通讯约束下的网络控制系统跟踪性能极限研究
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摘要
随着计算机、电子和网络通信技术的飞速发展，网络控制系统应运而生。网络控制系统指的是将分布于不同地理位置的传感器、控制器和执行器等设备通过一个有限带宽的数字通信网连接起来，形成的一种空间分布实时反馈闭环控制系统，克服了传统控制系统存在的成本高、可靠性差、故障诊断和维护难等诸多弊端，并由于具有信息资源能够资源共享、易于维护与扩展、高可靠性、高效率和灵活性强等优点，在工业自动化、分布式移动通信和无人机等众多领域都得到了广泛的应用。
控制系统的稳定性和性能，一直是控制领域备受关注的两大重要课题。稳定是系统正常工作的前提，而控制系统性能极限研究的是在系统稳定的基础上，设计控制器使得系统性能达到最优。目前相关研究成果揭示出控制系统的跟踪性能极限由参考输入信号和被控对象的本质特征共同决定。然而由于网络的引入，使得基于网络的控制系统，即网络控制系统的稳定性和性能极限的研究，面临着前所未有的挑战。本文正是基于此研究通讯约束下的网络控制系统跟踪性能极限问题，全文的研究内容归纳如下：
研究了网络控制系统在信道输入能量约束，以及输入扰动和高斯噪声影响下的跟踪性能极限。得到了系统跟踪性能极限的精确表达式。研究结果表明，网络控制系统的跟踪性能极限与被控对象的本质特征如非最小相位零点和不稳定极点的位置与方向密切相关，并揭示了输入扰动和高斯白噪声在一定程度上会恶化系统的跟踪性能，而信道允许输入的信号能量越大，网络控制系统跟踪性能越好。
研究了数据丢包影响下的网络控制系统的跟踪性能极限。基于二进制随机过程对数据丢包进行建模，分别采用单位反馈和双自由度控制结构，得到了系统跟踪性能的一个下确界和一个精确表达式。研究结果揭示了双自由度控制结构相对于单位反馈控制可在一定程度上消除噪声等因素对网络控制系统跟踪性能的影响；而数据丢包的频繁发生，即随着数据丢包概率的增大，系统的跟踪性能将急剧恶化，严重时会使系统失稳。
研究了基于编码-解码结构的网络控制系统跟踪性能极限。基于通信网络中编码-解码存在的不同位置（反馈通道或前馈通道），采用双自由度控制结构，跟踪给定的随机参考输入信号。研究结果表明系统的跟踪性能与被控对象的非最小相位零点、不稳定极点的位置和方向相关外，还与编码器-解码器的本质属性相关，揭示出编码器-解码器的设计可以在一定程度上提高系统的跟踪性能。
研究了离散网络控制系统在信道输入能量约束下的跟踪性能极限，以及在控制能量约束下的调节性能极限。提出了新的优化性能指标，基于不等式约束的最优化方法，得到了跟踪性能的下界以及调节性能的精确表达式确定了信道输入能量约束下达到跟踪性能极限，以及控制能量约束下达到调节性能极限的控制器设计方法。
研究了数据丢包、输入扰动和高斯噪声影响下的网络控制系统的稳定性。基于传递函数矩阵的全通分解、控制器的Youla参数化和不等式约束的最优化方法，得到了保证网络控制系统稳定的信噪比的最小值的表达式。研究结果定量地揭示出非最小相位零点和不稳定极点对信噪比性能的影响。所得结果从另一方面理解为网络控制系统稳定时，通信基本参量（信噪比等）和通信诱导参量（数据丢包等）之间的关系，从而可为通信信道的设计提供指导。
针对非方阵型被控对象，以及输入扰动和高斯噪声影响下的网络控制系统跟踪性能极限进行了研究。确定了基于非方阵型被控对象的控制器Youla参数化形式，采用内外分解技术，得到了系统跟踪性能的精确表达式，并揭示出当被控对象中非最小相位零点和不稳定极点的位置充分接近时，网络控制系统的跟踪性能急剧下降。
最后对全文进行了归纳总结，并对网络控制系统性能极限的研究和发展方向进行了展望。
With the fast development of computer, electronic and network communicationtechnique, networked control systems (NCSs) arise at the historic moment. NCSs consistsof geographically distributed sensor, controller and actuators, which are connected by abandwidth limited digital communication network, and it is a kind of spatial distributionof real-time feedback closed loop control systems. NCSs do not have shortcomings oftraditional control systems the high cost, such as poor reliability, difficulty in diagnosingand maintaining fault, and so on. Due to the advantages including shared informationresources, easy to maintain and extend, high reliability, high efficiency, flexibility, and soon, NCSs have been widely used in industrial automation, distributed mobilecommunications, unmanned aerial vehicle and many other fields.
Being two important topics in control fields, the stability and performance of controlsystems have attracted much attention all the time. Stability is the premise for systemworking normally. While the study of performance of control systems aim to achieveperformance limitation of stable systems by designing controllers. Currently, relevantresults have revealed that the tracking performance limitations of control systems aredetermined by the essential characteristics of reference signals and the plant. However,with networks introduced into control systems, the stability and performance of NCSshave unprecedented challenges, and thus this thesis focus on the study of trackingperformance limitations of NCSs with communication constraints. The research content ofthis dissertation is outlined as follows:
This dissertation investigated the tracking performance limitations of NCSs withchannel input power constraints, and under the effects of input disturbance and Gaussianwhite noise. The exact expression of tracking performance limitations of NCSs has beenobtained, which show that the tracking performance limitations of NCSs is closely related to the essential characteristics of the plant such as locations and directions of nonminimumphase zeros and unstable poles, and reveal that the tracking performance may be badlydegraded by input disturbance and Gaussian white noise in some degree. In anther aspect,the tracking performance of NCSs becoming better with the increase of the allowedchannel input power.
Also, the tracking performance limitation of NCSs under effects of packet dropouts isinvestigated. The packet dropouts are modeled as a binary stochastic process. With unityfeedback and two-freedom-of-degree control structure, a lower bound and an exactexpression of tracking performance have been obtained respectively. The results revealthat compared with the unity feedback, the two-freedom-of-degree control can eliminatethe negative effect of noise on tracking performance of NCSs. In addition, due to thefrequentlyly occurs of packet dropouts, that is, with the increase with packet dropouts’probability the tracking performance will be badly degraded, even makes the NCSsunstable.
This dissertation studied the tracking performance limitations of multi-inputmulti-output NCSs with encoder-decoder. Based on different locations of encoder-decoder(feedforward channel and feedback channel), two-freedom-of-degree controller is adoptedto track the given stochastic reference signal. The results show that the trackingperformance is tightly dependent on the characteristics of the plant and encoder-decoder,and well-designed encoder-decoder can improve the tracking performance limitations ofNCSs.
Moreover, the tracking performance of discrete-time NCSs with channel input powerconstraints, and the regulation performance of NCSs with control energy constraints werestudied in this dissertation. A new performance index for the tracking performance isproposed. Based on the optimization method with the inequality constraints, a lowerbound of tracking performance and exact expression of regulation performance areobtained. In addition, the design methods of controllers of the tracking performance with channel input power constraints and regulation performance of NCSs with control energyconstraints have also been obtained.
The stability problem of NCSs with packet dropouts, input disturbance and additiveGaussian white noise is studied. Base on the all-pass factorization of transfer functionmatrices, Youla parameterization of controllers and optimization method with theinequality constraints, the minimum values of signal-to-noise ratio guaranteeing thestability of NCSs are derived. The results quantitatively reveal how the signal-to-noiseratio performance is affected by the nonminimum phase zeros and unstable poles, whichcan also be understood in a different way that when NCSs is stable, the explicitrelationship between communication basic parameters (signal-to-noise ratio, etc.) andcommunication induced parameters (packet dropouts, etc.), which can give some guidancefor the design of communication channel.
For general non-square plant, this dissertation studied the tracking performancelimitations under the effects of input disturbance and Gaussian noise. The form of Youlaparameterization of controllers for non-square plant model has been determined. Theexplicit expression of tracking performance limitations have been obtained based oninner-outer factorization.
Finally, a summary has been proposed for all discussions in this dissertation. Thefurther study and research works are presented for the network systems.
控制系统的稳定性和性能，一直是控制领域备受关注的两大重要课题。稳定是系统正常工作的前提，而控制系统性能极限研究的是在系统稳定的基础上，设计控制器使得系统性能达到最优。目前相关研究成果揭示出控制系统的跟踪性能极限由参考输入信号和被控对象的本质特征共同决定。然而由于网络的引入，使得基于网络的控制系统，即网络控制系统的稳定性和性能极限的研究，面临着前所未有的挑战。本文正是基于此研究通讯约束下的网络控制系统跟踪性能极限问题，全文的研究内容归纳如下：
研究了网络控制系统在信道输入能量约束，以及输入扰动和高斯噪声影响下的跟踪性能极限。得到了系统跟踪性能极限的精确表达式。研究结果表明，网络控制系统的跟踪性能极限与被控对象的本质特征如非最小相位零点和不稳定极点的位置与方向密切相关，并揭示了输入扰动和高斯白噪声在一定程度上会恶化系统的跟踪性能，而信道允许输入的信号能量越大，网络控制系统跟踪性能越好。
研究了数据丢包影响下的网络控制系统的跟踪性能极限。基于二进制随机过程对数据丢包进行建模，分别采用单位反馈和双自由度控制结构，得到了系统跟踪性能的一个下确界和一个精确表达式。研究结果揭示了双自由度控制结构相对于单位反馈控制可在一定程度上消除噪声等因素对网络控制系统跟踪性能的影响；而数据丢包的频繁发生，即随着数据丢包概率的增大，系统的跟踪性能将急剧恶化，严重时会使系统失稳。
研究了基于编码-解码结构的网络控制系统跟踪性能极限。基于通信网络中编码-解码存在的不同位置（反馈通道或前馈通道），采用双自由度控制结构，跟踪给定的随机参考输入信号。研究结果表明系统的跟踪性能与被控对象的非最小相位零点、不稳定极点的位置和方向相关外，还与编码器-解码器的本质属性相关，揭示出编码器-解码器的设计可以在一定程度上提高系统的跟踪性能。
研究了离散网络控制系统在信道输入能量约束下的跟踪性能极限，以及在控制能量约束下的调节性能极限。提出了新的优化性能指标，基于不等式约束的最优化方法，得到了跟踪性能的下界以及调节性能的精确表达式确定了信道输入能量约束下达到跟踪性能极限，以及控制能量约束下达到调节性能极限的控制器设计方法。
研究了数据丢包、输入扰动和高斯噪声影响下的网络控制系统的稳定性。基于传递函数矩阵的全通分解、控制器的Youla参数化和不等式约束的最优化方法，得到了保证网络控制系统稳定的信噪比的最小值的表达式。研究结果定量地揭示出非最小相位零点和不稳定极点对信噪比性能的影响。所得结果从另一方面理解为网络控制系统稳定时，通信基本参量（信噪比等）和通信诱导参量（数据丢包等）之间的关系，从而可为通信信道的设计提供指导。
针对非方阵型被控对象，以及输入扰动和高斯噪声影响下的网络控制系统跟踪性能极限进行了研究。确定了基于非方阵型被控对象的控制器Youla参数化形式，采用内外分解技术，得到了系统跟踪性能的精确表达式，并揭示出当被控对象中非最小相位零点和不稳定极点的位置充分接近时，网络控制系统的跟踪性能急剧下降。
最后对全文进行了归纳总结，并对网络控制系统性能极限的研究和发展方向进行了展望。
With the fast development of computer, electronic and network communicationtechnique, networked control systems (NCSs) arise at the historic moment. NCSs consistsof geographically distributed sensor, controller and actuators, which are connected by abandwidth limited digital communication network, and it is a kind of spatial distributionof real-time feedback closed loop control systems. NCSs do not have shortcomings oftraditional control systems the high cost, such as poor reliability, difficulty in diagnosingand maintaining fault, and so on. Due to the advantages including shared informationresources, easy to maintain and extend, high reliability, high efficiency, flexibility, and soon, NCSs have been widely used in industrial automation, distributed mobilecommunications, unmanned aerial vehicle and many other fields.
Being two important topics in control fields, the stability and performance of controlsystems have attracted much attention all the time. Stability is the premise for systemworking normally. While the study of performance of control systems aim to achieveperformance limitation of stable systems by designing controllers. Currently, relevantresults have revealed that the tracking performance limitations of control systems aredetermined by the essential characteristics of reference signals and the plant. However,with networks introduced into control systems, the stability and performance of NCSshave unprecedented challenges, and thus this thesis focus on the study of trackingperformance limitations of NCSs with communication constraints. The research content ofthis dissertation is outlined as follows:
This dissertation investigated the tracking performance limitations of NCSs withchannel input power constraints, and under the effects of input disturbance and Gaussianwhite noise. The exact expression of tracking performance limitations of NCSs has beenobtained, which show that the tracking performance limitations of NCSs is closely related to the essential characteristics of the plant such as locations and directions of nonminimumphase zeros and unstable poles, and reveal that the tracking performance may be badlydegraded by input disturbance and Gaussian white noise in some degree. In anther aspect,the tracking performance of NCSs becoming better with the increase of the allowedchannel input power.
Also, the tracking performance limitation of NCSs under effects of packet dropouts isinvestigated. The packet dropouts are modeled as a binary stochastic process. With unityfeedback and two-freedom-of-degree control structure, a lower bound and an exactexpression of tracking performance have been obtained respectively. The results revealthat compared with the unity feedback, the two-freedom-of-degree control can eliminatethe negative effect of noise on tracking performance of NCSs. In addition, due to thefrequentlyly occurs of packet dropouts, that is, with the increase with packet dropouts’probability the tracking performance will be badly degraded, even makes the NCSsunstable.
This dissertation studied the tracking performance limitations of multi-inputmulti-output NCSs with encoder-decoder. Based on different locations of encoder-decoder(feedforward channel and feedback channel), two-freedom-of-degree controller is adoptedto track the given stochastic reference signal. The results show that the trackingperformance is tightly dependent on the characteristics of the plant and encoder-decoder,and well-designed encoder-decoder can improve the tracking performance limitations ofNCSs.
Moreover, the tracking performance of discrete-time NCSs with channel input powerconstraints, and the regulation performance of NCSs with control energy constraints werestudied in this dissertation. A new performance index for the tracking performance isproposed. Based on the optimization method with the inequality constraints, a lowerbound of tracking performance and exact expression of regulation performance areobtained. In addition, the design methods of controllers of the tracking performance with channel input power constraints and regulation performance of NCSs with control energyconstraints have also been obtained.
The stability problem of NCSs with packet dropouts, input disturbance and additiveGaussian white noise is studied. Base on the all-pass factorization of transfer functionmatrices, Youla parameterization of controllers and optimization method with theinequality constraints, the minimum values of signal-to-noise ratio guaranteeing thestability of NCSs are derived. The results quantitatively reveal how the signal-to-noiseratio performance is affected by the nonminimum phase zeros and unstable poles, whichcan also be understood in a different way that when NCSs is stable, the explicitrelationship between communication basic parameters (signal-to-noise ratio, etc.) andcommunication induced parameters (packet dropouts, etc.), which can give some guidancefor the design of communication channel.
For general non-square plant, this dissertation studied the tracking performancelimitations under the effects of input disturbance and Gaussian noise. The form of Youlaparameterization of controllers for non-square plant model has been determined. Theexplicit expression of tracking performance limitations have been obtained based oninner-outer factorization.
Finally, a summary has been proposed for all discussions in this dissertation. Thefurther study and research works are presented for the network systems.
引文
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