Adaptive fault‐tolerant control for a nonlinear flexible aircraft wing system

Fault‐tolerant control problems have been extensively studied in all kinds of control systems. However, there is little work on fault‐tolerant control for distributed parameter systems. In this paper, a novel adaptive fault‐tolerant boundary control scheme is proposed for a nonlinear flexible aircraft wing system against actuator faults. The whole system is regarded as a distributed parameter system, and the dynamic model of the flexible wing system is described by a set of partial differential equations (PDEs) and ordinary differential equations (ODEs). The proposed controller is designed by using the Lyapunov's direct method and adaptive control strategies. Based on the online estimation of actuator faults, the adaptive controller parameters can update automatically to compensate the actuator faults of the system. Besides, a fault‐tolerant controller is also developed for this system in the presence of external disturbances. Differing from existing works about adaptive fault‐tolerant control, the adaptive controller presented in this paper is designed for a distributed parameter system. Finally, numerical simulations are carried out to illustrate the effectiveness of the proposed control scheme.     

具有量化输入和边界扰动的柔性臂边界振动滑模控制

本文针对量化输入和有界扰动下柔性臂系统的振动抑制和边界滑模控制器设计问题开展研究. 柔性臂的动态特性由偏微分方程表示的分布参数模型描述. 对于具有未知有界干扰的柔性臂系统, 其主要控制目标是减小干扰的影响, 使柔性臂到达期望角度并同时抑制系统的振动. 首先, 利用边界输出信号构造滑模函数和滑模面. 其次, 结合所构造的滑模面, 设计一种边界滑模控制器, 并利用算子半群理论证明了闭环系统的适定性. 所提出的边界滑模控制策略保证了系统状态能够在有限时间内到达滑模面, 并且系统状态在滑模面上是指数收敛的. 最后, 通过物理实验验证了所提出控制策略的有效性.     

带非同位干扰执行动态有限维系统的输出追踪

本文考虑了边界带有非同位干扰的波动方程和常微分方程串联系统的性能输出追踪问题. 边界带有非同位干扰的波动方程可以看作常微分方程控制系统的执行动态. 通过利用轨道规划方法将非同位干扰变换到控制通道, 于是克服了非同位干扰带来的困难. 与现有Backstepping方法不同, 文章利用动态补偿法给出了一个新的状态反馈控制器, 使得控制器设计以及所设计的控制器本身更加简单, 证明了闭环系统解的一致有界性与性能输出的指数追踪. 数值模拟表明, 所给的方法是非常有效的     

Robust distributed controller design of rotational single-link smart materials beam

A dynamic modelling and controller design were presented for a single-link smart materials beam, a flexible beam bonded with piezoelectric actuators and sensors for better control performance. Taking into account bounded disturbances, a robust distributed controller was constructed based on the system model, which was described by a set of partial differential equations (PDEs) and boundary conditions (BCs) . Subsequently, a finite dimensional controller was further developed, and it was proven that this controller can stabilize the finite dimensional model with arbitrary number of flexible modes.     

Boundary Control of a Flexible Robotic Manipulator With Output Constraints

In this study, we consider a boundary control problem of a flexible manipulator with input disturbances and output constraints, achieving pre‐set performance attributes on position tracking error and the deflection error at the end of the beam. The dynamics of the system are represented by partial differential equations (PDEs). With the Lyapunov's direct method, a boundary controller with disturbance observer is designed to regulate the angular position and suppress elastic vibration simultaneously. The proposed control scheme allows the errors to converge to an arbitrarily small residual set, with convergence rate larger than a pre‐specified value. Numerical simulations demonstrate the effectiveness of the proposed scheme.     

Active vibration control of a flexible beam,based on flow source control

This paper presents a new method of actively controlling the vibration of a flexible beam by using a rigid body motion actuator based on flow source control. The proposed flow source controller generates a control input of a rotating angle instead of a torque that acts as an effort source control input. It is shown that the proposed flow source control improves the vibration suppression performance when disturbance forces such as friction forces are involved in the rigid body motion dynamics. The stability and the robustness to disturbance of the flow source controller are compared with an effort source controller. An optimal control theory is used to design the flow source vibration controller and a conventional PD controller is used for the motor position controller. Computer simulations and experimental results on a rotating beam system show that the vibration control performance achieved by the proposed flow source control method is superior to that of an effort source control method.     

Boundary feedback stabilisation of a flexible robotic manipulator with constraint

In this paper, the flexible robotic manipulator is modelled as a distributed parameter system, represented by a group of partial differential equations and ordinary differential equations. Control is designed at the boundary of the robotic manipulator based on integral-barrier Lyapunov function to suppress the vibration of the elastic deflection and track the desired angular position. With the proposed boundary control, the manipulator can be driven to the desired set-point with angular position and elastic deflection stay under the former setting constraint. Uniformed boundedness of the closed-loop system under the unknown time-varying disturbance is achieved. Stability analysis of the closed-loop system is given by employing the Lyapunov stability theory. Simulation results illustrate the effectiveness of the proposed boundary controller for ensuring output constraint and suppressing vibrations.     

具有边界扰动的不确定Euler-Bernoulli梁方程输出反馈控制

针对带有边界扰动、内部不确定扰动和外部扰动的Euler-Bernoulli梁方程,为克服传统扰动观测器引入的高增益及未知扰动导数难以准确求解问题,本文将主动干扰抑制控制(ADRC)技术应用到Euler-Bernoulli梁方程这个偏微分方程(PDE)系统上,提出并设计了一种新的在线扰动观测器,可实时估计扰动值.依据估计扰动值,设计了一个边界输出反馈控制器.仿真结果表明,本文所提出的方法可很好地实现对内部不确定扰动和外部扰动的估计,配合输出反馈控制器,可对边界扰动进行有效抑制,进而实现系统的指数稳定.     

自适应广义滑模观测器之状态估计和故障重构

针对一类同时具有执行机构故障和输出扰动的不确定性系统,提出了一种自适应广义滑模观测器,实现系统状态的估计和执行机构故障的重构.首先,进行系统变换及状态增广构成一类奇异系统,使得执行机构故障和输出扰动解耦,且输出扰动成为增广系统的状态之一;随后,受未知输入观测器和滑模观测器的启发,设计了一种广义滑模观测器,放宽了传统方法对输出维数的严格约束,并通过融入自适应技术放宽了对故障和不确定性上界已知的要求;最后,利用等效误差注入的思想实现故障重构.针对可重复使用运载器再入段进行的仿真实例,验证了所提方法的有效性.     

Partial differential equation modeling and vibration control for a nonlinear 3D rigid‐flexible manipulator system with actuator faults

In this paper, modeling and controlling problem for a two‐link rigid‐flexible manipulator in three‐dimensional (3D) space is studied under actuator faults. For modeling, the dynamics of the 3D mechanical system is represented by nonlinear partial differential equations, which is first derived in infinite dimension form. Based on the nonlinear model, the controller is proposed, which can achieve joint angle control and vibration suppression control in the presence of actuator faults. The stability analysis of the closed‐loop system is given based on LaSalle invariance principle. Numerical simulations illustrate the effectiveness of the proposed controller. This study will promote the development of nonlinear flexible manipulator systems in 3D space.     

Active Vibration Control for a Flexible‐Link Manipulator with Input Constraint Based on a Disturbance Observer

This paper mainly focuses on designing an active vibration control for a flexible‐link manipulator in the presence of input constraint and unknown spatially infinite dimensional disturbances. The manipulator we studied can be taken as an Euler–Bernoulli beam, the dynamic model of which has the form of partial differential equations. As the existence of spatially infinite dimensional disturbances on the beam, we first design a disturbance observer to estimate infinite dimensional disturbances. The proposed disturbance observer is guaranteed exponentially stable. Then, taking input saturation into account, a novel disturbance‐observer‐based controller is developed to regulate the joint angular position and rapidly suppress vibrations on the beam, which is the main contribution of this study. The closed‐loop system is validated asymptotically stable by theoretical analysis. The effectiveness of the proposed scheme is demonstrated by numerical simulations.     

A Novel Robust Attitude Control for Quadrotor Aircraft Subject to Actuator Faults and Wind Gusts

A novel robust fault tolerant controller is developed for the problem of attitude control of a quadrotor aircraft in the presence of actuator faults and wind gusts in this paper. Firstly, a dynamical system of the quadrotor taking into account aerodynamical effects induced by lateral wind and actuator faults is considered using the Newton-Euler approach. Then, based on active disturbance rejection control (ADRC), the fault tolerant controller is proposed to recover faulty system and reject perturbations. The developed controller takes wind gusts, actuator faults and measurement noises as total perturbations which are estimated by improved extended state observer (ESO) and compensated by nonlinear feedback control law. So, the developed robust fault tolerant controller can successfully accomplish the tracking of the desired output values. Finally, some simulation studies are given to illustrate the effectiveness of fault recovery of the proposed scheme and also its ability to attenuate external disturbances that are introduced from environmental causes such as wind gusts and measurement noises.      

LMI-based boundary and distributed control design for a flexible string subject to disturbance

In this paper, boundary and distributed controllers are proposed to reduce the vibration of a flexible string with external disturbance. To accurately represent the flexible string's behaviour, partial differential equations are introduced for the flexible string modelling. Boundary and distributed disturbance observers, which are proved exponentially stable, are designed to compensate unknown disturbance. Based on the proposed disturbance observers, the boundary and distributed controllers are developed by linear matrix inequality and the asymptotic stability of the system with controllers is demonstrated by Lyapunov's direct method. Extensive numerical simulations are presented to validate the good performance of the proposed control laws.     

Boundary control of a Timoshenko beam system with input dead-zone

In this paper, boundary control is designed for a Timoshenko beam system with the input dead-zone. By the Hamilton’s principle, the dynamics of the Timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations. The bounded part is separated from the input dead-zone and then forms the disturbance-like term together with the boundary disturbance, which finally acts on the Timoshenko beam system. Boundary control, based on the Lyapunov’s direct method, is proposed to ensure the Timoshenko beam converge into a small neighbourhood of zero, where stability of the system is also analysed. Besides, the existence and uniqueness of the solution of the Timoshenko beam system are proved. Simulations are provided to reveal the applicability and effectiveness of the proposed control scheme.     

执行机构部分失效的挠性航天器多界依赖容错控制

针对挠性航天器在轨运行时受到的外部干扰,输入时滞以及执行机构部分失效问题,本文提出了一种基于不确定参数的鲁棒H_∞容错控制方法.首先,将执行机构部分失效容错控制问题转化为不确定参数的鲁棒控制问题.然后,设计了一个新型的多界依赖状态反馈鲁棒H_∞控制算法.此算法不仅依赖时滞积分不等式分割参数和时滞界信息,还依赖部分失效因子.因此,本文设计的控制器能同时实现对输入时滞的敏感,对部分失效故障的容错及对外部干扰的抑制.最后,通过一系列的仿真验证本文方法的有效性.     

输入有界的自由漂浮柔性空间机器人轨迹跟踪控制

针对自由漂浮柔性空间机器人轨迹跟踪控制问题, 首先利用拉格朗日和假设模态法建立了动力学模型. 分析系统动力学模型, 综合考虑欠驱动、柔性振动等特点, 将其简化为一种带有柔性振动扰动完全可控的动力学模型; 在此基础上, 考虑控制输入受限, 提出一种自适应状态反馈控制策略. 该策略采用自适应技术实时在线学习柔性振动扰动参数, 从而保证控制律对柔性振动扰动具有良好的鲁棒性; 最后, 基于Lyapunov方法证明了该控制策略能够实现关节期望轨迹的跟踪. 仿真验证了该控制策略对控制输入受限系统轨迹跟踪控制的有效性和可靠性.     

Adaptive fault-tolerant control of linear systems with actuator saturation and L2-disturbances

This paper studies the problem of designing adaptive fault-tolerant H-infinity controllers for linear timeinvariant systems with actuator saturation. The disturbance tolerance ability of the closed-loop system is measured by an optimal index. The notion of an adaptive H-infinity performance index is proposed to describe the disturbance attenuation performances of closed-loop systems. New methods for designing indirect adaptive fault-tolerant controllers via state feedback are presented for actuator fault compensations. Based on the on-line estimation of eventual faults, the adaptive fault-tolerant controller parameters are updated automatically to compensate for the fault effects on systems. The designs are developed in the framework of the linear matrix inequality （LMI） approach, which can guarantee the disturbance tolerance ability and adaptive H-infinity performances of closed-loop systems in the cases of actuator saturation and actuator failures. An example is given to illustrate the efficiency of the design method.     

柔性卫星系统的振动自适应边界控制

针对受外部干扰和具有结构参数不确定性的柔性卫星系统,为了抑制其振动和避免控制溢出问题,采用Hamilton变分原理和Euler-Bernoulli梁理论建立了结构无穷维偏微分方程模型,随后基于该无穷维模型设计了带有干扰自适应律的自适应边界控制对柔性卫星振动进行主动控制,并证明了闭环柔性卫星控制系统解的存在性、唯一性和收敛性.最后,仿真结果验证了所设计的自适应边界控制算法的有效性.     

A new actuator activation policy for performance enhancement of controlled diffusion processes

The present work aims at the development of a framework within which a moving actuator activation policy and feedback controller synthesis are integrated for diffusion processes modelled by parabolic partial differential equations. It is assumed that the process of interest has either: (i) multiple actuators and the desirable arrangement is to activate only one while keeping the remaining ones dormant, or (ii) a single actuator capable of moving at a priori selected positions within the spatial domain. Practical advantages associated with arrangement (i) are energy cost savings and simplification of the local controller synthesis and the overall switching scheme, and with (ii) is enhanced spatiotemporal disturbance compensation. Feedback controller synthesis methods based on linear matrix inequality techniques are employed for a finite-dimensional Galerkin approximation of the original distributed parameter system. Along with standard controllability criteria, additional conditions are imposed that ensure robustness with respect to a certain class of disturbances. The value of a performance functional is then explicitly calculated by solving a location-parameterized family of Lyapunov matrix equations, and then optimized with respect to the set of admissible actuator locations. Finally, a case study of a moving bed adsorber is presented where the performance-enhancing capabilities of the proposed method is evaluated through simulation studies.     

Sliding Mode Control for Flexible-link Manipulators Based on Adaptive Neural Networks

This paper mainly focuses on designing a sliding mode boundary controller for a single flexible-link manipulator based on adaptive radial basis function (RBF) neural network. The flexible manipulator in this paper is considered to be an Euler-Bernoulli beam. We first obtain a partial differential equation (PDE) model of single-link flexible manipulator by using Hamiltons approach. To improve the control robustness, the system uncertainties including modeling uncertainties and external disturbances are compensated by an adaptive neural approximator. Then, a sliding mode control method is designed to drive the joint to a desired position and rapidly suppress vibration on the beam. The stability of the closed-loop system is validated by using Lyapunov’s method based on infinite dimensional model, avoiding problems such as control spillovers caused by traditional finite dimensional truncated models. This novel controller only requires measuring the boundary information, which facilitates implementation in engineering practice. Favorable performance of the closed-loop system is demonstrated by numerical simulations.