几类网络控制系统的建模与控制分析
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摘要
网络控制系统是一种全分布、网络化实时反馈控制系统,它是计算机技术、通信技术与控制技术发展与融合的产物,具有信息资源能够共享、系统成本低、使用灵活、易于维护等优点,在工业自动化等方面已产生了深远影响。然而,控制系统引入网络后,由于带宽有限、分时复用、数据传输路径不确定等的影响,导致信息在网络传输中出现等待、乱序及丢包等现象。这些都会不同程度的影响控制系统性能,甚至导致系统失稳,给网络控制系统的分析、设计与控制带来很大困难。因此,如何解决上述问题,成为当今学术界最具挑战的课题之一。本文针对网络控制系统中存在的时延、丢包、乱序等问题,研究单包,多包传输,有线及无线网络控制系统的建模,包丢失检测和控制器设计算法。
首先,针对同时具有时变时延和包丢失的单包传输网络控制系统,假设在一个采样周期末,若传感器数据未能成功被执行器接收,则丢弃该数据,将时变的网络条件看成是Markov状态的跳变,体现包丢失和网络诱导时延(为采样周期的任意倍)随机特征的等价时延由潜在的Markov状态来控制,应用迭代方法,将网络控制系统建模为离散时间Markov跳变系统,从而满足网络的时变特性。然后,利用随机稳定分析方法,通过线性矩阵不等式给出了系统稳定的充分条件和相应的控制器。数值算例验证了结果的有效性和优越性。
其次,针对单包传输网络中存在的长时延、丢包及乱序问题,利用增广矩阵方法,考虑了网络控制系统的联合建模,将该网络控制系统建模为一个简单的离散时间切换系统,该模型更符合网络的时变特性。基于建立的模型,利用系统定性分析方法,给出了最大包丢失数目的计算公式和更具一般性的系统稳定结果,同时设计了相应的控制器。数值算例验证了结果的有效性。
再次,针对多包传输网络控制系统,根据包丢失和量化的特性,将未知和随机的包丢失考虑为一种故障,而将量化误差建模为一种扰动。多包传输网络控制系统被建模为具有扰动和故障的增广离散时间线性切换系统。然后,通过鲁棒故障检测方法设计了最优滤波器,成功的检测到包丢失的发生。进一步,使用网络内模控制算法,设计了多包传输网络控制系统的高性能控制器,从而解决了系统性能和网络特性之间的冲突。仿真算例说明了方法的有效性。
最后,本文给出了应用自适应编码调制的无线网络控制系统的建模及控制器设计方法,该方法可以提高能量效率,增加衰减信道传输的数据率。通过引入系统时延的概念,将无线传输通道的时变速率,干扰和路由特性包含到整个系统中。基于时变的网络条件,给出了系统时延的上下界。执行器为事件驱动时,将该系统建模为多控制器切换系统,用LMI的方法获得了闭环系统稳定的充分条件和状态反馈控制器;执行器为时间驱动时,将无线网络控制系统建模为具有时变输入延迟和结构不确定性的离散时间线性系统,利用新的时滞系统技术给出了系统保成本控制器设计方法。数值算例表明了本章方法的有效性。
Networked control system is a distributed real-time feedback control system, it is the syncretic results for computer technology, communication technology and control technology, and has a lot of advantages, such as shared information source, low cost, flexible use, simple maintenance. Thus it makes great sense in industrial automation. However, because of networks introduced in control system, information is delayed, disordered or dropout for the finite bandwidth, time division multiple access and the uncertain data transmission path. All of these will affect the performance of control system in different degree, even make it unstable, and bring great difficulty in system analyzing, designing and controlling. Thus, how to solve the problems above is becoming one of the most challenging tasks in today’s academe. This paper studies the modeling, packet detection and controller design algorithm for single-packet and multi-packet transmission, wire and wireless networked control system control system under consideration of delay, packet loss and disorder problems.
Firstly, aiming at single-packet transmission networked control system with time-varying delay and packet loss, we assume that the packet will be dropped out if it does not arrive at actuator in one sampling period. Then the time-varying network conditions are considered as the jump of Markov states, and Equivalent Delay, which embodies stochastic character of packet loss and network induced delay (the random times of sampling period), is controlled by those Markov states, networked control system is modeled as discrete time Markov jump system using iterative approach. Thus, the dynamic characteristic of network is satisfied. Then, by stochastic stable analysis method, the sufficient stability conditions and the corresponding controllers are given in terms of Linear Matrix Inequality. Numerical examples show the validity and advantages.
Secondly, through augmented matrix method, the paper considers the combined model for networked control system with single-packet transmission under consideration of delay, packet loss and disorder, the networked control system is modeled as a simple discrete time switched system. Based on this model, the qualitative analysis method is proposed, maximum number of packet loss and general stable results are given for the closed-loop networked control system. Meanwhile, the corresponding controller can be obtained. Numerical example shows the validity of our methods.
Thirdly, aiming at networked control system with multi-packet transmission, the unknown and stochastic packet loss is considered as a kind of fault, and the quantization error is regarded as disturbance according to the character of packet dropout and quantization error. Networked control system is modeled as augmented discrete time switched linear system with disturbance and fault. Then, by robust fault detection method, optimal packet loss detection filter is designed to detect packet loss successfully. Further, using the networked internal model control algorithm, the high performance controller is design for networked control system with multi-packet transmission. Then the conflict between system performance and network characteristic is overcome. Simulation example shows the validity of our method.
Finally, the modeling and controller design are developed for wireless networked control system applying adaptive coded modulation, which can improve the energy efficiency and increase the data rate over a fading channel. Through the introduction of System Delay, the characteristics of varying rate, interference, and routing in wireless transmission channel is contained in the whole system. Based on the time-varying network condition, the analytic lower and upper bounds of System Delays are given. If the actuator is event-driven, the networked control system is modeled as multi-controller switched system, sufficient stabilization condition and state feedback controller is given in terms of Linear Matrix Inequality; When the actuator is time-driven, it is modeled as a discrete-time system with time-varying input delay and structure uncertainty. The guaranteed cost control method of the networked control system is derived by novel techniques of time-delay system. Numerical result shows the validity of our proposed strategies.
首先,针对同时具有时变时延和包丢失的单包传输网络控制系统,假设在一个采样周期末,若传感器数据未能成功被执行器接收,则丢弃该数据,将时变的网络条件看成是Markov状态的跳变,体现包丢失和网络诱导时延(为采样周期的任意倍)随机特征的等价时延由潜在的Markov状态来控制,应用迭代方法,将网络控制系统建模为离散时间Markov跳变系统,从而满足网络的时变特性。然后,利用随机稳定分析方法,通过线性矩阵不等式给出了系统稳定的充分条件和相应的控制器。数值算例验证了结果的有效性和优越性。
其次,针对单包传输网络中存在的长时延、丢包及乱序问题,利用增广矩阵方法,考虑了网络控制系统的联合建模,将该网络控制系统建模为一个简单的离散时间切换系统,该模型更符合网络的时变特性。基于建立的模型,利用系统定性分析方法,给出了最大包丢失数目的计算公式和更具一般性的系统稳定结果,同时设计了相应的控制器。数值算例验证了结果的有效性。
再次,针对多包传输网络控制系统,根据包丢失和量化的特性,将未知和随机的包丢失考虑为一种故障,而将量化误差建模为一种扰动。多包传输网络控制系统被建模为具有扰动和故障的增广离散时间线性切换系统。然后,通过鲁棒故障检测方法设计了最优滤波器,成功的检测到包丢失的发生。进一步,使用网络内模控制算法,设计了多包传输网络控制系统的高性能控制器,从而解决了系统性能和网络特性之间的冲突。仿真算例说明了方法的有效性。
最后,本文给出了应用自适应编码调制的无线网络控制系统的建模及控制器设计方法,该方法可以提高能量效率,增加衰减信道传输的数据率。通过引入系统时延的概念,将无线传输通道的时变速率,干扰和路由特性包含到整个系统中。基于时变的网络条件,给出了系统时延的上下界。执行器为事件驱动时,将该系统建模为多控制器切换系统,用LMI的方法获得了闭环系统稳定的充分条件和状态反馈控制器;执行器为时间驱动时,将无线网络控制系统建模为具有时变输入延迟和结构不确定性的离散时间线性系统,利用新的时滞系统技术给出了系统保成本控制器设计方法。数值算例表明了本章方法的有效性。
Networked control system is a distributed real-time feedback control system, it is the syncretic results for computer technology, communication technology and control technology, and has a lot of advantages, such as shared information source, low cost, flexible use, simple maintenance. Thus it makes great sense in industrial automation. However, because of networks introduced in control system, information is delayed, disordered or dropout for the finite bandwidth, time division multiple access and the uncertain data transmission path. All of these will affect the performance of control system in different degree, even make it unstable, and bring great difficulty in system analyzing, designing and controlling. Thus, how to solve the problems above is becoming one of the most challenging tasks in today’s academe. This paper studies the modeling, packet detection and controller design algorithm for single-packet and multi-packet transmission, wire and wireless networked control system control system under consideration of delay, packet loss and disorder problems.
Firstly, aiming at single-packet transmission networked control system with time-varying delay and packet loss, we assume that the packet will be dropped out if it does not arrive at actuator in one sampling period. Then the time-varying network conditions are considered as the jump of Markov states, and Equivalent Delay, which embodies stochastic character of packet loss and network induced delay (the random times of sampling period), is controlled by those Markov states, networked control system is modeled as discrete time Markov jump system using iterative approach. Thus, the dynamic characteristic of network is satisfied. Then, by stochastic stable analysis method, the sufficient stability conditions and the corresponding controllers are given in terms of Linear Matrix Inequality. Numerical examples show the validity and advantages.
Secondly, through augmented matrix method, the paper considers the combined model for networked control system with single-packet transmission under consideration of delay, packet loss and disorder, the networked control system is modeled as a simple discrete time switched system. Based on this model, the qualitative analysis method is proposed, maximum number of packet loss and general stable results are given for the closed-loop networked control system. Meanwhile, the corresponding controller can be obtained. Numerical example shows the validity of our methods.
Thirdly, aiming at networked control system with multi-packet transmission, the unknown and stochastic packet loss is considered as a kind of fault, and the quantization error is regarded as disturbance according to the character of packet dropout and quantization error. Networked control system is modeled as augmented discrete time switched linear system with disturbance and fault. Then, by robust fault detection method, optimal packet loss detection filter is designed to detect packet loss successfully. Further, using the networked internal model control algorithm, the high performance controller is design for networked control system with multi-packet transmission. Then the conflict between system performance and network characteristic is overcome. Simulation example shows the validity of our method.
Finally, the modeling and controller design are developed for wireless networked control system applying adaptive coded modulation, which can improve the energy efficiency and increase the data rate over a fading channel. Through the introduction of System Delay, the characteristics of varying rate, interference, and routing in wireless transmission channel is contained in the whole system. Based on the time-varying network condition, the analytic lower and upper bounds of System Delays are given. If the actuator is event-driven, the networked control system is modeled as multi-controller switched system, sufficient stabilization condition and state feedback controller is given in terms of Linear Matrix Inequality; When the actuator is time-driven, it is modeled as a discrete-time system with time-varying input delay and structure uncertainty. The guaranteed cost control method of the networked control system is derived by novel techniques of time-delay system. Numerical result shows the validity of our proposed strategies.
引文
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