FAULT TOLERANT CONTROL OF FLEXIBLE SMART STRUCTURES USING ROBUST DECENTRALIZED FAST OUTPUT SAMPLING FEEDBACK TECHNIQUE

This paper presents the modeling, design and simulation of a Robust Decentralized Fast Output Sampling (RDFOS) feedback controller for the vibration control of a smart structure (flexible cantilever beam) when there is actuator failure. The beam is divided into 8 finite elements and the sensors / actuators are placed at finite element positions 2, 4, 6, and 8 as collocated pairs. The smart structure is modeled using the concepts of piezoelectric theory, Euler‐Bernoulli beam theory, Finite Element Method (FEM) techniques and the state space techniques. Four multi‐variable state‐space models of the smart structure plant are obtained when there is a failure of one of the four actuators to function. The effect of failure of one of the piezo actuators to function during the vibration of the beam is observed. The tip displacements, open and closed loop responses with and without the controller are observed. For all of these models, a common stabilizing state feedback gain F is obtained. A robust decentralized fast output sampling feedback gain L which realizes this state feedback gain is obtained using the LMI approach. In this designed control law, the control inputs to each actuator of the multi‐model representation of the smart structure is a function of the output of that corresponding sensor only and the gain matrix has got all off‐diagonal terms zero and this makes the control design a robust decentralized one. Then, the performance of the designed smart system is evaluated for Active Vibration Control (AVC). The robust decentralized FOS controller obtained by the designed method requires only constant gains and hence may be easier to implement in real time.     

线性不确定系统具有完整性的一种设计方法

研究了参数不确定状态反馈控制系统的鲁棒容错问题,目的是设计状态反馈控制器使得对可容许的参数不确定性及传感器失效故障或／和执行器失效故障,系统依然保持全局渐近稳定,具有完整性。基于Lyapunov稳定性理论,应用矩阵的谱半径和最小特征值等概念,分别针对传感器失效、执行器失效以及传感器和执行器同时失效三种情况,推导出使闭环系统渐近稳定的三个定理,给出了一种新的、简单的控制律设计方法和设计步骤。最后,给出了一个设计算例,并就各种可能的传感器或／和执行器失效故障情况进行了仿真分析,应用研究结果验证了所提出方法的有效性和简单性。     

Robust mixed H 2 /H ∞ control of time-varying delay systems

This paper describes the mixed H 2 /H X controller design method of linear systems with time-varying delays in both state and control input. More specifically, the proposed mixed H 2 /H X controller minimizes the H 2 performance measure when satisfying a prescribed H X norm bound on the closed loop system. The sufficient conditions for the existence of controller, the mixed H 2 /H X controller design method and the upper bound of performance measure are presented using the linear matrix inequality (LMI) technique. Also, all solutions including controller gain and the upper bound of performance measure are obtained simultaneously. Furthermore, the proposed controller design method can be easily extended into the problem of robust mixed H 2 /H X controller design method for parameter uncertain systems with time-varying delays in both state and control input.     

线性连续时滞系统最优预见重复控制

针对一类线性连续时滞系统,提出一种最优预见重复控制设计方法.首先,通过一种等价变换,将被控时滞系统转化为无时滞系统.然后,利用L阶差分算子提升技巧,获得包含状态变量导数和跟踪误差的增广连续系统.在此基础上,通过定义一种新的性能指标,将预见重复控制设计问题转化为连续非自治系统的线性二次调节问题.进一步,基于最优控制理论,得到包含状态反馈、误差积分、重复控制、时滞补偿和预见补偿的最优预见重复控制器.该控制器包含了已有文献的多种控制器形式.最后,通过一个数值仿真实例,说明所提方法的有效性.     

基于ADP的导引控制一体化全状态受限反演控制

针对导引控制一体化设计中状态受限及非线性最优问题，提出了一种结合反演控制与自适应动态规划（ADP）技术，考虑全状态受限的新型导引控制一体化设计方法.首先，将状态受限的严格反馈系统通过坐标变换转化为非状态受限系统.然后，采用前馈反演控制与反馈最优控制相结合的设计思路，利用ADP技术在线求解非线性HJB方程得到最优解.最后通过李亚普诺夫理论证明了系统的闭环稳定性与所有信号的一致有界性.与传统方法的对比仿真验证了该设计方法的可行性与优越性.     

Model predictive control of axial dispersion chemical reactor

This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dominant dynamics of the PDEs system is derived for controller design through Galerkin's method and modal decomposition technique. Tustin's discretization and Cayley transform are used to obtain infinite-dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is constructed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints.     

状态反馈鲁棒解耦控制器的设计

本文基于状态反馈解耦理论，提出一种状态反馈鲁棒解耦控制器的设计方法。将该方法应用于串联多关节机器人控制，有效地解决了机器人控制中存在的复杂的变量耦合问题。     

区间2型T-S模糊系统的事件触发预测控制

本文研究了前提不匹配的区间2型(IT2)模糊系统的事件触发预测控制问题. 首先, 提出了一个IT2模糊系统 模型, 包括动态事件触发机制(ETM)和预测控制器, ETM可以通过减少传输的数据包数量来节省有限的网络资源, 预测控制器可以预测两个成功传输时刻之间的系统状态来处理不可靠的通信网络. 其次, 根据李雅普诺夫稳定性理 论和前提不匹配方法, 得到了系统稳定的充分条件. 然后, 根据线性矩阵不等式(LMI)得到控制器增益. 最后通过数 值模拟验证了方法的有效性.     

A nonparametric approach to design robust controllers for uncertain systems: Application to an air flow heating system

This paper presents an approach to design robust fixed structure controllers for uncertain systems using a finite set of measurements in the frequency domain. In traditional control system design, usually, based on measurements, a model of the plant, which is only an approximation of the physical system, is first built, and then control approaches are used to design a controller based on the identified model. Errors associated with the identification process as well as the inevitable uncertainties associated with plant parameter variations, external disturbances, measurement noise, etc. are expected to all contribute to the degradation of the performance of such a scheme. In this paper, we propose a nonparametric method that uses frequency-domain data to directly design a robust controller, for a class of uncertainties, without the need for model identification. The proposed technique, which is based on interval analysis, allows us to take into account the plant uncertainties during the controller synthesis itself. The technique relies on computing the controller parameters for which the set of all possible frequency responses of the closed-loop system are included in the envelope of a desired frequency response. Such an inclusion problem can be solved using interval techniques. The main advantages of the proposed approach are: (1) the control design does not require any mathematical model, (2) the controller is robust with respect to plant uncertainties, and (3) the controller structure can be chosen a priori, which allows us to select low-order controllers. To illustrate the proposed method and demonstrate its efficacy, an application to an air flow heating system is presented.     

基于PI 观测器的奇异摄动系统故障诊断和最优容错控制

针对线性奇异摄动系统, 提出一种基于PI (proportional integral) 观测器的故障诊断和最优容错控制方法. 基于奇异摄动系统相关理论和矩阵变换技术, 给出PI 全维观测器存在的条件, 该观测器可以观测系统的快慢状态和故障系统的状态. 在估测到系统状态的基础上进一步考虑最优性, 应用最优控制理论, 设计状态反馈控制器, 提出基于PI 观测器的故障诊断器和最优容错控制器的设计方法. 最后的数值算例验证了所提出方法的可行性和正确性.

     

An optimal control method for linear systems with time delay

An optimal control method for linear systems with time delay is developed in this paper. In the proposed control method, the differential equation with time delay of the system dynamics is first rewritten into a form without any time delay through a particular transformation. Then, the optimal controller is designed by using the classical optimal control theory. A numerical algorithm for control implementation is presented, since the obtained expression of the optimal controller contains an integral term that is not convenient for online calculation. The time delay is considered at the very beginning of the control design, and no approximation and estimation are made in the control system. Thus the system performance and stability are prone to be guaranteed. Instability in responses might occur only if a system with time delay is controlled by the optimal controller that was designed with no consideration of time delay. The effectiveness of the proposed optimal controller is demonstrated by simulation studies.     

Analysis and design of fuzzy control systems using dynamicfuzzy-state space models

A discrete-time fuzzy control system which is composed of a dynamic fuzzy model and a fuzzy-state feedback controller is proposed. Stability of the fuzzy control system is discussed and two sufficient conditions to guarantee the stability of the system are given in terms of uncertain linear system theory. An algorithm is developed to check the stability condition. The controller design method is divided into two procedures, one is to get the state feedback matrix by linear system theory in every local rule map; the other is to determine conditions of global stability by using a nonlinear analysis method. Two examples are used to show the design method     

Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation

In this paper, an adaptive neural networks (NNs) tracking controller is proposed for a class of single-input/singleoutput (SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter. Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature. In controller design of the proposed approach, a state observer, based on the strictly positive real (SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.      

Sensor fault tolerant control of nonlinear Takagi–Sugeno systems. Application to vehicle lateral dynamics

This paper presents a new scheme for sensor fault tolerant control for nonlinear systems based on the Takagi–Sugeno modeling. First, a structured residual generator aimed at detecting and isolating sensor faults is designed. A bank of observers controlled either by only one system output or a set of outputs is then implemented, leading to a set of state estimates. The parallel distributed compensation structure is adopted to design the fault tolerant controller. The novelty in this paper is that the estimated state used in the controller is a weighted state vector obtained from all the estimated states provided by the different observers. The weighting functions depend on the residual vector signals delivered by the residual generator. They are designed to avoid crisp switches in the control law. Indeed, the interesting feature of the proposed approach is to avoid the commonly used switching strategy. For each residual component, the greater its magnitude is, the less the weight affected to the corresponding state estimate is. Consequently, the controller only uses estimations computed on the basis of healthy measurements. The closed‐loop stability is studied with the Lyapunov theory, and the obtained conditions are expressed as a set of linear matrix inequalities. The proposed residual generation and fault tolerant controller are applied to a vehicle lateral dynamics affected by sensor faults. Copyright © 2015 John Wiley & Sons, Ltd.     

Characteristic model based adaptive controller design and analysis for a class of SISO systems一类SISO系统基于特征模型的极点配置自适应控制设计与分析

The design of an adaptive controller and stability analysis of the corresponding closed loop system are discussed for a class of SISO systems based on the characteristic model method. The obtained characteristic model is a second-order slow time-varying linear system with a compress mapping function for the system modeling error. The pole placement method is used to design the controller, and sufficient conditions for the stability of the closed loop system are obtained based on the robust control theory of slow time-varying systems with perturbations. The effectiveness of the proposed method is illustrated by two numerical examples.     

具有执行器完整性的容错控制器设计

利用Ｌｙａｐｕｎｏｖ方程和广义逆理论,提出一种多变量控制系统设计方法。所设计的状态反馈控制器使得闭环系统的极点配置在一指定的圆形区域内,并且系统具有良好的动态特性,在执行器失效时仍能稳定,具有完整性,进而把结果广到传感器失效的情形。设计实例验证了该方法的有效性。     

Observer-based reliable passive control for uncertain T–S fuzzy systems with time-delay

This paper is concerned with the problem of observer-based reliable passive control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-delay and actuator faults. By employing Lyapunov stability theory, fault treatment method and linear matrix inequalities (LMIs), a sufficient condition on the existence of an observer-based reliable passive controller is given. Further, the LMI conditions are proposed for the observer-based reliable passive controller design. The gain of reliable controller and observer can be obtained by solving the proposed LMIs. Using the reliable passive controller, the closed-loop system is not only internally stable but also strictly passive even though some actuator components fail and system state fails to be measured completely. Finally, a truck-trailer system example is given to verify the effectiveness and advantages of the designed approach.     

A new controller design for a flexible one-link manipulator

A novel controller design for noncollocated flexible one-link manipulator arm tip position control based on variable structure sliding mode control is presented. Using the assumed-mode method, the plant model is derived. The discontinuous control law based on the variable structure system theory for the noncollocated manipulator tip position control is then designed. The position state variables are obtained directly from the inversion of the output submatrix multiplied by the sensor measurements. The velocity state variables are estimated through decoupled estimators-a separate first-order observer for each of the system's modes under consideration. Different sampling periods are used for the estimator and the controller. The performance of the controller is evaluated through a series of simulations, followed by an analysis of the designed control system     

Variable structure model following controller using non-dynamic multirate output feedback

The paper presents a new algorithm for a variable structure model following controller (VSMFC) design for discrete time systems using a fast output sampling technique. The reaching law approach is used to guarantee the sliding mode motion. This methodology is easy to implement since the method is based on output feedback. It is shown that the proposed fast output sampling variable structure model following controller (FOS VSMFC) gives the same results as obtained by state feedback VSMFC. To demonstrate the design technique a VSMFC is designed for the tip position control of a single flexible link. The simulation results show the effectiveness of the proposed method.