【作者】 赵虹；

【导师】 吴敏；

【作者基本信息】 中南大学 ， 控制理论与控制工程， 2011， 博士

【摘要】 随着计算机技术、网络技术和通信技术的快速发展,网络控制系统在许多控制领域都得到越来越广泛的应用。在网络控制系统中,传感器、执行器和控制器之间通过通信网络相互连接,不可避免地会产生时滞。网络诱导时滞的存在会降低系统的控制性能,甚至会导致系统不稳定。而且网络诱导时滞往往是时变的,这使得网络控制系统的分析与设计更为复杂。如何求得网络控制系统的最大允许时滞上界(MADB)并设计有效的控制器,以确保在MADB的范围内系统的稳定性和控制性能,这是本文的研究目的。借助于Lyapunov稳定性理论和自由权矩阵方法,本文讨论网络控制系统的稳定性分析与镇定控制、保成本控制、鲁棒H∞控制以及鲁棒H∞滤波器的设计等问题。论文的主要研究成果如下：(1)提出网络控制系统的稳定性条件以及状态反馈镇定控制器设计方法。针对带有时变时滞的连续时间网络控制系统,利用Lyapunov-Krasovskii泛函和改进的自由权矩阵方法,通过保留Lyapunov-Krasovskii泛函导数中的所有项,获得网络控制系统的稳定性条件,并推广到带有时变结构不确定性的网络控制系统,在此基础上提出状态反馈镇定控制器的设计方法,并采用基于线性矩阵不等式(LMI)的改进锥补偿算法(ICCL)求解非线性矩阵不等式(NLMI),获得保证网络控制系统稳定的MADB以及控制器的参数。同时,利用类似的方法获得离散时间网络控制系统的稳定性条件以及镇定控制器设计方法。数值实例表明所提方法的有效性和相比已有方法较低的保守性。(2)提出网络控制系统的保成本控制器设计方法。根据网络控制系统的性能要求,利用Lyapunov-Krasovskii泛函和改进的自由权矩阵方法,研究连续时间网络控制系统保成本控制器的设计方法。通过ICCL算法求解控制器的参数,得到满足给定性能要求的保成本控制器。同时提出离散时间保成本控制器设计方法。数值实例表明所提方法的有效性和相比已有方法更小的保成本性能指标。(3)提出网络控制系统的鲁棒H∞控制器设计方法。针对一类连续时间网络控制系统,利用Lyapunov-Krasovskii泛函和改进的自由权矩阵方法,建立网络控制系统的H∞性能准则,在此基础上提出H∞状态反馈控制器的设计方法,并推广到鲁棒H∞控制器的设计。同时采用类似方法得到离散时间网络控制系统的H∞控制器的设计方法。数值实例表明该方法是有效的并具有较好的H∞性能。(4)提出基于网络的鲁棒H∞滤波器设计方法。针对连续时间网络控制系统,利用Lyapunov-Krasovskii泛函和改进的自由权矩阵方法,通过保留Lyapunov-Krasovskii泛函导数中的所有项,并对系统中不同部分的不确定性进行分别处理,建立基于网络的滤波器误差系统鲁棒H∞性能分析准则,在此基础上得到基于LMI的鲁棒H∞滤波器设计方法。采用类似的方法,获得基于网络的离散H∞滤波器设计方法。数值实例表明该方法的有效性以及相比已有方法的较小保守性。更多还原

【Abstract】 With the rapid developments of computer, network and communication technologies, networked control systems (NCSs) have been widely applied in many control fields. In NCSs, sensors, actuators, and controllers interconnect by communication networks, which always cause time delays. Network-induced delays degrade the control performance, even make NCSs unstable. Moreover, since network-induced delays are usually time-varying, it makes the analysis and design of NCSs more complex. The purpose of this dissertation is to find the maximum allowable delay bound (MADB) and design valid controllers to guarantee the stability and control performance of NCSs within the MADB. By using Lyapunov stability theory and free-weighting matrix approach, the issues, including stability analysis, stabilization control, guaranteed cost control, robust H∞control and robust H∞filter design of NCSs, are investigated. The main achievements in the dissertation are outlined as follows:(1) The stability conditions of both continuous-time and discrete-time NCSs, and the design methods of state feedback stabilizing controllers are proposed.For the continuous-time NCSs with time-varying delay, using Lyapunov-Krasovskii functional and the improved free-weighting matrix approach, the stability conditions of NCSs are presented with all terms in the derivative of Lyapunov-Krasovskii functional reserved. Moreover, the conditions are extended to the NCSs with time-varying structured uncertainties. Based on the stability criteria derived, the design method of state feedback stabilizing controller is proposed. The improved cone complementarity linearization (ICCL) algorithm based on linear matrix inequalities (LMIs) is employed to deal with nonlinear matrix inequalities (NLMIs), so that the MADB guaranteeing the stability of NCSs and the parameter of stabilizing controller are obtained. Similarly, the stability conditions for discrete-time NCSs and the design method of discrete stabilizing controller are proposed. The numerical examples demonstrate the effectiveness and less conservativeness over the existing methods.(2) The design methods of guaranteed cost controllers of both continuous-time and discrete-time NCSs are presented.According to the given control performance conditions of continuous-time NCSs, the design method of guaranteed cost controller of NCSs is investigated by using Lyapunov-Krasovskii functional and the improved free-weighting matrix approach. The parameter of controller to guarantee given performance is obtained by employing the ICCL algorithm. Meanwhile, the design method of guaranteed cost controller for discrete-time plants is proposed. The numerical examples show the less guaranteed cost performance comparing with the existing methods.(3) The design methods of robust H∞controllers of both continuous-time and discrete-time NCSs are proposed.For the continuous-time NCSs with time-varying delay, the criteria for H∞performance of NCSs are presented using Lyapunov-Krasovskii functional and the improved free-weighting matrix approach. Based on the criteria derived, the design method of H∞state feedback controller is obtained, and it is extended to robust H∞controller. The discrete H∞controller can be designed by the similar method. The results of the numerical examples demonstrate the better H∞performance over the existing methods.(4) The design methods of robust H∞filters of both continuous-time and discrete-time NCSs are proposed.Lyapunov-Krasovskii functional and the improved free-weighting matrix approach are employed to design robust H∞filter of continuous-time NCSs. The criteria for robust H∞performance analysis of the filtering-error systems are proposed by reserving all terms in the derivative of Lyapunov-Krasovskii functional and dealing with the different parts of uncertainties separately. Based on the derived criteria, the design method of robust H∞filter is obtained in term of LMIs. Similarly, the design method of robust H∞filter for discrete-time NCSs is proposed. Numerical examples are given to demonstrate the validity and the less conservativeness over the existing methods.更多还原