线性和非线性网络控制系统及其电气工程应用研究
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摘要
通过网络实现闭环的网络化控制系统（NCS—Networked Control System）已经日渐成为一个极具挑战性和富有前景的研究领域。论文在近年来国内、外关于网络控制系统理论研究成果的基础上，针对从电气工程领域抽象出来的两类受控对象—线性时不变被控对象和Lurie非线性被控对象，研究了NCS的建模、镇定、保性能最优控制、H∞最优控制、绝对稳定性等问题，主要研究成果如下:
1.对于具有时钟驱动传感器节点，事件驱动控制器和执行器节点，且不确定时延不超过一个采样周期的线性时不变被控对象网络控制系统，利用Lyapunov方法和线性矩阵不等式研究了状态反馈NCS的建模、鲁棒镇定、保性能最优控制和对于噪声扰动的H∞最优控制问题。状态反馈NCS可建模为含有不确定性的离散时变系统，分别给出了状态反馈NCS鲁棒稳定的条件和鲁棒镇定律、保性能最优控制律和H∞最优控制律设计方法。
2.对于具有时钟驱动传感器和控制器节点、事件驱动执行器节点和存在有界的时变网络时延和数据包丢失的线性时不变被控对象网络控制系统，可以将其建模为具有时变时滞的等效系统。利用Lyapunov-Krasovskii泛函和线性矩阵不等式，可得到变量数目少、无需知道调节参数且求解时无需使用重复迭代的NCS状态反馈次优和最优H∞控制律的设计方法；
3.研究了Lurie非线性被控对象中存在随机时变网络时延的状态反馈网络化控制系统的绝对稳定性问题。首先将Lurie网络化控制系统建模为一个时滞Lurie系统，然后利用Newton-Leibniz公式和添加自由权矩阵的方法给出时滞依赖的稳定性条件,并给出状态反馈控制器增益矩阵的求解方法。
4.在针对Lurie非线性被控对象的，存在随机时变的网络时延、丢包和乱序的动态输出反馈Lurie网络化控制系统的绝对稳定性研究中，首先将Lurie网络化控制系统建模为一个多时滞的Lurie系统,利用添加自由权矩阵的方法给出了时滞依赖的稳定性条件。在此基础上通过添加一等式约束，将系统转化为以线性矩阵不等式表示的可解问题，从而获得动态输出反馈控制律。
论文对上述成果进行了理论验证和控制器综合。以直流驱动系统等被控对象进行了仿真研究，而仿真结果验证了所设计控制器的有效性。在全文的最后，给出了论文的总结以及今后研究工作的展望。
The networked control system（NCS）, that closes control loops by network communication,becomes a promising field due to its obvious merits, and also a challenge to the system designers dueto its problems aroused from its inherited characteristics, thus needs to be comprehensively studied.Based on the author’s work experience, the dissertation attributes some electrical engineering objectsto two types of system, i.e. linear time-invariant controlled plant and Lurie nonlinear controlledplant，and puts the focus on the control problems such as modeling, stabilization, guaranteed costoptimal control, H∞optimal control, absolute stability, etc.
The main points of the dissertation may be summarized as following:
For the NCS of a linear time-invariant controlled plant that is of clock-driven sensor nodes,event-driven controller and actuator nodes, and with uncertain network induced delay less than orequals to a sampling period, the modeling, robust stabilization, guaranteed cost optimal control, andH∞optimal control under noise of the state feedback NCS are studied based on the Lyapunovapproach and linear matrix inequality. The system is modeled as a discrete time-variant system withuncertainty, and the condition of robust stability, the design methods for robust control, guaranteedcost optimal control and H∞optimal control are presented respectively.
For the NCS of a linear time-invariant controlled plant that is of clock-driven sensor andcontroller nodes, event-driven actuator nodes, bounded time-varying network-induced delay and datapacket dropout, the NCS can be modeled as an equivalent system with time-varying delay. By usingthe Lyapunov-Krasovskii functional and linear matrix inequality, the design of state feedbacksuboptimum and optimum H∞control can be achieved with fewer variables, needless of tuningparameters and calculation iteration.
The absolute stability of the state feedback NCS is studied for the Lurie nonlinear controlledplant wherein the random time-varying network-induced delay exists. The system is first modeled asa delay Lurie system, and then by using Newton-Leibniz formula and the method of adding freeweighting matrices, a delay-dependent stability condition is deduced and the method to solving thegain matrix of the state feedback controller is developed.
For the study on the absolute stability of dynamic output feedback NCS applied to Lurienonlinear controlled plant, where exist random and time-varying network-induced delay, data packetdropout and data packet disorder, the system is first modeled as a Lurie system with multiple delays,and the delay-dependent stability condition is deduced by adding free weighting matrices. By addingan equation constraint, the system is transformed into a solvability problem described by linearmatrix inequality, and then the dynamic output feedback control law is then obtained.
The dissertation performs theoretical verification and controller synthesis for the above mentioned results. The controlled plants such as DC drive system are used in simulation study andthe simulated results validated the effectiveness of the designed controllers. A summary withprospective outlook is at the end of the dissertation.
1.对于具有时钟驱动传感器节点，事件驱动控制器和执行器节点，且不确定时延不超过一个采样周期的线性时不变被控对象网络控制系统，利用Lyapunov方法和线性矩阵不等式研究了状态反馈NCS的建模、鲁棒镇定、保性能最优控制和对于噪声扰动的H∞最优控制问题。状态反馈NCS可建模为含有不确定性的离散时变系统，分别给出了状态反馈NCS鲁棒稳定的条件和鲁棒镇定律、保性能最优控制律和H∞最优控制律设计方法。
2.对于具有时钟驱动传感器和控制器节点、事件驱动执行器节点和存在有界的时变网络时延和数据包丢失的线性时不变被控对象网络控制系统，可以将其建模为具有时变时滞的等效系统。利用Lyapunov-Krasovskii泛函和线性矩阵不等式，可得到变量数目少、无需知道调节参数且求解时无需使用重复迭代的NCS状态反馈次优和最优H∞控制律的设计方法；
3.研究了Lurie非线性被控对象中存在随机时变网络时延的状态反馈网络化控制系统的绝对稳定性问题。首先将Lurie网络化控制系统建模为一个时滞Lurie系统，然后利用Newton-Leibniz公式和添加自由权矩阵的方法给出时滞依赖的稳定性条件,并给出状态反馈控制器增益矩阵的求解方法。
4.在针对Lurie非线性被控对象的，存在随机时变的网络时延、丢包和乱序的动态输出反馈Lurie网络化控制系统的绝对稳定性研究中，首先将Lurie网络化控制系统建模为一个多时滞的Lurie系统,利用添加自由权矩阵的方法给出了时滞依赖的稳定性条件。在此基础上通过添加一等式约束，将系统转化为以线性矩阵不等式表示的可解问题，从而获得动态输出反馈控制律。
论文对上述成果进行了理论验证和控制器综合。以直流驱动系统等被控对象进行了仿真研究，而仿真结果验证了所设计控制器的有效性。在全文的最后，给出了论文的总结以及今后研究工作的展望。
The networked control system（NCS）, that closes control loops by network communication,becomes a promising field due to its obvious merits, and also a challenge to the system designers dueto its problems aroused from its inherited characteristics, thus needs to be comprehensively studied.Based on the author’s work experience, the dissertation attributes some electrical engineering objectsto two types of system, i.e. linear time-invariant controlled plant and Lurie nonlinear controlledplant，and puts the focus on the control problems such as modeling, stabilization, guaranteed costoptimal control, H∞optimal control, absolute stability, etc.
The main points of the dissertation may be summarized as following:
For the NCS of a linear time-invariant controlled plant that is of clock-driven sensor nodes,event-driven controller and actuator nodes, and with uncertain network induced delay less than orequals to a sampling period, the modeling, robust stabilization, guaranteed cost optimal control, andH∞optimal control under noise of the state feedback NCS are studied based on the Lyapunovapproach and linear matrix inequality. The system is modeled as a discrete time-variant system withuncertainty, and the condition of robust stability, the design methods for robust control, guaranteedcost optimal control and H∞optimal control are presented respectively.
For the NCS of a linear time-invariant controlled plant that is of clock-driven sensor andcontroller nodes, event-driven actuator nodes, bounded time-varying network-induced delay and datapacket dropout, the NCS can be modeled as an equivalent system with time-varying delay. By usingthe Lyapunov-Krasovskii functional and linear matrix inequality, the design of state feedbacksuboptimum and optimum H∞control can be achieved with fewer variables, needless of tuningparameters and calculation iteration.
The absolute stability of the state feedback NCS is studied for the Lurie nonlinear controlledplant wherein the random time-varying network-induced delay exists. The system is first modeled asa delay Lurie system, and then by using Newton-Leibniz formula and the method of adding freeweighting matrices, a delay-dependent stability condition is deduced and the method to solving thegain matrix of the state feedback controller is developed.
For the study on the absolute stability of dynamic output feedback NCS applied to Lurienonlinear controlled plant, where exist random and time-varying network-induced delay, data packetdropout and data packet disorder, the system is first modeled as a Lurie system with multiple delays,and the delay-dependent stability condition is deduced by adding free weighting matrices. By addingan equation constraint, the system is transformed into a solvability problem described by linearmatrix inequality, and then the dynamic output feedback control law is then obtained.
The dissertation performs theoretical verification and controller synthesis for the above mentioned results. The controlled plants such as DC drive system are used in simulation study andthe simulated results validated the effectiveness of the designed controllers. A summary withprospective outlook is at the end of the dissertation.
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