多变量网络控制系统建模、控制与调度初探
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摘要
自上世纪90年代以来,随着计算机技术、通信技术、网络技术以及控制理论的发展,网络控制技术以及在网络平台上构筑而成的网络控制系统已成为自动化领域技术发展的热点。它不仅在实践上为解决远程实时控制中已经遇到或将要遇到的诸多技术难题带来新的解决思路和方法,而且在理论上将促进自动控制技术、计算机技术和通信技术等多学科的相互渗透和交叉发展。因此,进行网络控制系统的研究对我国工业、农业、军事与民用网络控制系统的建设具有十分重要的理论和应用价值。
本文主要针对工业过程中日益广泛的多变量网络控制系统所特有的建模和控制难度大、调度复杂的问题,进行了系统的理论分析和实验研究,构建出该类网络控制系统连续、离散以及多采样时间模型;并采用时滞系统理论、线性矩阵不等式和自由权矩阵方法,得到系统存在诸多不确定性条件下保守性低的稳定性和鲁棒性条件,设计出一种新颖的自适应灰色预测动态反馈调度器和多种先进的鲁棒H∞控制器、鲁棒容错控制器以及非线性网络迭代学习跟踪控制器;最后,基于所得到的理论研究结果,以双并联倒立摆控制系统为对象,开发出一套基于局域网的多变量网络控制系统的实验平台。其主要研究成果概括如下:
1.建立了多变量网络控制系统的模型:首先对多变量网络控制系统进行了详细地分析,得出一个具有多时延函数微分方程的连续时间模型;并依据离散系统理论,推导了传感器、控制器为时间驱动,执行器为事件驱动条件下的多变量网络控制系统的离散时间模型;最后,利用提升技术推导出一类多采样周期的多变量网络控制系统增广状态空间模型,为多采样网络控制系统的研究提供了基础。
2.研究了多包、单包传输情况下多变量网络控制系统的稳定性和鲁棒性:充分考虑系统各状态之间的相关性以及系统参数的不确定,构造新的增广Lyapunov- Krasovskii函数,并采用线性矩阵不等式和自由权矩阵的方法对多变量网络控制系统的时滞独立和时滞依赖稳定性进行分析,从理论上推导出更加宽松的稳定性和鲁棒性定理。仿真实验验证了所提定理的有效性。
3.设计了多变量网络控制系统鲁棒控制器和自适应灰色预测控制器:采用自由权矩阵方法,推导出更为简单、宽松的线性矩阵不等式形式的鲁棒性能指标的充分条件,设计了鲁棒H∞控制器以及执行器失效情况下的鲁棒容错控制器;在此基础上引入预测思想,利用新陈代谢原理建立等维新息GM(1,1)模型,提出了一种自适应灰色预测网络控制策略,以有效减小网络不确定性所带来的影响。
4.研究了非线性多变量网络控制系统稳定性和迭代学习跟踪控制策略:针对一类通用不确定非线性多变量被控对象,采用时滞理论和线性矩阵不等式方法,推导该类系统网络控制环境下的渐近稳定性条件,并利用迭代学习策略设计出具有全局学习收敛能力和保证所构成系统稳健性的先进学习跟踪控制器。
5.提出了一种新型自适应灰色预测动态反馈调度策略:首先对多变量网络控制系统信息调度原理进行了解析描述,推导出保证系统渐近稳定的条件;并基于反馈调度思想研究了一种基于灰色预测网络运行状况的动态调度方法,通过动态调整控制系统各回路采样周期和优先级来合理分配网络资源,给性能较差的回路分配较多的网络资源和较高的优先级,以减小该回路网络诱导时延,从而克服了现有RM等调度方法的不足,有效地处理动态网络环境下的系统控制,为多变量网络控制系统的联合设计提供一种新思路。
6.基于局域网构建了一种多变量网络控制实验平台:详细探讨了多变量网络控制系统的软硬件实验设计方案,并采用自适应灰色预测控制和模型预测最优控制两种策略,分别对校园网环境下分布式两单级倒立摆的跟踪控制和双并联耦合倒立摆的稳定控制进行了仿真和实验研究。
以上研究,进一步拓宽了网络环境下被控对象的适用范围,为网络控制系统的推广、应用提供了理论支持和实验基础。
With the fast development of computer technology, communication technology, network technology and control theory etc, the networked control technology and the networked control systems constructed upon network platform had been a hot research issue in the field of automation technology since the 1990s of the 20th century. It not only in practice can provide new ideas and methods to solve a lot of technical problems which had met or will meet in the remote real-time control systems, but also in theory can promote mutual infiltration and cross development of automatic control technology, computer technology and communication technology etc. Therefore the research of NCSs for our national industry, agriculture, military and civil is of great theory and application values.
In this dissertation, these issues about modeling, control and scheduling of multi-variable networked control systems, which is increasing in the industry, are deeply studied. The complete continuous-time model, discrete-time model and multi-sample-time model are derived. The loose conservative sufficient conditions for convergence and robustness are given based on the research of time-delay systems theory, linear matrix inequality and free-weighting matrix method. And some new control methods are presented to perfectly solve the uncertainties problem about multi-variable networked control systems, such as dynamic feedback adaptive grey prediction scheduler, robust H∞controller, robust fault-tolerant controller and non-linear iterative learning tracking controller. At last, the local area network control systems of parallel coupled inverted pendulum are constructed to show the efficacy and feasibility of the proposed methods. The main research work is described as follows:
1) The modeling of multi-variable networked control systems is presented. Based on the detailed analysis of networked control systems, the continuous-time differential mathematical model with multi-delay of networked control systems is described. Then using discrete-time system theory, the discrete-time mathematical model of networked control systems is proposed when the sensor node and controller node is time triggered, actuator is event triggered. At last the extended multi-sample-time mathematical model with short time-delay of multi-variable networked control systems is given by using lifting technology. It provides the basis for multi-sample-time networked control systems research.
2)The issue of stability and robustness analysis for multi-variable networked control systems is researched under the condition of multi-packet transfer or single-packet transfer. Considering the correlation of the system states and the uncertainty of the system parameters, a new extended function of Lyapunov-Krasovskii is constructed. Then the delay-dependent sufficient conditions and the delay-independent sufficient conditions for systems are derived by using linear matrix inequality theory and free-weighting matrix method. Based on the above research, the more loose stability theorem and robustness theorem is given. The efficacy and feasibility of the proposed theory is shown by presenting simulation results.
3) The robust controller and the adaptive grey predictive controller are designed. By using free-weighting matrix method, the simple and loose linear matrix inequality's condition for robust asymptotic stability is derived. The robust H∞controller and the robust fault-tolerant controller for uncertain continuous-time multi-variable networked control systems with actuators failure is designed based on the research of H∞control theory, where its network transmission is connected with network-induced delay and packet dropout. Then using grey theory and adaptive switching method, a new adaptive grey prediction control strategy for multi-variable networked control systems is proposed to reduce the effects of the system uncertainties. The whole modeling procedure of this method is established. The equal dimension GM (1,1) model is established by using metabolic principle. This method only identifies two parameters, and avoids online solving the Diophantine equation and inverse matrix. So the computation load of the algorithm can be reduced greatly, and real-time property is advanced.
4) The stability and the iterative learning control approach for nonlinear multi-variable networked control systems are studied. By using the time-delay theory and linear matrix inequality method, the asymptotic stability conditions are derived for a class of general nonlinear plant with uncertainty. The tracking control method of iterative learning control for networked control systems is designed, which can track the desired trajectory for any arbitrary precision in a fixed finite interval. The tracking error of this approach tends to be zero as the number of iteration increases. And the convergence in the iteration domain can also be ensured.
5) The issue of dynamic feedback scheduling strategy for multi-variable networked control systems is studied. A discrete time-variant mathematic model integrating control and information scheduling for multi-variable networked control systems is developed based on the research of the communication sequence notion and mixed logical dynamical framework. And the posedness conditions which can make system stable are derived too. Then using feedback scheduling ideas, the adaptive grey prediction dynamic feedback scheduling strategy is proposed. By on-line adjusting sample periods of the control systems sharing network resource, more network resources and higher priority is set for the control loop with poor performance. Then the network bandwidth are allocate to each control system dynamically so as to adapt to the variation of network load. The proposed algorithm can deal effectively with the dynamic network environment to overcome the shortcoming of traditional rate monotonic and reduce the network-induced delay, and can successfully give a solution to the problem of scheduling and control co-design.
6) The novel multi-variable networked control systems experiment platform based on local area network is designed. The complete hardware and software design program of parallel coupled inverted pendulum is deeply researched. Then using adaptive grey prediction control and optimal control based model, the tracking control of campus network based distributed two inverted pendulum system and the stability control of campus network based parallel coupled inverted pendulum are realized on the developed networked control systems platform respectively. This platform can serves as a useful tool for theoretical researchers on multi-variable networked control systems. In conclusion, all the research work in this dissertation further expands the scope of plant in the application networked control systems, and provides the experimental foundation and the theoretical support for networked control systems promotion.
本文主要针对工业过程中日益广泛的多变量网络控制系统所特有的建模和控制难度大、调度复杂的问题,进行了系统的理论分析和实验研究,构建出该类网络控制系统连续、离散以及多采样时间模型;并采用时滞系统理论、线性矩阵不等式和自由权矩阵方法,得到系统存在诸多不确定性条件下保守性低的稳定性和鲁棒性条件,设计出一种新颖的自适应灰色预测动态反馈调度器和多种先进的鲁棒H∞控制器、鲁棒容错控制器以及非线性网络迭代学习跟踪控制器;最后,基于所得到的理论研究结果,以双并联倒立摆控制系统为对象,开发出一套基于局域网的多变量网络控制系统的实验平台。其主要研究成果概括如下:
1.建立了多变量网络控制系统的模型:首先对多变量网络控制系统进行了详细地分析,得出一个具有多时延函数微分方程的连续时间模型;并依据离散系统理论,推导了传感器、控制器为时间驱动,执行器为事件驱动条件下的多变量网络控制系统的离散时间模型;最后,利用提升技术推导出一类多采样周期的多变量网络控制系统增广状态空间模型,为多采样网络控制系统的研究提供了基础。
2.研究了多包、单包传输情况下多变量网络控制系统的稳定性和鲁棒性:充分考虑系统各状态之间的相关性以及系统参数的不确定,构造新的增广Lyapunov- Krasovskii函数,并采用线性矩阵不等式和自由权矩阵的方法对多变量网络控制系统的时滞独立和时滞依赖稳定性进行分析,从理论上推导出更加宽松的稳定性和鲁棒性定理。仿真实验验证了所提定理的有效性。
3.设计了多变量网络控制系统鲁棒控制器和自适应灰色预测控制器:采用自由权矩阵方法,推导出更为简单、宽松的线性矩阵不等式形式的鲁棒性能指标的充分条件,设计了鲁棒H∞控制器以及执行器失效情况下的鲁棒容错控制器;在此基础上引入预测思想,利用新陈代谢原理建立等维新息GM(1,1)模型,提出了一种自适应灰色预测网络控制策略,以有效减小网络不确定性所带来的影响。
4.研究了非线性多变量网络控制系统稳定性和迭代学习跟踪控制策略:针对一类通用不确定非线性多变量被控对象,采用时滞理论和线性矩阵不等式方法,推导该类系统网络控制环境下的渐近稳定性条件,并利用迭代学习策略设计出具有全局学习收敛能力和保证所构成系统稳健性的先进学习跟踪控制器。
5.提出了一种新型自适应灰色预测动态反馈调度策略:首先对多变量网络控制系统信息调度原理进行了解析描述,推导出保证系统渐近稳定的条件;并基于反馈调度思想研究了一种基于灰色预测网络运行状况的动态调度方法,通过动态调整控制系统各回路采样周期和优先级来合理分配网络资源,给性能较差的回路分配较多的网络资源和较高的优先级,以减小该回路网络诱导时延,从而克服了现有RM等调度方法的不足,有效地处理动态网络环境下的系统控制,为多变量网络控制系统的联合设计提供一种新思路。
6.基于局域网构建了一种多变量网络控制实验平台:详细探讨了多变量网络控制系统的软硬件实验设计方案,并采用自适应灰色预测控制和模型预测最优控制两种策略,分别对校园网环境下分布式两单级倒立摆的跟踪控制和双并联耦合倒立摆的稳定控制进行了仿真和实验研究。
以上研究,进一步拓宽了网络环境下被控对象的适用范围,为网络控制系统的推广、应用提供了理论支持和实验基础。
With the fast development of computer technology, communication technology, network technology and control theory etc, the networked control technology and the networked control systems constructed upon network platform had been a hot research issue in the field of automation technology since the 1990s of the 20th century. It not only in practice can provide new ideas and methods to solve a lot of technical problems which had met or will meet in the remote real-time control systems, but also in theory can promote mutual infiltration and cross development of automatic control technology, computer technology and communication technology etc. Therefore the research of NCSs for our national industry, agriculture, military and civil is of great theory and application values.
In this dissertation, these issues about modeling, control and scheduling of multi-variable networked control systems, which is increasing in the industry, are deeply studied. The complete continuous-time model, discrete-time model and multi-sample-time model are derived. The loose conservative sufficient conditions for convergence and robustness are given based on the research of time-delay systems theory, linear matrix inequality and free-weighting matrix method. And some new control methods are presented to perfectly solve the uncertainties problem about multi-variable networked control systems, such as dynamic feedback adaptive grey prediction scheduler, robust H∞controller, robust fault-tolerant controller and non-linear iterative learning tracking controller. At last, the local area network control systems of parallel coupled inverted pendulum are constructed to show the efficacy and feasibility of the proposed methods. The main research work is described as follows:
1) The modeling of multi-variable networked control systems is presented. Based on the detailed analysis of networked control systems, the continuous-time differential mathematical model with multi-delay of networked control systems is described. Then using discrete-time system theory, the discrete-time mathematical model of networked control systems is proposed when the sensor node and controller node is time triggered, actuator is event triggered. At last the extended multi-sample-time mathematical model with short time-delay of multi-variable networked control systems is given by using lifting technology. It provides the basis for multi-sample-time networked control systems research.
2)The issue of stability and robustness analysis for multi-variable networked control systems is researched under the condition of multi-packet transfer or single-packet transfer. Considering the correlation of the system states and the uncertainty of the system parameters, a new extended function of Lyapunov-Krasovskii is constructed. Then the delay-dependent sufficient conditions and the delay-independent sufficient conditions for systems are derived by using linear matrix inequality theory and free-weighting matrix method. Based on the above research, the more loose stability theorem and robustness theorem is given. The efficacy and feasibility of the proposed theory is shown by presenting simulation results.
3) The robust controller and the adaptive grey predictive controller are designed. By using free-weighting matrix method, the simple and loose linear matrix inequality's condition for robust asymptotic stability is derived. The robust H∞controller and the robust fault-tolerant controller for uncertain continuous-time multi-variable networked control systems with actuators failure is designed based on the research of H∞control theory, where its network transmission is connected with network-induced delay and packet dropout. Then using grey theory and adaptive switching method, a new adaptive grey prediction control strategy for multi-variable networked control systems is proposed to reduce the effects of the system uncertainties. The whole modeling procedure of this method is established. The equal dimension GM (1,1) model is established by using metabolic principle. This method only identifies two parameters, and avoids online solving the Diophantine equation and inverse matrix. So the computation load of the algorithm can be reduced greatly, and real-time property is advanced.
4) The stability and the iterative learning control approach for nonlinear multi-variable networked control systems are studied. By using the time-delay theory and linear matrix inequality method, the asymptotic stability conditions are derived for a class of general nonlinear plant with uncertainty. The tracking control method of iterative learning control for networked control systems is designed, which can track the desired trajectory for any arbitrary precision in a fixed finite interval. The tracking error of this approach tends to be zero as the number of iteration increases. And the convergence in the iteration domain can also be ensured.
5) The issue of dynamic feedback scheduling strategy for multi-variable networked control systems is studied. A discrete time-variant mathematic model integrating control and information scheduling for multi-variable networked control systems is developed based on the research of the communication sequence notion and mixed logical dynamical framework. And the posedness conditions which can make system stable are derived too. Then using feedback scheduling ideas, the adaptive grey prediction dynamic feedback scheduling strategy is proposed. By on-line adjusting sample periods of the control systems sharing network resource, more network resources and higher priority is set for the control loop with poor performance. Then the network bandwidth are allocate to each control system dynamically so as to adapt to the variation of network load. The proposed algorithm can deal effectively with the dynamic network environment to overcome the shortcoming of traditional rate monotonic and reduce the network-induced delay, and can successfully give a solution to the problem of scheduling and control co-design.
6) The novel multi-variable networked control systems experiment platform based on local area network is designed. The complete hardware and software design program of parallel coupled inverted pendulum is deeply researched. Then using adaptive grey prediction control and optimal control based model, the tracking control of campus network based distributed two inverted pendulum system and the stability control of campus network based parallel coupled inverted pendulum are realized on the developed networked control systems platform respectively. This platform can serves as a useful tool for theoretical researchers on multi-variable networked control systems. In conclusion, all the research work in this dissertation further expands the scope of plant in the application networked control systems, and provides the experimental foundation and the theoretical support for networked control systems promotion.
引文
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