基于动态输出反馈的非线性NCS鲁棒容错控制
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摘要
网络化控制系统(Networked Control System，简称NCS)是通过网络将不同地理位置的传感器、控制器和执行机构连接起来，形成的一种全分布实时反馈闭环控制系统，NCS的优势在于可以实现资源共享和远程分布控制，系统构建模块化、集成化、成本低、故障诊断和维护方便、易扩展、灵活性强。然而由于网络带宽的限制和信息传输的不可靠性，衍生出网络时延、数据丢包等新的问题，导致了控制系统的性能下降、甚至失稳。加之NCS规模庞大，结构复杂，不确定和故障诱发因素众多，因此，借助容错设计技术使NCS具有更高的安全可靠性，受到学术界的广泛关注。
就目前NCS容错研究的现状来看，其成果主要集中在线性系统，且更多采用状态反馈。由于受系统结构、环境及经济成本等因素制约，通常难于测取到系统的全部状态信息，因此状态反馈控制器的实际应用往往受限。而对于非线性NCS，基于动态输出反馈控制策略的容错控制研究还鲜有文献报道。基于此，本文针对一类非线性NCS，同时考虑网络延时、丢包的影响，采用动态输出反馈控制策略，基于T-S模糊模型建模，在对时延进行分段形式处理的前提下，较为系统的进行了容错控制和鲁棒容错控制的研究，具体内容如下：
1）标称和具有参数不确定的非线性NCS的完整性问题
对标称和具有参数不确定的非线性NCS，运用Lyapunov稳定性理论，LMI和自由权矩阵等方法，基于动态输出反馈控制策略，针对可能出现的执行器或传感器故障，推证出了使系统具有完整性和鲁棒完整性的时滞依赖充分条件，并通过求解LMIs给出了控制器的优化设计方法。
2）标称和具有参数不确定性的非线性NCS的H_∞完整性问题
对标称和具有参数不确定的非线性NCS，考虑有限能量的外部扰动影响，运用Lyapunov稳定性理论，LMI和自由权矩阵等方法，基于动态输出反馈控制策略，针对可能出现的执行器或传感器故障，推证出使系统具有H_∞完整性和鲁棒H_∞完整性的时滞依赖充分条件，并通过求解LMIs给出了控制器的次优及最优设计方法。
3）标称和具有参数不确定性的非线性NCS的保性能容错问题
对标称和具有参数不确定的非线性NCS，考虑动态性能指标的要求，运用Lyapunov稳定性理论，LMI和自由权矩阵等方法，基于动态输出反馈控制策略，针对可能出现的执行器或传感器故障，推证出系统具有保性能完整性和鲁棒保性能容错问题时滞依赖充分条件，并通过求解LMIs给出了控制器的设计方法，进而对系统性能和控制器进行最优设计。
在进行上述理论研究的基础上，采用相应的仿真算例对所有结果进行了正确性和有效性的仿真研究，文中对时延的分段处理，既符合实际情况，不失一般性，又可充分利用时延信息，有效减少结果的保守性；另外证明过程中自由权矩阵技术的应用，以及未对原系统进行模型变换，均可使结论具有小保守性，这对提高控制器设计的可行性和容错控制的满意度是有益的。
With the development and maturity of network technology, more control systemrealize the exchange of information and the transmission of control signal amongsensors, sensors and controller by communication network, which makes theclosed-loop control, that is the networked control systems. They have manyadvantages, such as less attachment, low cost, easily install and maintain, and alsofault diagnosis, so they are gotten the favour by people. They have been widely usedin the field of aerospace, equipment manufacture, process control, traffic control,remote medical treatment and dangerous, special environment control. However, dueto the limit of network bandwidth and the unreliability of information transmission,which make the new problem of network delay, data dropout and so on, leading to theperformance of control system down, even instability. In addition，NCS have largescale, complexed structure, uncertainty and many factors of induced faults. NCS havemore safety and reliability with the aid of fault tolerant control, so they are paid moreattention by academics.
In recent years, NCS research mainly focus on linear system, and more using thestate feedback,because of the factors of system structure, environment and economiccost, usually it’s difficult to measured the whole state information to the system, Sothe actual application of the state feedback controller is often limited. And fornonlinear NCS, fault-tolerant control study based on the dynamic output feedbackcontrol strategy has few reports in the literature. Based on this, this paper for a classof nonlinear NCS, considering the network delay, the influence of the lost package,based on T-S fuzzy model and dynamic output feedback strategy, Delay is processedby subsection forms, The conservatism of the results is reduced at the same time, faulttolerant control and the robust fault tolerant control is studied Systematicly, theconcrete content as follows:
1) Research on integrality problems for nonlinear NCS with nominal andparameter uncer-tainnty.
With nominal and parameter uncertainties of nonlinear NCS, using lyapunovstability theory, the LMI and liberty matrix method, based on the dynamic outputfeedback control strategy, for possible actuator fault and sensor fault, pushing cardthe time delay sufficient conditions of integrity and robust integrity, and throughsolving the LMIs, the design method of optimal controller is given.
2) Research on H_∞integrality problems for nonlinear NCS with nominal andparameter unc-ertaint.
With nominal and parameter uncertainties of nonlinear NCS, considering thelimited energy external disturbance effect, using lyapunov stability theory, the LMIand liberty matrix method, based on the dynamic output feedback control strategy, forpossible actuator fault and sensor fault, pushing card the time delay sufficientconditions of H_∞integrity and robust H_∞integrity, and through solving the LMIs, thedesign method of controller is given, and the controller parameters are optimized.
3) Research on guaranteed integrality problems for nonlinear NCS with nominaland parame-ter uncertainty.
With nominal and parameter uncertainties of nonlinear NCS, Consider therequirements of the dynamic performance, using Lyapunov stability theory, the LMIand liberty matrix method, based on the dynamic output feedback control strategy.For possible actuator fault and sensor fault, pushing card the time delay sufficientconditions of guaranteed integrity and robust guaranteed integrity, and throughsolving the LMIs, the design method of optimal controller is given. And the controllerparameters are optimized.
In the basis of the above-mentioned theory research, the correspondingsimulation examples are used to illustrate the correctness and effectiveness of thesimulation. In the paper, the delay of the section processing not only conform to theactual situation, but also can effectively reduce the conservatism of the results. In theprocess of proof of the application of free weighting matrix， which does’ttransformate the model of original system, and also does’t define a cross, so thegotten conditions have a more small conservative. So as to increase the feasibility ofthe controller design and the satisfaction of fault-tolerant control.
就目前NCS容错研究的现状来看，其成果主要集中在线性系统，且更多采用状态反馈。由于受系统结构、环境及经济成本等因素制约，通常难于测取到系统的全部状态信息，因此状态反馈控制器的实际应用往往受限。而对于非线性NCS，基于动态输出反馈控制策略的容错控制研究还鲜有文献报道。基于此，本文针对一类非线性NCS，同时考虑网络延时、丢包的影响，采用动态输出反馈控制策略，基于T-S模糊模型建模，在对时延进行分段形式处理的前提下，较为系统的进行了容错控制和鲁棒容错控制的研究，具体内容如下：
1）标称和具有参数不确定的非线性NCS的完整性问题
对标称和具有参数不确定的非线性NCS，运用Lyapunov稳定性理论，LMI和自由权矩阵等方法，基于动态输出反馈控制策略，针对可能出现的执行器或传感器故障，推证出了使系统具有完整性和鲁棒完整性的时滞依赖充分条件，并通过求解LMIs给出了控制器的优化设计方法。
2）标称和具有参数不确定性的非线性NCS的H_∞完整性问题
对标称和具有参数不确定的非线性NCS，考虑有限能量的外部扰动影响，运用Lyapunov稳定性理论，LMI和自由权矩阵等方法，基于动态输出反馈控制策略，针对可能出现的执行器或传感器故障，推证出使系统具有H_∞完整性和鲁棒H_∞完整性的时滞依赖充分条件，并通过求解LMIs给出了控制器的次优及最优设计方法。
3）标称和具有参数不确定性的非线性NCS的保性能容错问题
对标称和具有参数不确定的非线性NCS，考虑动态性能指标的要求，运用Lyapunov稳定性理论，LMI和自由权矩阵等方法，基于动态输出反馈控制策略，针对可能出现的执行器或传感器故障，推证出系统具有保性能完整性和鲁棒保性能容错问题时滞依赖充分条件，并通过求解LMIs给出了控制器的设计方法，进而对系统性能和控制器进行最优设计。
在进行上述理论研究的基础上，采用相应的仿真算例对所有结果进行了正确性和有效性的仿真研究，文中对时延的分段处理，既符合实际情况，不失一般性，又可充分利用时延信息，有效减少结果的保守性；另外证明过程中自由权矩阵技术的应用，以及未对原系统进行模型变换，均可使结论具有小保守性，这对提高控制器设计的可行性和容错控制的满意度是有益的。
With the development and maturity of network technology, more control systemrealize the exchange of information and the transmission of control signal amongsensors, sensors and controller by communication network, which makes theclosed-loop control, that is the networked control systems. They have manyadvantages, such as less attachment, low cost, easily install and maintain, and alsofault diagnosis, so they are gotten the favour by people. They have been widely usedin the field of aerospace, equipment manufacture, process control, traffic control,remote medical treatment and dangerous, special environment control. However, dueto the limit of network bandwidth and the unreliability of information transmission,which make the new problem of network delay, data dropout and so on, leading to theperformance of control system down, even instability. In addition，NCS have largescale, complexed structure, uncertainty and many factors of induced faults. NCS havemore safety and reliability with the aid of fault tolerant control, so they are paid moreattention by academics.
In recent years, NCS research mainly focus on linear system, and more using thestate feedback,because of the factors of system structure, environment and economiccost, usually it’s difficult to measured the whole state information to the system, Sothe actual application of the state feedback controller is often limited. And fornonlinear NCS, fault-tolerant control study based on the dynamic output feedbackcontrol strategy has few reports in the literature. Based on this, this paper for a classof nonlinear NCS, considering the network delay, the influence of the lost package,based on T-S fuzzy model and dynamic output feedback strategy, Delay is processedby subsection forms, The conservatism of the results is reduced at the same time, faulttolerant control and the robust fault tolerant control is studied Systematicly, theconcrete content as follows:
1) Research on integrality problems for nonlinear NCS with nominal andparameter uncer-tainnty.
With nominal and parameter uncertainties of nonlinear NCS, using lyapunovstability theory, the LMI and liberty matrix method, based on the dynamic outputfeedback control strategy, for possible actuator fault and sensor fault, pushing cardthe time delay sufficient conditions of integrity and robust integrity, and throughsolving the LMIs, the design method of optimal controller is given.
2) Research on H_∞integrality problems for nonlinear NCS with nominal andparameter unc-ertaint.
With nominal and parameter uncertainties of nonlinear NCS, considering thelimited energy external disturbance effect, using lyapunov stability theory, the LMIand liberty matrix method, based on the dynamic output feedback control strategy, forpossible actuator fault and sensor fault, pushing card the time delay sufficientconditions of H_∞integrity and robust H_∞integrity, and through solving the LMIs, thedesign method of controller is given, and the controller parameters are optimized.
3) Research on guaranteed integrality problems for nonlinear NCS with nominaland parame-ter uncertainty.
With nominal and parameter uncertainties of nonlinear NCS, Consider therequirements of the dynamic performance, using Lyapunov stability theory, the LMIand liberty matrix method, based on the dynamic output feedback control strategy.For possible actuator fault and sensor fault, pushing card the time delay sufficientconditions of guaranteed integrity and robust guaranteed integrity, and throughsolving the LMIs, the design method of optimal controller is given. And the controllerparameters are optimized.
In the basis of the above-mentioned theory research, the correspondingsimulation examples are used to illustrate the correctness and effectiveness of thesimulation. In the paper, the delay of the section processing not only conform to theactual situation, but also can effectively reduce the conservatism of the results. In theprocess of proof of the application of free weighting matrix， which does’ttransformate the model of original system, and also does’t define a cross, so thegotten conditions have a more small conservative. So as to increase the feasibility ofthe controller design and the satisfaction of fault-tolerant control.
引文
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