variable‐speed wind turbine is presented to show the reliability of the proposed scheme, and a comparative analysis with respect to a conventional linear disturbance observer based control is presented.     

一类不确定分数阶混沌系统的同步控制

针对一类参数未知,状态不能全部测量的分数阶混沌系统的同步控制问题,结合状态观测器和自适应方法,提出了一种更符合工程实际的新的控制方案,利用分数阶微积分稳定性理论,给出了基于状态观测器的控制律和自适应律。该同步方法理论严格,没有强加在系统上的限制条件,适用范围比较宽,便于实现,并且保留了非线性项,达到同步的时间短。以分数阶R~ssler系统为研究对象,实现了参数未知,状态不能全部测量的分数阶混沌系统同步。理论分析与计算机仿真结果证实了该方法的有效性。     

一类非线性系统的输出反馈容错控制

针对一类非线性系统,研究了故障情况下基于输出反馈的容错控制问题．首先基于Zhang的自适应观测器和Lin的输出反馈控制律设计了正常系统的标称控制律,分析了该控制律的性能,并得到了故障发生后仍然采用该控制律时闭环系统状态有界的充分条件．在此基础上,设计了故障系统的容错控制律,证明了若发生的故障满足前述的充分条件,则故障系统在该容错控制律下稳定．数值仿真表明了该方法的有效性．     

Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach

In this paper, a fault estimation and fault-tolerant control problem for a class of T-S fuzzy stochastic time-delay systems with actuator and sensor faults is investigated. A novel sliding mode observer is proposed, which can simultaneously estimate the system states, actuator and sensor faults with good accuracy. Based on the state and actuator fault estimation, a new sliding mode control scheme is developed, which can effectively eliminate the influence of actuator fault. Sufficient conditions for the existence of the proposed observer and fault-tolerant sliding mode controller are provided in terms of linear matrix inequality, and moreover, the reachability of the sliding mode surface can be guaranteed under the proposed control scheme. The propose sliding mode observer and fault-tolerant sliding mode controller can overcome the restrictive assumption that the input matrix of all local modes is the same. Finally, a numerical example is provided to verify the effectiveness of the proposed sliding mode observer and fault-tolerant sliding mode control technique.     

永磁同步直线电机的分数阶超螺旋滑模控制

为了提高永磁同步直线电机的跟踪性能,增强系统的鲁棒性,本文提出了分数阶超螺旋滑模控制策略.首先,针对外部扰动以及系统的未知状态设计广义超螺旋观测器,其能够精确估计永磁同步直线电机的速度和外部扰动.其次,将分数阶理论和终端滑模控制理论相结合,提出有限时间收敛的分数阶超螺旋滑模控制器,以实现永磁同步直线电机的跟踪控制.最后,通过仿真对比验证所提方案的有效性.     

Active disturbance rejection control for nonlinear fractional‐order systems

This paper investigates active disturbance rejection control involving the fractional‐order tracking differentiator, the fractional‐order PID controller with compensation and the fractional‐order extended state observer for nonlinear fractional‐order systems. Firstly, the fractional‐order optimal‐time control scheme is studied to propose the fractional‐order tracking differentiator by the Hamilton function and fractional‐order optimal conditions. Secondly, the linear fractional‐order extend state observer is offered to acquire the estimated value of the sum of nonlinear functions and disturbances existing in the investigated nonlinear fractional‐order plant. For the disturbance existing in the feedback output, the effect of the disturbance is discussed to choose a reasonable parameter in fractional‐order extended state observer. Thirdly, by this observed value, the nonlinear fractional‐order plant is converted into a linear fractional‐order plant by adding the compensation in the controller. With the aid of real root boundary, complex root boundary, and imaginary boot boundary, the approximate stabilizing boundary with respect to the integral and differential coefficients is determined for the given proportional coefficient, integral order and differential order. By choosing the suitable parameters, the fractional‐order active disturbance rejection control scheme can deal with the unknown nonlinear functions and disturbances. Finally, the illustrative examples are given to verify the effectiveness of fractional‐order active disturbance rejection control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

考虑输入饱和的近空间飞行器姿态容错控制

针对近空间飞行器姿态控制中出现的执行器故障,输入饱和与外部干扰等问题,设计了一种基于二阶滑模干扰观测器和辅助系统的鲁棒容错跟踪控制方法.首先,将系统不确定,外部扰动和执行器故障作为复合干扰,设计super-twisting二阶滑模干扰观测器对其进行估计.然后为解决输入饱和问题构造了辅助分析系统,并借助backstepping方法,设计姿态容错跟踪控制器.利用Lyapunov方法,严格证明了所有闭环系统信号的收敛性.最后将所设计的控制方法应用于近空间飞行器姿态控制中,仿真结果验证了该控制方法的有效性.     

Observer‐Based Adaptive Output Feedback Fault Tolerant Control for Nonlinear Hydro‐Turbine Governing System with State Delay

This paper focuses on the problem of adaptive output feedback fault tolerant control for a nonlinear hydro‐turbine governing system. A dynamic mathematical model of the system is established, which aims to investigate the dynamic performance of the model under servomotor delay and actuator faults. Then, a fault estimation adaptive observer is proposed to achieve online real‐time diagnosis of system faults. Based on the online fault estimation information, an observer‐based adaptive output feedback fault tolerant controller is designed. Furthermore, under reasonable assumptions, the results demonstrate that the closed‐loop control system can achieve global asymptotic stability by Lyapunov function. Finally, the numerical simulation results are presented to indicate the satisfaction control effectiveness of the proposed scheme.     

An extended observer-based robust nonlinear speed sensorless controller for a PMSM

This work focuses on the problem of observer-based robust speed sensorless control of a 3-phase permanent magnet synchronous motor (PMSM). Nonlinear design techniques are employed for designing robust speed controller and observer that are able to withstand the effects of modelling uncertainties and load variations. A new cascaded observer scheme is proposed comprising a continuous sliding mode observer (SMO) and an extended high-gain observer (EHGO). The proposed cascaded observer reduces chattering, exhibits reasonable insensitivity to modelling inaccuracies and is capable of withstanding errors due to the finite boundary layer of continuous SMO. For the robust speed control, an integral sliding mode controller is designed that yields fast and accurate speed tracking performance even in the presence of bounded uncertainties and external disturbances. The complete scheme has been evaluated using simulations and experiments.     

Nonlinear sliding mode high-gain observers for fault estimation

A robust high gain observer for state and unknown inputs/faults estimations for a special class of nonlinear systems is developed in this article. Ensuring the observability of the faults/unknown inputs with respect to the outputs, the faults can be estimated from the sliding surface. Under a Lipschitz condition for the nonlinear part, the high gain observers are designed under some regularity assumptions. In the sliding mode, the convergence of the estimation error dynamics is proven similar to the analysis of high-gain observers.     

A robust sensorless output feedback controller of the induction motor drives: new design and experimental validation

In this article, a sensorless output feedback controller is designed in order to drive the induction motor (IM) without the use of flux and speed sensors. First, an observer that uses only the measured stator currents is synthesised to estimate the mechanical variables (speed and load torque) and the magnetic variables (fluxes) by structurally taking into account the unobservability phenomena of the sensorless IM (SIM) and the parametric uncertainties. Second, a current-based field-oriented sliding mode control that uses the flux and the speed estimates given by the former observer is developed so as to steer the estimated speed and flux magnitude to the desired references. Since the observer error dynamic is independent from the known input control and depends on the IM parametric uncertainties, a kind of separation principle is introduced to guarantee the practical stability of the whole closed-loop system ‘observer–controller’ (‘O-C’) according to observability and unobservability time variation. A significant benchmark taking into account the unobservability phenomena of the SIM is presented to show the performances of the whole control scheme against experimental set-up.     

Sensorless speed control of PMSM via adaptive interconnected observer

In this article, a robust sensorless speed observer–controller scheme for a surface permanent magnet synchronous motor (PMSM) is proposed. First-of-all, following preliminary results in the framework of the induction motor that is less sensible to the position estimation error, an adaptive high gain interconnected observer is designed. It is only supplied by the electrical measurement: the motor currents and voltages. This observer estimates the rotor speed and position, the stator resistance and the load torque. A nonlinear backstepping controller is developed. The above observer is associated with this controller and the complete scheme practical stability proof is given. The overall system is tested by simulation in the framework of an industrial benchmark with a trajectory that particularly checks the motor unobservability condition. Some robustness tests have been carried out. The controller–observer scheme shows good performances in spite of the uncertainties and the unknown load torque.     

An adaptive integral sliding mode FTC scheme for dissimilar redundant actuation system of civil aircraft

ABSTRACT

This paper proposed a new adaptive integral sliding mode FTC scheme to deal with the actuator faults and failure. The scheme combines integral sliding mode control, control allocation scheme and adaptive strategy. The unknown actuator faults are handled by adaptive modulation gain of nonlinear ISMC law. To cope with complete failure, control allocation scheme is integrated with the baseline controller to provide tolerance. The proposed strategy relies on the estimate of actuator effectiveness. Therefore, an adaptive sliding mode observer based fault reconstruction scheme is proposed in this paper. The proposed scheme is implemented on dissimilar redundant actuation system driven by hydraulic and electro-hydraulic actuators. In nominal and faulty conditions, both actuators are contributing to achieving the desired control surface deflection. However, when the actuator failure occurs, the control signals are reallocated to the redundant actuator. The problem of dynamics mismatch is addressed using fractional order controller designed in an inner loop. The comparison with the existing literature is also conducted in the simulation to validate the dominant performance.     

Global Practical Mittag Leffler Stabilization by Output Feedback for a Class Of Nonlinear Fractional‐Order Systems

In this paper, the problem of a global practical Mittag Leffler feedback stabilization for a class of nonlinear fractional order systems by means of observer is described. The linear matrix inequality approach is used to guarantee the practical stability of the proposed feedback fractional order system. An illustrative example is given to show the applicability of the results.     

A nonlinear model predictive control scheme for sensor fault tolerance in observation processes

This article addresses the problem of designing a sensor fault‐tolerant controller for an observation process where a primary, controlled system observes, through a set of measurements, an exogenous system to estimate the state of this system. We consider sensor faults captured by a change in a set of sensor parameters affecting the measurements. Using this parametrization, we present a nonlinear model predictive control (NMPC) scheme to control the observation process and actively detect and estimate possible sensor faults, with adaptive controller reconfiguration to optimize the use of the remaining sensing capabilities. A key feature of the proposed scheme is the design of observability indices for the NMPC stage cost to improve the observability of both the state of the exogenous system and the sensor fault parameters. The effectiveness of the proposed scheme is illustrated through numerical simulations.     

Asymptotic output tracking of a class of nonlinear systems by means of an observer

An observer‐based controller strategy for the asymptotic output tracking of a class of nonlinear systems is proposed. The generalized observability canonical form (???????) introduced by Fliess, is the main ingredient in our approach. Our tracking controller actually achieves uniform asymptotic stability by linearizing the tracking error. Two examples are considered to illustrate the effectiveness of the suggested approach. Copyright © 2001 John Wiley & Sons, Ltd.     

A composite fractional order active disturbance rejection control method for a class of uncertain systems with multiple disturbances

The existing active disturbance rejection control (ADRC) method may not provide sufficient disturbance rejection to multiple mismatched disturbances for the fractional order systems. In this paper, a composite disturbance rejection approach is developed for a class of fractional order uncertain systems, by synthesizing the fractional order ADRC (FOADRC) approach and a disturbance observer (DO)-based compensation scheme. Taking advantage of more disturbance information and a filter structure, an improved DO is developed to achieve precise estimation of disturbances in the presence of sensor noises. In addition, a state transformation is developed to convert the system into a simple integral chain model with only matched disturbances. Then a composite control law is designed to compensate the disturbances and provide satisfying dynamic performance. The efficiency of the proposed method is demonstrated by a numerical simulation and an actual servo control simulation, as well as the comparison with two kinds of the existing ADRC methods and the commonly used integral sliding mode control (I-SMC) method.     

Fractional‐order–dependent global stability analysis and observer‐based synthesis for a class of nonlinear fractional‐order systems

This paper focuses on proposing novel conditions for stability analysis and stabilization of the class of nonlinear fractional‐order systems. First, by considering the class of nonlinear fractional‐order systems as a feedback interconnection system and applying small‐gain theorem, a condition is proposed for L₂‐norm boundedness of the solutions of these systems. Then, by using the Mittag‐Leffler function properties, we show that satisfaction of the proposed condition proves the global asymptotic stability of the class of nonlinear fractional‐order systems with fractional order lying in (0.5, 1) or (1.5, 2). Unlike the Lyapunov‐based methods for stability analysis of fractional‐order systems, the new condition depends on the fractional order of the system. Moreover, it is related to the H_∞‐norm of the linear part of the system and it can be transformed to linear matrix inequalities (LMIs) using fractional‐order bounded‐real lemma. Furthermore, the proposed stability analysis method is extended to the state‐feedback and observer‐based controller design for the class of nonlinear fractional‐order systems based on solving some LMIs. In the observer‐based stabilization problem, we prove that the separation principle holds using our method and one can find the observer gain and pseudostate‐feedback gain in two separate steps. Finally, three numerical examples are provided to demonstrate the advantage of the novel proposed conditions with the previous results.     

基于迭代学习观测器的航天器姿态主动容错控制

针对含有外部扰动和执行器故障的一类航天器姿态控制系统,本文提出基于迭代学习观测器的主动容错控制方案.首先,建立了含有外部扰动和执行器故障的航天器姿态控制系统的运动学和动力学模型.其次,为了提高观测器的故障估计精度,在传统迭代学习观测器设计基础上引入上一时刻状态估计误差信息,文章提出一种改进型学习估计算法.进一步,基于滑模控制和指定时间稳定理论,利用学习观测器的故障估计信息设计指定时间主动容错控制器.与现有的航天器主动容错控制方案相比,本文所提出的算法的优势在于可以使故障系统的姿态能在指定时间跟踪上指令信号.基于Lyapunov方法,本文从理论上证明了改进型学习观测器和姿态容错控制系统的稳定性.最后,通过数值仿真,说明了所提容错控制方案的有效性和可行性.