具有时延和丢包的线性NCS时滞依赖鲁棒容错控制研究
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摘要
网络化控制系统(Networked control system,NCS)是一种通过实时通讯网络构成闭环的反馈控制系统。因其连线少,成本低,资源共享,便于安装、维护、扩展和故障诊断等优点,已被广泛应用于航空航天、石油化工、制造业等复杂系统中。但通讯网络的介入,受带宽限制和传输不可靠的影响,网络时延、数据丢包不可避免,加之网络带来的各种不确定性,使网络传输的数据也失去了定常性、因果性和确定性;此外多数NCS规模更加庞大,结构更加复杂,且故障诱发因素众多,系统一旦发生故障,损失将难以估量,因此通过对NCS进行容错设计,使其具有高安全可靠性变得尤为复杂和重要。目前NCS容错控制研究还处于起步阶段,现有成果还存在诸多局限,如:对网络诱导时延和数据丢包考虑较为单一,时延多以小于一个采样周期的情况建模,控制策略主要采用状态反馈,系统性能以鲁棒完整性或鲁棒H∞完整性为主,其结论保守性相对较大等。
基于此,本文针对同时具有时变时延和丢包的线性不确定NCS,将数据包丢失看成一种特殊时延,从减少保守性入手,以时滞依赖的方法,综合应用Lyapunov稳定性理论、线性矩阵不等式(Linear matrix inequality,LMI)、积分不等式等方法和技术,分别采用状态反馈或动态输出反馈控制律,较为系统地在理论层面给出了系统具有鲁棒完整性及具有一定性能约束的鲁棒容错判别准则和相应控制器的设计方法,并对所有结果进行了有效性和正确性的仿真实验研究,主要工作可归结为以下几个方面:
1)基于状态反馈的不确定线性NCS鲁棒容错控制研究
针对不确定线性NCS,同时考虑时变时延和数据丢包、或不确定有界扰动的影响,采用状态反馈控制策略,以保守性相对较小的时滞依赖方法,通过构造适当的Lyapunov-Krasovskii泛函,采用积分不等式、自由权矩阵等技术,针对可能的执行器或传感器失效故障,推证出了系统具有鲁棒完整性及具有一定性能约束的鲁棒H∞、鲁棒保性能、鲁棒H∞保性能的时滞依赖充分条件,并以一个LMI约束的和线性目标函数的凸优化方式,给出了NCS最优性能指标或最小扰动抑制率的控制器优化设计方法。
2)基于动态输出反馈的不确定线性NCS的鲁棒容错控制研究针对不确定线性NCS,同时考虑时变时延和数据丢包、或不确定有界扰动的影响,采用动态输出反馈控制策略,以保守性相对较小的时滞依赖方法,通过构造一种包含三重积分项的Lyapunov-Krasovskii泛函,采用积分不等式技术,针对可能的执行器或传感器失效故障,推证出了系统具有鲁棒完整性及具有一定性能约束的鲁棒H∞、鲁棒保性能、鲁棒H∞保性能的时滞/时滞变化率依赖的充分条件,并以一个LMI约束的和线性目标函数的凸优化方式,给出NCS具有最优性能指标或最小扰动抑制率控制器的优化设计方法。
3)在采用动态输出反馈控制策略时,对时延进行了更切合实际和一般性的分段处理,并构造了一种同时包含二重积分和三重积分项的Lyapunov-Krasovskii泛函,推证中未进行模型转化,对于Lyapunov泛函导数上界的处理时,在尽可能少放大的基础上保留了所有有用项,所给结果充分运用了时延的各种信息,尤其是各段时延的下界信息,使结论具有较小的保守性;同时,积分不等式技术的使用减少了自由权矩阵的引入,降低了计算量,这些均使控制器设计的可行性及容错满意度得到了提高。
4)在上述理论研究的基础上,采用实例对所有结果进行了仿真研究,结果表明文中所给结论均是正确有效性,这为同时具有时变时延和丢包的线性不确定NCS容错设计提供了一定的理论依据。
Networked Control System (NCS) was a closed control system by a real time network. It had wild application in the aerospace industry, petrochemical industry, manufacturers and complex system due to its advandages, such as: reducing system wiring, cutting the cost, sharing the information, ease of the system maintenance, extending, diagnosis. However, because of the involvement of the communication network, the network delay and the data pactet dropout are caused inevitably by the limited of the bandwidth and influenced unreliable transmission. In addition, kinds of uncertainty which brought by network characteristic caused the data transmitted in network losing its steadiness, casuality and determinacy. Furthermore, the most NCS has huger scale, more complex structure, and many fault factors. Once the system breaks down, the losses will be tremendous. Then, NCS possesses high safety and reliability through the fault-tolerant control become very complex and important. At present, the research of NCS fault-tolerant control is in the beginning stage, and the existing results are still exist many limitations, such as: delay and data packet dropout are considered soley, and delay is smaller than a sampling period in modeling, and the control strategy mainly uses the state feedback control strategy, and major research of system performance is robust integrity or robust H∞integrity, the conservative conclusion is relative bigger.
Based on this, this paper aimed at a class of linear uncertain NCS with delay and data packet dropout, an robust intergrality, having certain performance restraint robust fault-tolerant criterion and the design method of corresponding controller were given in theoretical using dealy-dependent method. All the results were verified correctness and effectiveness using simulation examples. The data packet dropout is as a special kind of delay. Lyapunov stability theory, LMI, integral inequality method were comprehensive application. Some work was done as following by adopting state feedback control strategy and dynamic outpur feedback control strategy.
1) The problem of robust fault-tolerant control in linear uncertain NCS was studied using state feedback control starategy.
For linear uncertain NCS with delay and data packet dropout, and uncertain bounded disturbances, the delay-dependent sufficient conditions for system with robust integrity, robust H∞integrity, robust guaranteed cost and robust H∞guaranteed cost against actuator and sensor failures are derived using state feedback control starategy, and the corresponding design method of controller with optimal performance index or minimum disturbance rejection rate were presented. In the prove, a proper Lyapunov- Krasovakii functional is constructed, meanwhile, integral inequality and free-weighting matrices method were used.
2) The problem of robust fault-tolerant control in linear uncertain NCS was studied using dynamic outpur feedback control strategy. For linear uncertain NCS with delay and data packet dropout, and uncertain bounded disturbances, the delay-dependent or delay-rate-dependent sufficient conditions for system with robust integrity, robust H∞integrity, robust guaranteed cost and robust H∞guaranteed cost against actuator and sensor failures are derived using dynamic outpur feedback control starategy, and the corresponding design method of controller with optimal performance index or minimum disturbance rejection rate were presented. In the prove, a type of Lyapunov-Krasovakii functional is proposed which contains some triple-integral terms, meanwhile, integral inequality method were used.
3) When using dynamic outpur feedback control starategy, the delay is dealt with piecewise method, a type of less conservatism Lyapunov-Krasovakii functional is proposed which contains some triple-integral terms and double-integral terms, and the model transformation is not been adopted, and the usefulness item is hold based on less amplificatory, while the delay information is full used especially the lower bound of delay information of each section. These make the results possess less conservativeness. Meanwhile, the introduction of less free-weighting matrices reduce the computation. These improve the feasibility of controller design and the degree of fault-tolerant satisfaction and usability.
4) In the above research conclusion, the accuracy and efficiency for all the result of the simulation is dissused using simulation example. All of conclusion is correct and effective.This provides certain theoretical basis for linear uncertain NCS with time-varying delay and date packet dropout.
基于此,本文针对同时具有时变时延和丢包的线性不确定NCS,将数据包丢失看成一种特殊时延,从减少保守性入手,以时滞依赖的方法,综合应用Lyapunov稳定性理论、线性矩阵不等式(Linear matrix inequality,LMI)、积分不等式等方法和技术,分别采用状态反馈或动态输出反馈控制律,较为系统地在理论层面给出了系统具有鲁棒完整性及具有一定性能约束的鲁棒容错判别准则和相应控制器的设计方法,并对所有结果进行了有效性和正确性的仿真实验研究,主要工作可归结为以下几个方面:
1)基于状态反馈的不确定线性NCS鲁棒容错控制研究
针对不确定线性NCS,同时考虑时变时延和数据丢包、或不确定有界扰动的影响,采用状态反馈控制策略,以保守性相对较小的时滞依赖方法,通过构造适当的Lyapunov-Krasovskii泛函,采用积分不等式、自由权矩阵等技术,针对可能的执行器或传感器失效故障,推证出了系统具有鲁棒完整性及具有一定性能约束的鲁棒H∞、鲁棒保性能、鲁棒H∞保性能的时滞依赖充分条件,并以一个LMI约束的和线性目标函数的凸优化方式,给出了NCS最优性能指标或最小扰动抑制率的控制器优化设计方法。
2)基于动态输出反馈的不确定线性NCS的鲁棒容错控制研究针对不确定线性NCS,同时考虑时变时延和数据丢包、或不确定有界扰动的影响,采用动态输出反馈控制策略,以保守性相对较小的时滞依赖方法,通过构造一种包含三重积分项的Lyapunov-Krasovskii泛函,采用积分不等式技术,针对可能的执行器或传感器失效故障,推证出了系统具有鲁棒完整性及具有一定性能约束的鲁棒H∞、鲁棒保性能、鲁棒H∞保性能的时滞/时滞变化率依赖的充分条件,并以一个LMI约束的和线性目标函数的凸优化方式,给出NCS具有最优性能指标或最小扰动抑制率控制器的优化设计方法。
3)在采用动态输出反馈控制策略时,对时延进行了更切合实际和一般性的分段处理,并构造了一种同时包含二重积分和三重积分项的Lyapunov-Krasovskii泛函,推证中未进行模型转化,对于Lyapunov泛函导数上界的处理时,在尽可能少放大的基础上保留了所有有用项,所给结果充分运用了时延的各种信息,尤其是各段时延的下界信息,使结论具有较小的保守性;同时,积分不等式技术的使用减少了自由权矩阵的引入,降低了计算量,这些均使控制器设计的可行性及容错满意度得到了提高。
4)在上述理论研究的基础上,采用实例对所有结果进行了仿真研究,结果表明文中所给结论均是正确有效性,这为同时具有时变时延和丢包的线性不确定NCS容错设计提供了一定的理论依据。
Networked Control System (NCS) was a closed control system by a real time network. It had wild application in the aerospace industry, petrochemical industry, manufacturers and complex system due to its advandages, such as: reducing system wiring, cutting the cost, sharing the information, ease of the system maintenance, extending, diagnosis. However, because of the involvement of the communication network, the network delay and the data pactet dropout are caused inevitably by the limited of the bandwidth and influenced unreliable transmission. In addition, kinds of uncertainty which brought by network characteristic caused the data transmitted in network losing its steadiness, casuality and determinacy. Furthermore, the most NCS has huger scale, more complex structure, and many fault factors. Once the system breaks down, the losses will be tremendous. Then, NCS possesses high safety and reliability through the fault-tolerant control become very complex and important. At present, the research of NCS fault-tolerant control is in the beginning stage, and the existing results are still exist many limitations, such as: delay and data packet dropout are considered soley, and delay is smaller than a sampling period in modeling, and the control strategy mainly uses the state feedback control strategy, and major research of system performance is robust integrity or robust H∞integrity, the conservative conclusion is relative bigger.
Based on this, this paper aimed at a class of linear uncertain NCS with delay and data packet dropout, an robust intergrality, having certain performance restraint robust fault-tolerant criterion and the design method of corresponding controller were given in theoretical using dealy-dependent method. All the results were verified correctness and effectiveness using simulation examples. The data packet dropout is as a special kind of delay. Lyapunov stability theory, LMI, integral inequality method were comprehensive application. Some work was done as following by adopting state feedback control strategy and dynamic outpur feedback control strategy.
1) The problem of robust fault-tolerant control in linear uncertain NCS was studied using state feedback control starategy.
For linear uncertain NCS with delay and data packet dropout, and uncertain bounded disturbances, the delay-dependent sufficient conditions for system with robust integrity, robust H∞integrity, robust guaranteed cost and robust H∞guaranteed cost against actuator and sensor failures are derived using state feedback control starategy, and the corresponding design method of controller with optimal performance index or minimum disturbance rejection rate were presented. In the prove, a proper Lyapunov- Krasovakii functional is constructed, meanwhile, integral inequality and free-weighting matrices method were used.
2) The problem of robust fault-tolerant control in linear uncertain NCS was studied using dynamic outpur feedback control strategy. For linear uncertain NCS with delay and data packet dropout, and uncertain bounded disturbances, the delay-dependent or delay-rate-dependent sufficient conditions for system with robust integrity, robust H∞integrity, robust guaranteed cost and robust H∞guaranteed cost against actuator and sensor failures are derived using dynamic outpur feedback control starategy, and the corresponding design method of controller with optimal performance index or minimum disturbance rejection rate were presented. In the prove, a type of Lyapunov-Krasovakii functional is proposed which contains some triple-integral terms, meanwhile, integral inequality method were used.
3) When using dynamic outpur feedback control starategy, the delay is dealt with piecewise method, a type of less conservatism Lyapunov-Krasovakii functional is proposed which contains some triple-integral terms and double-integral terms, and the model transformation is not been adopted, and the usefulness item is hold based on less amplificatory, while the delay information is full used especially the lower bound of delay information of each section. These make the results possess less conservativeness. Meanwhile, the introduction of less free-weighting matrices reduce the computation. These improve the feasibility of controller design and the degree of fault-tolerant satisfaction and usability.
4) In the above research conclusion, the accuracy and efficiency for all the result of the simulation is dissused using simulation example. All of conclusion is correct and effective.This provides certain theoretical basis for linear uncertain NCS with time-varying delay and date packet dropout.
引文
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