鲁棒控制在网络控制系统中的应用研究
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摘要
随着计算机、网络和通信技术的飞跃发展,智能化传感器、执行机构和驱动设备的诞生奠定了网络控制系统(NCS, Networked Control Systems)的物质基础,高速以太网和现场总线技术的不断发展和成功应用解决了NCS的可靠性和开放性问题,推动了NCS的广泛应用。NCS充分体现了控制系统网络化、集成化、分布化及节点智能化的发展趋势。然而,NCS由于网络的介入,不可避免地带来了许多问题:如网络传输导致的反馈和控制输入中的时延、网络带宽的限制使得数据必须分批传送、通信失败造成的数据包丢失、不同的网络节点之间系统时钟的异步等等。这些问题的存在,不但会降低系统的控制性能,而且还是引起系统不稳定的潜在因素。因此,本文考虑了网络诱导时延、数据包丢失和外部扰动等主要问题,以控制网络的服务质量为基础,围绕着NCS的性能指标,研究了NCS的建模、稳定性分析、鲁棒控制、非脆弱保性能最优控制、H∞最优控制等问题,主要工作如下:
研究了短时延NCS的非脆弱保性能控制器设计问题。针对闭环网络控制系统离散化模型,把回路时延的不确定性转化为被控对象系统方程系数矩阵的不确定性,然后利用Lyapunov理论和线性矩阵不等式(LMI)方法,分别给出了具有加性和乘性控制器增益扰动的非脆弱保性能控制器存在的条件和控制器的设计方法。最后,在满足性能指标条件的基础上,将次优保性能控制器的设计问题转化为一组线性矩阵不等式约束下的优化问题。
研究了存在有限能量外部扰动时的短时延NCS的鲁棒H∞控制问题。分两个部分内容:(1)针对具有控制约束和网络诱导时延小于一个采样周期的NCS,在建立其数学模型的基础上,利用LMI方法设计了使闭环系统鲁棒稳定的状态反馈H∞控制器。(2)考虑到网络控制系统中状态往往难于被检测的实际情况,研究了具有动态补偿功能的动态输出反馈鲁棒H∞控制问题,给出了H∞控制律存在的条件和和控制器的实现形式。研究了一类长时延网络控制系统的鲁棒H∞控制问题。考虑了网络诱导时延大于一个采样周期的情况,采用状态反馈控制策略设计了使闭环NCS鲁棒稳定的控制器,利用Lyapunov理论和LMI方法,推导出了依赖于网络诱导时延大小的闭环NCS渐近稳定的充分条件,并给出了相应的状态反馈H∞控制器设计方法和网络诱导时延最大值的求解方法。
研究了具有时延和数据包丢失的NCS建模、稳定性分析和控制器设计问题。对于给定的数据包丢失率,系统被建模为具有两个结构事件率约束的异步动态系统。随后,利用异步动态系统理论和LMI方法推导出使系统指数稳定的充分条件并且给出了相应的控制器设计方法。
With the rapid developments of computer, network and communication technology, the naissance of intelligentized sensor, actuator and drive device consists of the substance foundation of networked control systems (NCS). The reliability and open issues of NCS have been solved by the sustained developments and successful applications of high speed Ethernet and fieldbus control technology, which promote the extensive applications of NCS. NCS incarnates enough the development tendency of control systems i.e. network, integration, decentralization, intelligence. However, with the impact of network circumstance, many issues emerged inevitably, such as network-induced transmission delay, multi-channel transmission brought by the limited bandwidth, data packet dropouts for the failed communication, the asynchronous clock among network nodes etc. These problems not only depress the performance of normally designed control systems, but also destroy the system stability. So, we consider the main problems of network-induced delay, data packet dropout and external disturbance in NCS. Basing on the quality of service of control networks, surrounding the performance index of NCS, we study the issues of modeling, stability analysis, robust control, non-fragile guaranteed cost optimal control, H∞optimal control for NCS. The main achievements are listed as follows:
The problem of robust and non-fragile guaranteed cost controller design for NCS with network-induced delay less than or equals to one sampling period is studied. Aiming at the discrete model of closed-loop NCS, the uncertainty caused by loop time-delay is transformed into the matrix parameter uncertainty of the equation of the controlled plant. Thus, by using the Lyapunov theory and linear matrix inequality (LMI) approach, sufficient conditions about the existence of the non-fragile state feedback controller with two classes of control gain perturbations, and the controller design method is presented. Furthermore, the design problem of the suboptimal guaranteed cost controller is turned into a convex optimization problem with linear matrix inequalities constraints.
The problem of robust H∞control for a class of networked control systems with short transmission delay and limited external disturbance is investigated. There are two parts. (1) The state feedback NCS with control input constraints and uncertain delay less than or equals to one sampling period is modeled as a linear time-variant discrete system. Basing on the model built, we development the condition of robust stability and the design method of robust H∞control law for the system. (2) In practical control systems, the state of NCS can’t always be measured. So we derive the sufficient condition and robust H∞controller design method of asymptotic stability of dynamical output feedback NCS.
For a class of linear time-invariant normal controlled plant with network-induced delay more than one sampling period, we study the problem of modeling and robust H∞controller design. By using the Lyapunov theory and LMI approach, the sufficient condition of network induce delay-independent asymptotic stability is derived. Then, the methods of H∞controller design and obtaining maximum allowable delay bound are also presented.
For a class of linear time-invariant normal controlled plant with network-induced delay and date packet dropout, the problem of modeling, exponential stability and controller design for NCS. For the given date packet dropout rate, the networked control systems can be modeled as an asynchronous dynamical system constrained by two configuration event rates. Based on the theory of asynchronous dynamical system, the sufficient condition of exponential stability for NCS is derived. Meanwhile, the dynamical output feedback controller can be solved by a set of linear matrix inequalities.
研究了短时延NCS的非脆弱保性能控制器设计问题。针对闭环网络控制系统离散化模型,把回路时延的不确定性转化为被控对象系统方程系数矩阵的不确定性,然后利用Lyapunov理论和线性矩阵不等式(LMI)方法,分别给出了具有加性和乘性控制器增益扰动的非脆弱保性能控制器存在的条件和控制器的设计方法。最后,在满足性能指标条件的基础上,将次优保性能控制器的设计问题转化为一组线性矩阵不等式约束下的优化问题。
研究了存在有限能量外部扰动时的短时延NCS的鲁棒H∞控制问题。分两个部分内容:(1)针对具有控制约束和网络诱导时延小于一个采样周期的NCS,在建立其数学模型的基础上,利用LMI方法设计了使闭环系统鲁棒稳定的状态反馈H∞控制器。(2)考虑到网络控制系统中状态往往难于被检测的实际情况,研究了具有动态补偿功能的动态输出反馈鲁棒H∞控制问题,给出了H∞控制律存在的条件和和控制器的实现形式。研究了一类长时延网络控制系统的鲁棒H∞控制问题。考虑了网络诱导时延大于一个采样周期的情况,采用状态反馈控制策略设计了使闭环NCS鲁棒稳定的控制器,利用Lyapunov理论和LMI方法,推导出了依赖于网络诱导时延大小的闭环NCS渐近稳定的充分条件,并给出了相应的状态反馈H∞控制器设计方法和网络诱导时延最大值的求解方法。
研究了具有时延和数据包丢失的NCS建模、稳定性分析和控制器设计问题。对于给定的数据包丢失率,系统被建模为具有两个结构事件率约束的异步动态系统。随后,利用异步动态系统理论和LMI方法推导出使系统指数稳定的充分条件并且给出了相应的控制器设计方法。
With the rapid developments of computer, network and communication technology, the naissance of intelligentized sensor, actuator and drive device consists of the substance foundation of networked control systems (NCS). The reliability and open issues of NCS have been solved by the sustained developments and successful applications of high speed Ethernet and fieldbus control technology, which promote the extensive applications of NCS. NCS incarnates enough the development tendency of control systems i.e. network, integration, decentralization, intelligence. However, with the impact of network circumstance, many issues emerged inevitably, such as network-induced transmission delay, multi-channel transmission brought by the limited bandwidth, data packet dropouts for the failed communication, the asynchronous clock among network nodes etc. These problems not only depress the performance of normally designed control systems, but also destroy the system stability. So, we consider the main problems of network-induced delay, data packet dropout and external disturbance in NCS. Basing on the quality of service of control networks, surrounding the performance index of NCS, we study the issues of modeling, stability analysis, robust control, non-fragile guaranteed cost optimal control, H∞optimal control for NCS. The main achievements are listed as follows:
The problem of robust and non-fragile guaranteed cost controller design for NCS with network-induced delay less than or equals to one sampling period is studied. Aiming at the discrete model of closed-loop NCS, the uncertainty caused by loop time-delay is transformed into the matrix parameter uncertainty of the equation of the controlled plant. Thus, by using the Lyapunov theory and linear matrix inequality (LMI) approach, sufficient conditions about the existence of the non-fragile state feedback controller with two classes of control gain perturbations, and the controller design method is presented. Furthermore, the design problem of the suboptimal guaranteed cost controller is turned into a convex optimization problem with linear matrix inequalities constraints.
The problem of robust H∞control for a class of networked control systems with short transmission delay and limited external disturbance is investigated. There are two parts. (1) The state feedback NCS with control input constraints and uncertain delay less than or equals to one sampling period is modeled as a linear time-variant discrete system. Basing on the model built, we development the condition of robust stability and the design method of robust H∞control law for the system. (2) In practical control systems, the state of NCS can’t always be measured. So we derive the sufficient condition and robust H∞controller design method of asymptotic stability of dynamical output feedback NCS.
For a class of linear time-invariant normal controlled plant with network-induced delay more than one sampling period, we study the problem of modeling and robust H∞controller design. By using the Lyapunov theory and LMI approach, the sufficient condition of network induce delay-independent asymptotic stability is derived. Then, the methods of H∞controller design and obtaining maximum allowable delay bound are also presented.
For a class of linear time-invariant normal controlled plant with network-induced delay and date packet dropout, the problem of modeling, exponential stability and controller design for NCS. For the given date packet dropout rate, the networked control systems can be modeled as an asynchronous dynamical system constrained by two configuration event rates. Based on the theory of asynchronous dynamical system, the sufficient condition of exponential stability for NCS is derived. Meanwhile, the dynamical output feedback controller can be solved by a set of linear matrix inequalities.
引文
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