时变采样间隔网络控制系统的研究
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摘要
网络控制系统（Networked Control Systems, NCSs）是将传感器、执行器和控制器等单元通过网络连接起来的分布式控制系统。网络系统因为有很多优点，如减少成本、减轻重量、降低能耗、易于安装和维护、安全性高等，被广泛应用于各个领域。但是引入网络会导致诸如时延、丢包、时变采样间隔、传输受限和量化误差等问题，这些都会严重降低系统的性能甚至导致系统不稳定。因此，对网络控制系统稳定性分析、控制器设计、故障检测及容错控制具有十分重大的理论和实践意义。
相比于网络控制系统时延、丢包、传输受限和量化误差方面所取得的丰富成果，对时变采样间隔的研究结果还比较少。特别，研究时变采样间隔网络控制系统的故障检测和容错控制基本上是一个空白领域。因此，本文研究了时变采样间隔网络控制系统的建模、稳定性分析、控制器设计，故障检测及容错控制问题。主要工作和贡献如下：
总结了网络控制系统中以往有关采样间隔的研究工作，包括网络节点驱动方式、采样间隔选取方法，采样间隔对系统性能的影响、建模方法和研究方向等，同时指出了尚需要继续研究的问题。
提出了同时描述时变采样间隔和时变时延的新模型。针对网络控制系统中存在的有界、未知、时变的采样间隔和时延，利用矩阵Jordan分解与变换，将采样间隔和时延的不确定性转变为系统结构参数的不确定性，建立了凸多面体描述的离散时间不确定性系统模型。利用离散时间多面体不确定系统的凸性，即在凸多面体顶点进行的设计和求解，所得结果对整个多面体系统都是合适的，对时变采样间隔网络控制系统进行研究。
基于Lyapunov稳定性定理，有界实引理和线性矩阵不等式(LMIs)方法，分别设计了参数依赖和参数不依赖的状态反馈控制器，保性能状态反馈控制器及动态输出反馈控制器，给出了时变采样间隔网络控制系统保持渐近稳定的充分条件。利用最优控制理论的常用H2范数和H∞范数性能指标，考虑系统中的噪声干扰，提出满足混合鲁棒H2/H∞性能的控制器设计方法。分别设计了满足混合鲁棒H2/H∞性能的参数依赖和参数不依赖的状态反馈和动态输出反馈控制器。控制器参数通过求解以LMIs为约束条件的凸优化问题得到。数值仿真验证了控制器设计的有效性，同时也对参数依赖和参数不依赖设计结果的保守性进行了比较。
设计了鲁棒H∞故障检测滤波器，将故障检测问题设计归结为H∞鲁棒滤波问题，利用Lyapunov稳定性定理和LMIs方法，给出了滤波器存在的充分条件及其具体参数的表达式。同时设计了满足混合H∞/H－性能的故障观测器，对有限频率范围的故障进行检测。利用广义KYP引理和有界实引理，将H∞/H－性能指标优化问题转化为以LMIs为约束条件的凸优化问题。对两种不同的故障检测器，设计相同的检测阈值、残差评价函数和故障判断逻辑。通过数值仿真，验证了所提方法的有效性并分析两种方法的优缺点。
考虑可能发生的执行器故障，分两步设计了主动容错控制器。首先设计了观测器对系统的故障进行估计。接着，利用估计故障来实时调整控制律，分别设计了基于状态反馈和基于动态输出反馈的鲁棒容错控制器。应用Lyapunov稳定性理论和LMIs方法，给出了时变采样间隔网络控制系统鲁棒H∞容错控制器存在的充分条件，将控制器设计问题转化为以LMIs为约束条件的凸优化问题，给出了最优H∞鲁棒容错控制器的参数表达式。数值仿真验证了该设计方法的有效性。
Networked control systems (NCSs) are some feedback control systems where thefeedback loops are closed by some communication networks. NCS offers manyadvantages such as less wiring, increased system’s flexibility, easy installation andmaintenance, etc. But for imperfect communication and limited band constraints, there aresome disadvantages such as time-delay, packet dropouts, variable sampling/transmission,quantization errors, which will degrade the performance of the systems significantly.Therefore, study on networked control systems such as stability analysis, controller design,fault detection and fault tolerant is very important in both theory and applications.
Compared with the rich results on time-delay, packet dropouts and quantization errors,there are few results on variable sampling intervals in networked control systems.Moreover, very limited papers take time varying sampling intervals into account for theresearch of fault detection and fault tolerant control. Therefore, based on a newly proposedmodel, the dissertation investigates the sufficient condition for existence controller to keepasymptotically stable, robust controller design, fault detection and fault tolerant control forNCS with variable sampling intervals and time-delay. The main work and contributionsare as followings.
We give a review of the previous work on networked control systems, including theresearch topics, the modeling approaches, and the achieved results about the variablesampling intervals. Meanwhile, some problems which need further study are pointed out.
A new model is proposed which simultaneously describes variable and boundedsampling intervals and time-delay. A discrete-time model with time-varying parameterslying inside a convex polytopic system framework whose vertices are determined throughthe Real Jordan form approximation is built. Using the convexity of the discrete-timepolytopic uncertain systems, i.e., the result of a finite number of the vertices will beapplicable to the entire polytopic system and the new model becomes the basis of laterdesign and analysis.
Based on Lyapunov stability theory and linear matrix inequalities (LMIs) method,parameter-dependent and parameter-independent states feedback controller, guaranteed cost states feedback controller and dynamic output feedback controller are designedrespectively. The sufficient conditions of existence the above controllers are given in theform of LMIs. Considering the disturbance and noise, the mixed robust H2/H∞performance of the discrete-time polytopic uncertain system is proposed out, which isused to improve the system transient performance and to ensure the robustness of thesystem simultaneously. The robust states feedback and dynamic output feedbackcontrollers are designed.
An optimal H∞robust fault detection filter is built. For all unknown inputs, uncertainparameters, the error between the residual signal and the fault signal is made as small aspossible. The sufficient conditions for existence of the desired robust fault detection filterare established in terms of LMIs. Based on H∞index performance for minimizing thedisturbance and the corresponding the finite frequency H－index performance formaximizing the worst-case fault sensitivity, a fault detection observer is designed forresidual generation. With the aid of Bounded Real lemma and the generalizedKalman-Yakubovich-Popov (GKYP) lemma, the existence condition of such a mixedH∞/H－fault detection observer is given in terms of LMIs.
Considering the possible actuator failures, an observer-based integrated robust faultestimation and fault tolerant controller are studied. First, an augumented fault estimationobserver containing an exponential stability performance index and an H∞performanceindex are proposed not only to guarantee the convergence speed of fault estimation butalso restrict the uncertainties to be as small as possible. Second, two robust fault tolerantcontrollers based on states feedback and dynamic output feedback are designed to ensurethe robust stability of the closed-loop system in the presence of disturbance and faults. Forthe optimal robust H∞fault tolerant control, the parmeters of the controllers are obtainedby solving some convex optimization problem with LMIs constraints.
At the end of each subsection, some numerical simulations which demonstrate theeffectiveness of our results are given. Meanwhile the comparison and analysis of thecontrol performance between the various controllers, fault detectors and fault tolerantcontrollers are given.
相比于网络控制系统时延、丢包、传输受限和量化误差方面所取得的丰富成果，对时变采样间隔的研究结果还比较少。特别，研究时变采样间隔网络控制系统的故障检测和容错控制基本上是一个空白领域。因此，本文研究了时变采样间隔网络控制系统的建模、稳定性分析、控制器设计，故障检测及容错控制问题。主要工作和贡献如下：
总结了网络控制系统中以往有关采样间隔的研究工作，包括网络节点驱动方式、采样间隔选取方法，采样间隔对系统性能的影响、建模方法和研究方向等，同时指出了尚需要继续研究的问题。
提出了同时描述时变采样间隔和时变时延的新模型。针对网络控制系统中存在的有界、未知、时变的采样间隔和时延，利用矩阵Jordan分解与变换，将采样间隔和时延的不确定性转变为系统结构参数的不确定性，建立了凸多面体描述的离散时间不确定性系统模型。利用离散时间多面体不确定系统的凸性，即在凸多面体顶点进行的设计和求解，所得结果对整个多面体系统都是合适的，对时变采样间隔网络控制系统进行研究。
基于Lyapunov稳定性定理，有界实引理和线性矩阵不等式(LMIs)方法，分别设计了参数依赖和参数不依赖的状态反馈控制器，保性能状态反馈控制器及动态输出反馈控制器，给出了时变采样间隔网络控制系统保持渐近稳定的充分条件。利用最优控制理论的常用H2范数和H∞范数性能指标，考虑系统中的噪声干扰，提出满足混合鲁棒H2/H∞性能的控制器设计方法。分别设计了满足混合鲁棒H2/H∞性能的参数依赖和参数不依赖的状态反馈和动态输出反馈控制器。控制器参数通过求解以LMIs为约束条件的凸优化问题得到。数值仿真验证了控制器设计的有效性，同时也对参数依赖和参数不依赖设计结果的保守性进行了比较。
设计了鲁棒H∞故障检测滤波器，将故障检测问题设计归结为H∞鲁棒滤波问题，利用Lyapunov稳定性定理和LMIs方法，给出了滤波器存在的充分条件及其具体参数的表达式。同时设计了满足混合H∞/H－性能的故障观测器，对有限频率范围的故障进行检测。利用广义KYP引理和有界实引理，将H∞/H－性能指标优化问题转化为以LMIs为约束条件的凸优化问题。对两种不同的故障检测器，设计相同的检测阈值、残差评价函数和故障判断逻辑。通过数值仿真，验证了所提方法的有效性并分析两种方法的优缺点。
考虑可能发生的执行器故障，分两步设计了主动容错控制器。首先设计了观测器对系统的故障进行估计。接着，利用估计故障来实时调整控制律，分别设计了基于状态反馈和基于动态输出反馈的鲁棒容错控制器。应用Lyapunov稳定性理论和LMIs方法，给出了时变采样间隔网络控制系统鲁棒H∞容错控制器存在的充分条件，将控制器设计问题转化为以LMIs为约束条件的凸优化问题，给出了最优H∞鲁棒容错控制器的参数表达式。数值仿真验证了该设计方法的有效性。
Networked control systems (NCSs) are some feedback control systems where thefeedback loops are closed by some communication networks. NCS offers manyadvantages such as less wiring, increased system’s flexibility, easy installation andmaintenance, etc. But for imperfect communication and limited band constraints, there aresome disadvantages such as time-delay, packet dropouts, variable sampling/transmission,quantization errors, which will degrade the performance of the systems significantly.Therefore, study on networked control systems such as stability analysis, controller design,fault detection and fault tolerant is very important in both theory and applications.
Compared with the rich results on time-delay, packet dropouts and quantization errors,there are few results on variable sampling intervals in networked control systems.Moreover, very limited papers take time varying sampling intervals into account for theresearch of fault detection and fault tolerant control. Therefore, based on a newly proposedmodel, the dissertation investigates the sufficient condition for existence controller to keepasymptotically stable, robust controller design, fault detection and fault tolerant control forNCS with variable sampling intervals and time-delay. The main work and contributionsare as followings.
We give a review of the previous work on networked control systems, including theresearch topics, the modeling approaches, and the achieved results about the variablesampling intervals. Meanwhile, some problems which need further study are pointed out.
A new model is proposed which simultaneously describes variable and boundedsampling intervals and time-delay. A discrete-time model with time-varying parameterslying inside a convex polytopic system framework whose vertices are determined throughthe Real Jordan form approximation is built. Using the convexity of the discrete-timepolytopic uncertain systems, i.e., the result of a finite number of the vertices will beapplicable to the entire polytopic system and the new model becomes the basis of laterdesign and analysis.
Based on Lyapunov stability theory and linear matrix inequalities (LMIs) method,parameter-dependent and parameter-independent states feedback controller, guaranteed cost states feedback controller and dynamic output feedback controller are designedrespectively. The sufficient conditions of existence the above controllers are given in theform of LMIs. Considering the disturbance and noise, the mixed robust H2/H∞performance of the discrete-time polytopic uncertain system is proposed out, which isused to improve the system transient performance and to ensure the robustness of thesystem simultaneously. The robust states feedback and dynamic output feedbackcontrollers are designed.
An optimal H∞robust fault detection filter is built. For all unknown inputs, uncertainparameters, the error between the residual signal and the fault signal is made as small aspossible. The sufficient conditions for existence of the desired robust fault detection filterare established in terms of LMIs. Based on H∞index performance for minimizing thedisturbance and the corresponding the finite frequency H－index performance formaximizing the worst-case fault sensitivity, a fault detection observer is designed forresidual generation. With the aid of Bounded Real lemma and the generalizedKalman-Yakubovich-Popov (GKYP) lemma, the existence condition of such a mixedH∞/H－fault detection observer is given in terms of LMIs.
Considering the possible actuator failures, an observer-based integrated robust faultestimation and fault tolerant controller are studied. First, an augumented fault estimationobserver containing an exponential stability performance index and an H∞performanceindex are proposed not only to guarantee the convergence speed of fault estimation butalso restrict the uncertainties to be as small as possible. Second, two robust fault tolerantcontrollers based on states feedback and dynamic output feedback are designed to ensurethe robust stability of the closed-loop system in the presence of disturbance and faults. Forthe optimal robust H∞fault tolerant control, the parmeters of the controllers are obtainedby solving some convex optimization problem with LMIs constraints.
At the end of each subsection, some numerical simulations which demonstrate theeffectiveness of our results are given. Meanwhile the comparison and analysis of thecontrol performance between the various controllers, fault detectors and fault tolerantcontrollers are given.
引文
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