基于LMI技术的网络控制系统优化设计
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摘要
在现代工业系统中,通过网络连接传感器、控制器与执行器而形成的闭环系统称为网络控制系统。与传统的点对点结构的控制系统相比,网络控制系统具有可以实现资源共享、具有较高的容错与故障诊断能力、安装与维护简单、能有效减少系统的体积、增加系统的可靠性等优点。
与传统的控制系统相比,网络控制系统虽然有诸多优点,但是网络的引入也会给系统分析与设计带来新的挑战,如网络诱导时延、数据包丢失、数据包时序错乱、多包传输、通信限制、时变采样周期等。现有文献中的结果主要考虑具有时延及丢包的网络控制系统的稳定性分析,控制器设计等问题,通过合理的设计控制器并采用合适的时延及丢包补偿方案来优化网络控制系统H∞性能的问题并未得到充分考虑。
本论文在总结前人工作的基础上,针对网络控制系统中的时延及丢包现象,提出了主动变采样周期方法以充分利用网络带宽,与基于常数采样周期的方法相比,该方法既可以保证网络带宽的充分利用又可以减小发生网络拥塞的可能性。提出了时延切换的方法来处理网络诱导时变时延,并通过理论推导证明了时延切换的方法比基于参数不确定性的方法具有更小的保守性；提出了时延切换与参数不确定性相结合的方法,该方法的计算量比时延切换方法要小,而保守性比基于参数不确定性的方法要小。改进了现有文献中基于预测控制的方法以补偿时延及丢包的负面影响,改进后的方法可有效减小预测误差的负面影响；提出了基于线性估计的方法及基于多通信通道共享的方法来补偿时延及丢包的负面影响,与不考虑补偿的方法相比,可在较大程度上改善系统性能；研究了网络控制系统的H∞输出跟踪性能优化及控制器设计问题,即使存在外部扰动,所设计的控制器仍可以保证系统有较好的跟踪性能。下面详细介绍本文的主要工作。
第一、二章系统地分析和总结了网络控制系统这一前沿研究领域的发展现状及研究方法,并给出了与本文相关的一些预备知识。
第三章考虑具有被动时变采样周期及主动变采样周期网络控制系统的稳定性分析及H∞控制器设计问题。对具有被动时变采样周期的网络控制系统,考虑了时延大于一个采样周期且连续丢包数大于一个的情况,也考虑了执行器在一个采样周期内收到两个及两个以上控制输入的情况,而这两种情况现有文献中很少考虑。提出了一种主动变采样周期方法,其核心是在网络空闲时缩短采样周期从而改善系统性能,在网络负载比较大的时候延长采样周期从而减少网络上数据包的个数并相应地减小发生网络拥塞的可能性。对具有被动时变及主动时变采样周期的网络控制系统,首先给出了系统的模型,通过定义适当的Lyapunov函数并结合多目标优化方法、线性矩阵不等式方法、自由加权矩阵方法及Jensen不等式方法,给出了系统渐进稳定的充分条件并设计了系统的控制器。仿真结果表明,本章所提出的方法具有较小的保守性,同时计算复杂性也比较小(由于Jensen不等式的采用)。
第四章采用时延切换方法及时延切换与参数不确定性相结合的方法处理网络控制系统中的随机时延。考虑到现有文献中基于参数不确定性的方法具有较大保守性,本章提出了时延切换的方法来处理网络诱导时延,并通过理论推导证明了时延切换的方法比基于参数不确定性的方法具有更小的保守性。考虑到时延切换方法会增大计算量,本章又提出了时延切换与参数不确定性相结合的方法,该方法的计算量比时延切换方法要小,而保守性比基于参数不确定性的方法要小。由于上一章中提出的主动变采样周期方法不能避免采样周期的频繁切换,本章提出了一个改进的主动变采样周期方法,该方法既可以保证网络带宽的充分利用又可以避免采样周期的频繁切换。
第五章采用预测控制与基于线性估计的方法来补偿时延及丢包的负面影响,研究了线性时不变系统的H∞性能优化及状态反馈控制器设计问题。对基于预测控制的补偿方法而言,在为系统选择控制输入时,本文充分考虑了网络时延的大小：如果某个控制输入的传输时延小于一个给定的阈值,则使用该控制输入,如果时延大于该阈值,则使用预测的控制输入,这样可以有效减小预测误差的负面影响。提出了一个新的基于线性估计的方法来补偿时延及丢包的负面影响,与基于预测控制的补偿方法相比,由于该方法无需提前p步估计控制输入并发送到执行器,因而可以有效地减小网络负载。基于以上两种补偿方法,本章给出了两个新的系统模型,并利用线性矩阵不等式方法给出了系统的H∞控制器设计方法。仿真例子验证了所提出的补偿方法的优越性。
第六章提出一个基于多通信通道共享的方法来补偿时延及丢包的负面影响,研究了网络控制系统的H∞性能优化及控制器设计问题。与基于单通信通道的方法相比,对空闲通信通道的共享可以补偿时延及丢包的负面影响,而且不会增加系统的硬件成本。与基于预测控制或估计的补偿方法相比,基于多通信通道共享的方法可以避免预测误差或估计误差可能给系统带来的负面影响。通过定义合适的Lyapunov函数并结合线性矩阵不等式方法,研究了网络控制系统的H∞控制器设计及H∞性能优化问题。由于在设计过程中避免了对向量交叉积的放大,因而本章的结果具有较小的保守性,而仿真例子也验证了这一点。
第七章研究了具有时延及丢包的离散化网络控制系统的H∞输出跟踪性能优化及控制器设计问题。利用基于线性矩阵不等式的方法及离散Jensen不等式,研究了具有常数采样周期的网络控制系统的H∞输出跟踪性能优化及控制器设计。对于具有时变采样周期的网络控制系统,采用多目标优化方法来优化系统的H∞输出跟踪性能,并相应的给出了控制器设计方法。由于采用了离散Jensen不等式,本章所提出的H∞输出跟踪控制器设计方法比基于自由加权矩阵的方法具有更小的计算复杂性。即使存在外部扰动,所设计的控制器仍可以保证受控对象的输出渐进跟踪给定的参考模型的输出,数值例子进一步验证了这一点。
最后对全文所做的工作进行了总结,并指明了下一步研究的方向。
In modern industrial systems, sensors, controllers and actuators are often connected over a network medium, which are called networked control systems (NCSs). Compared with the traditional control systems having point to point structure, advantages of NCSs include resource sharing, good fault-tolerant and fault detection ability, less wiring and easy maintenance, high reliability, etc.
Although the introduction of NCSs may lead to many advantages when compared with the traditional control systems, inserting network into control systems will also introduce new challenges for the analysis and design of control systems, such as network-induced time delay, packet dropout, packet disordering, multi-packet transmission, communication constraints, time-varying sampling period, etc. The existing results mainly focus on such problems as stability analysis, controller design, etc. for NCSs with time delay and packet dropout. By designing the controllers appropriately and adopting new methods to compensate the negative influences of time delay and packet dropout, th H∞performance of NCSs may be optimized, however, such problems are not taken into full consideration.
This thesis, based on previous works of others, taking time delay and packet dropout in NCSs into full consideration, proposes an active varying sampling period method to make full use of network bandwidth, compared with the constant sampling period based methods, the proposed method can both ensure the sufficient use of network bandwidth and reduce the possibility of network congestion. A delay switching method is proposed to deal with network-induced time delay, and it is proved theoretically to be less conservative than the parameter uncertainty-based method; a both delay switching and parameter uncertainty-based method is also proposed, which method may reduce the high computational complexity of the delay switching method and introduce less conservativeness than the parameter uncertainty-based method. The prediction control-based method is improved to compensate the negative influences of packet dropout, and the improved method may reduce the negative influences of prediction errors; a linear estimation-based approach and a multiple communication channels sharing-based method are proposed to overcome the negative influences of time delay and packet dropout, compared with the methods without compensation, the proposed methods may improve the performance of systems greatly; the problems of H∞output tracking performance optimization and controller design for NCSs are studied, the designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The details of this thesis are as follows.
Chapters 1-2 first summarize and analyze the development and main research methods in networked control systems. Preliminaries about the considered problems are also given.
Chapter 3 investigates the problems of stability analysis and H∞controller design for NCSs with passive time-varying sampling period and active time-varying sampling period. For NCSs with passive time-varying sampling period, the cases that time delay is longer than a sampling period and the number of consecutive packet dropout is larger than one are taken into consideration, and we also take the case that actuator receives two or more than two control inputs during a sampling period into consideration, which are seldom considered in the literature. The active varying sampling period method is proposed to make full use of network bandwidth, the main idea of this method is that the sensor should shorten the sampling period when the network is idle and improve the performance of control systems correspondingly, when the network is occupied by the most users, the sensor should enlarge the sampling period to reduce the number of packets transmitted through the network and reduce the possibility of network congestion correspondingly. For NCSs with passive time-varying and active time-varying sampling periods, the system models are presented firstly, then by defining appropriate Lyapunov functions and combining multi-objective optimization method, linear matrix inequality approach, free-weighting matrix method and Jensen inequality method, this chapter presents the sufficient conditions and controller design ensuring the asymptotic stability of systems. The simulation examples illustrate the less conservativeness and reduced computational complexity (which is achieved by adopting the Jensen inequality) of the proposed design methods.
In Chapter 4, the delay switching-based method and the both delay switching and parameter uncertainty-based method are proposed to deal with stochastic time-varying delay of NCSs. Considering that the existing parameter uncertainty-based method may lead to much conservativeness, this chapter proposes the delay switching method to deal with network-induced time delay, and it is proved theoretically to be less conservative than the parameter uncertainty-based method. Considering that the delay switching method may lead to the increase of computational complexity, the both delay switching and parameter uncertainty method is proposed, which method may reduce the high computational complexity of the delay switching method and introduce less conservativeness than the parameter uncertainty-based method. Since the active varying sampling period method proposed in Chapter 3 can not avoid the frequent switching of sampling periods, this chapter proposes an improved active varying sampling period method, which can both ensure the sufficient use of network bandwidth and avoid frequent switching of sampling period.
Chapter 5 investigates the H∞performance optimization and state feedback controller design for linear time-invariant systems, the prediction control-based method and the linear estimation-based approach are proposed to overcome the negative influences of time delay and packet dropout. For the prediction-based compensation method, the actual time delay is taken into full consideration when determining which control input should be used:if the transmission time delay of a control input is smaller than a predefined deadline, it should be used directly, otherwise, the predicted control input should be used, then the negative influences of prediction errors may be reduced effectively. A linear estimation-based time delay and packet dropout compensation method is proposed, compared with the prediction-based method, since it is unnecessary to predict the control inputs p-step-ahead and transmit the predicted control inputs to the actuator, the proposed linear estimation-based method may reduce the network load. Based on the proposed compensation methods, two new system models are presented, and the problem of H∞controller design is discussed by using LMI-based method. The simulation examples illustrate the merits of the proposed compensation methods.
Chapter 6 proposes the multiple communication channels sharing-based method to compensate the negative influences of time delay and packet dropout, and H∞performance optimization and controller design are also studied. Compared with the single communication channel-based method, the sharing of the idle communication channels may compensate the negative influences of time delay and packet dropout without leading to the increase of the cost of hardware. Compared with the prediction-based method or the estimation-based method, the proposed multiple communication channels sharing-based method can avoid the negative influences of prediction error or estimation error. By defining appropriate Lyapunov functions and using LMI-based method, H∞controller design and performance optimization are studied. The merit of the proposed controller design methods lies in their less conservativeness, which is achieved by avoiding the utilization of bounding inequalities for cross products of vectors, and the simulation examples illustrate the less conservatism of the proposed methods.
Chapter 7 studies the problems of H∞output tracking performance optimization and controller design for discretized networked control systems with time delay and packet dropout. For NCSs with constant sampling period, H∞output tracking performance optimization and controller design are presented by using LMI-based method and discrete Jensen inequality. For NCSs with time-varying sampling period, a multi-objective optimization method is proposed to optimize H∞output tracking performance of systems, and output tracking controller design is presented correspondingly. Since the discrete Jensen inequality is adopted for H∞output tracking controller design, the proposed design methods may introduce less computational complexity than the free weighting matrix-based method. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances, which has also been illustrated by numerical examples.
Finally, the results of the dissertation are summarized and further research topics are pointed out.
与传统的控制系统相比,网络控制系统虽然有诸多优点,但是网络的引入也会给系统分析与设计带来新的挑战,如网络诱导时延、数据包丢失、数据包时序错乱、多包传输、通信限制、时变采样周期等。现有文献中的结果主要考虑具有时延及丢包的网络控制系统的稳定性分析,控制器设计等问题,通过合理的设计控制器并采用合适的时延及丢包补偿方案来优化网络控制系统H∞性能的问题并未得到充分考虑。
本论文在总结前人工作的基础上,针对网络控制系统中的时延及丢包现象,提出了主动变采样周期方法以充分利用网络带宽,与基于常数采样周期的方法相比,该方法既可以保证网络带宽的充分利用又可以减小发生网络拥塞的可能性。提出了时延切换的方法来处理网络诱导时变时延,并通过理论推导证明了时延切换的方法比基于参数不确定性的方法具有更小的保守性；提出了时延切换与参数不确定性相结合的方法,该方法的计算量比时延切换方法要小,而保守性比基于参数不确定性的方法要小。改进了现有文献中基于预测控制的方法以补偿时延及丢包的负面影响,改进后的方法可有效减小预测误差的负面影响；提出了基于线性估计的方法及基于多通信通道共享的方法来补偿时延及丢包的负面影响,与不考虑补偿的方法相比,可在较大程度上改善系统性能；研究了网络控制系统的H∞输出跟踪性能优化及控制器设计问题,即使存在外部扰动,所设计的控制器仍可以保证系统有较好的跟踪性能。下面详细介绍本文的主要工作。
第一、二章系统地分析和总结了网络控制系统这一前沿研究领域的发展现状及研究方法,并给出了与本文相关的一些预备知识。
第三章考虑具有被动时变采样周期及主动变采样周期网络控制系统的稳定性分析及H∞控制器设计问题。对具有被动时变采样周期的网络控制系统,考虑了时延大于一个采样周期且连续丢包数大于一个的情况,也考虑了执行器在一个采样周期内收到两个及两个以上控制输入的情况,而这两种情况现有文献中很少考虑。提出了一种主动变采样周期方法,其核心是在网络空闲时缩短采样周期从而改善系统性能,在网络负载比较大的时候延长采样周期从而减少网络上数据包的个数并相应地减小发生网络拥塞的可能性。对具有被动时变及主动时变采样周期的网络控制系统,首先给出了系统的模型,通过定义适当的Lyapunov函数并结合多目标优化方法、线性矩阵不等式方法、自由加权矩阵方法及Jensen不等式方法,给出了系统渐进稳定的充分条件并设计了系统的控制器。仿真结果表明,本章所提出的方法具有较小的保守性,同时计算复杂性也比较小(由于Jensen不等式的采用)。
第四章采用时延切换方法及时延切换与参数不确定性相结合的方法处理网络控制系统中的随机时延。考虑到现有文献中基于参数不确定性的方法具有较大保守性,本章提出了时延切换的方法来处理网络诱导时延,并通过理论推导证明了时延切换的方法比基于参数不确定性的方法具有更小的保守性。考虑到时延切换方法会增大计算量,本章又提出了时延切换与参数不确定性相结合的方法,该方法的计算量比时延切换方法要小,而保守性比基于参数不确定性的方法要小。由于上一章中提出的主动变采样周期方法不能避免采样周期的频繁切换,本章提出了一个改进的主动变采样周期方法,该方法既可以保证网络带宽的充分利用又可以避免采样周期的频繁切换。
第五章采用预测控制与基于线性估计的方法来补偿时延及丢包的负面影响,研究了线性时不变系统的H∞性能优化及状态反馈控制器设计问题。对基于预测控制的补偿方法而言,在为系统选择控制输入时,本文充分考虑了网络时延的大小：如果某个控制输入的传输时延小于一个给定的阈值,则使用该控制输入,如果时延大于该阈值,则使用预测的控制输入,这样可以有效减小预测误差的负面影响。提出了一个新的基于线性估计的方法来补偿时延及丢包的负面影响,与基于预测控制的补偿方法相比,由于该方法无需提前p步估计控制输入并发送到执行器,因而可以有效地减小网络负载。基于以上两种补偿方法,本章给出了两个新的系统模型,并利用线性矩阵不等式方法给出了系统的H∞控制器设计方法。仿真例子验证了所提出的补偿方法的优越性。
第六章提出一个基于多通信通道共享的方法来补偿时延及丢包的负面影响,研究了网络控制系统的H∞性能优化及控制器设计问题。与基于单通信通道的方法相比,对空闲通信通道的共享可以补偿时延及丢包的负面影响,而且不会增加系统的硬件成本。与基于预测控制或估计的补偿方法相比,基于多通信通道共享的方法可以避免预测误差或估计误差可能给系统带来的负面影响。通过定义合适的Lyapunov函数并结合线性矩阵不等式方法,研究了网络控制系统的H∞控制器设计及H∞性能优化问题。由于在设计过程中避免了对向量交叉积的放大,因而本章的结果具有较小的保守性,而仿真例子也验证了这一点。
第七章研究了具有时延及丢包的离散化网络控制系统的H∞输出跟踪性能优化及控制器设计问题。利用基于线性矩阵不等式的方法及离散Jensen不等式,研究了具有常数采样周期的网络控制系统的H∞输出跟踪性能优化及控制器设计。对于具有时变采样周期的网络控制系统,采用多目标优化方法来优化系统的H∞输出跟踪性能,并相应的给出了控制器设计方法。由于采用了离散Jensen不等式,本章所提出的H∞输出跟踪控制器设计方法比基于自由加权矩阵的方法具有更小的计算复杂性。即使存在外部扰动,所设计的控制器仍可以保证受控对象的输出渐进跟踪给定的参考模型的输出,数值例子进一步验证了这一点。
最后对全文所做的工作进行了总结,并指明了下一步研究的方向。
In modern industrial systems, sensors, controllers and actuators are often connected over a network medium, which are called networked control systems (NCSs). Compared with the traditional control systems having point to point structure, advantages of NCSs include resource sharing, good fault-tolerant and fault detection ability, less wiring and easy maintenance, high reliability, etc.
Although the introduction of NCSs may lead to many advantages when compared with the traditional control systems, inserting network into control systems will also introduce new challenges for the analysis and design of control systems, such as network-induced time delay, packet dropout, packet disordering, multi-packet transmission, communication constraints, time-varying sampling period, etc. The existing results mainly focus on such problems as stability analysis, controller design, etc. for NCSs with time delay and packet dropout. By designing the controllers appropriately and adopting new methods to compensate the negative influences of time delay and packet dropout, th H∞performance of NCSs may be optimized, however, such problems are not taken into full consideration.
This thesis, based on previous works of others, taking time delay and packet dropout in NCSs into full consideration, proposes an active varying sampling period method to make full use of network bandwidth, compared with the constant sampling period based methods, the proposed method can both ensure the sufficient use of network bandwidth and reduce the possibility of network congestion. A delay switching method is proposed to deal with network-induced time delay, and it is proved theoretically to be less conservative than the parameter uncertainty-based method; a both delay switching and parameter uncertainty-based method is also proposed, which method may reduce the high computational complexity of the delay switching method and introduce less conservativeness than the parameter uncertainty-based method. The prediction control-based method is improved to compensate the negative influences of packet dropout, and the improved method may reduce the negative influences of prediction errors; a linear estimation-based approach and a multiple communication channels sharing-based method are proposed to overcome the negative influences of time delay and packet dropout, compared with the methods without compensation, the proposed methods may improve the performance of systems greatly; the problems of H∞output tracking performance optimization and controller design for NCSs are studied, the designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances. The details of this thesis are as follows.
Chapters 1-2 first summarize and analyze the development and main research methods in networked control systems. Preliminaries about the considered problems are also given.
Chapter 3 investigates the problems of stability analysis and H∞controller design for NCSs with passive time-varying sampling period and active time-varying sampling period. For NCSs with passive time-varying sampling period, the cases that time delay is longer than a sampling period and the number of consecutive packet dropout is larger than one are taken into consideration, and we also take the case that actuator receives two or more than two control inputs during a sampling period into consideration, which are seldom considered in the literature. The active varying sampling period method is proposed to make full use of network bandwidth, the main idea of this method is that the sensor should shorten the sampling period when the network is idle and improve the performance of control systems correspondingly, when the network is occupied by the most users, the sensor should enlarge the sampling period to reduce the number of packets transmitted through the network and reduce the possibility of network congestion correspondingly. For NCSs with passive time-varying and active time-varying sampling periods, the system models are presented firstly, then by defining appropriate Lyapunov functions and combining multi-objective optimization method, linear matrix inequality approach, free-weighting matrix method and Jensen inequality method, this chapter presents the sufficient conditions and controller design ensuring the asymptotic stability of systems. The simulation examples illustrate the less conservativeness and reduced computational complexity (which is achieved by adopting the Jensen inequality) of the proposed design methods.
In Chapter 4, the delay switching-based method and the both delay switching and parameter uncertainty-based method are proposed to deal with stochastic time-varying delay of NCSs. Considering that the existing parameter uncertainty-based method may lead to much conservativeness, this chapter proposes the delay switching method to deal with network-induced time delay, and it is proved theoretically to be less conservative than the parameter uncertainty-based method. Considering that the delay switching method may lead to the increase of computational complexity, the both delay switching and parameter uncertainty method is proposed, which method may reduce the high computational complexity of the delay switching method and introduce less conservativeness than the parameter uncertainty-based method. Since the active varying sampling period method proposed in Chapter 3 can not avoid the frequent switching of sampling periods, this chapter proposes an improved active varying sampling period method, which can both ensure the sufficient use of network bandwidth and avoid frequent switching of sampling period.
Chapter 5 investigates the H∞performance optimization and state feedback controller design for linear time-invariant systems, the prediction control-based method and the linear estimation-based approach are proposed to overcome the negative influences of time delay and packet dropout. For the prediction-based compensation method, the actual time delay is taken into full consideration when determining which control input should be used:if the transmission time delay of a control input is smaller than a predefined deadline, it should be used directly, otherwise, the predicted control input should be used, then the negative influences of prediction errors may be reduced effectively. A linear estimation-based time delay and packet dropout compensation method is proposed, compared with the prediction-based method, since it is unnecessary to predict the control inputs p-step-ahead and transmit the predicted control inputs to the actuator, the proposed linear estimation-based method may reduce the network load. Based on the proposed compensation methods, two new system models are presented, and the problem of H∞controller design is discussed by using LMI-based method. The simulation examples illustrate the merits of the proposed compensation methods.
Chapter 6 proposes the multiple communication channels sharing-based method to compensate the negative influences of time delay and packet dropout, and H∞performance optimization and controller design are also studied. Compared with the single communication channel-based method, the sharing of the idle communication channels may compensate the negative influences of time delay and packet dropout without leading to the increase of the cost of hardware. Compared with the prediction-based method or the estimation-based method, the proposed multiple communication channels sharing-based method can avoid the negative influences of prediction error or estimation error. By defining appropriate Lyapunov functions and using LMI-based method, H∞controller design and performance optimization are studied. The merit of the proposed controller design methods lies in their less conservativeness, which is achieved by avoiding the utilization of bounding inequalities for cross products of vectors, and the simulation examples illustrate the less conservatism of the proposed methods.
Chapter 7 studies the problems of H∞output tracking performance optimization and controller design for discretized networked control systems with time delay and packet dropout. For NCSs with constant sampling period, H∞output tracking performance optimization and controller design are presented by using LMI-based method and discrete Jensen inequality. For NCSs with time-varying sampling period, a multi-objective optimization method is proposed to optimize H∞output tracking performance of systems, and output tracking controller design is presented correspondingly. Since the discrete Jensen inequality is adopted for H∞output tracking controller design, the proposed design methods may introduce less computational complexity than the free weighting matrix-based method. The designed controllers can guarantee asymptotic tracking of prescribed reference outputs while rejecting disturbances, which has also been illustrated by numerical examples.
Finally, the results of the dissertation are summarized and further research topics are pointed out.
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