摘要
时延系统的研究具有重要的理论和应用价值,本文针对连续时间和离散时间时延系统,研究存在参数和时延不确定性时的鲁棒控制。设计并实现网络化数字布光系统,并且将本文的控制方法应用于网络化控制系统,同时还将研究高速网络通信系统的鲁棒控制。本文的主要内容和研究成果包括:
(1) 针对不确定时变时延连续时间系统,当系统含有输入时延时,通过求解线性矩阵不等式(LMI)构造无记忆静态反馈控制器使得闭环系统鲁棒渐近稳定。当时延系统的状态变量不可全部直接测量得到时,构造状态观测器估计系统的状态变量。观测器和控制器的增益矩阵不需事先假定形式,而通过求解一个LMI可以直接得到,进而实现闭环系统状态的鲁棒渐近稳定。本文的设计方法不仅依赖于状态时延的变化量,同时依赖于状态时延导数的变化范围。
(2) 针对不确定时变时延离散时间系统,构造改进的适用于此类离散时间系统的Lyapunov函数,并结合代数Riccati不等式(ARI)和H∞鲁棒控制理论,使得系统不含外界未知扰动时,通过状态的静态反馈控制达到闭环系统的二次稳定;系统含有外界未知扰动时,实现闭环系统理想的干扰抑制率。然后研究离散时间时延系统的鲁棒跟踪控制问题,通过求解一个LMI得到控制器的增益矩阵,进而使得闭环系统的状态变量渐近跟踪上任意预先设定的轨迹。
(3) 设计并实现网络化数字布光系统,然后研究基于现场总线的网络化控制系统的鲁棒控制问题,将系统时延的不确定性转换为系数矩阵的不确定性,把网络化控制系统的状态向量扩张为增广状态向量,再利用ARI(LMI)和H∞鲁棒控制理论相结合的方法,实现闭环系统的二次稳定和理想的干扰抑制率。针对具有一个瓶颈和多用户的高速通信网络系统,当网络带宽恒定时,基于线性矩阵不等式(LMI)和时延相关控制方法,设计控制器以实现指数稳定的跟踪控制效果,提高了网络的利用率和带宽分配的公平性。最后针对有效网络带宽是时变且未知的情况,设计控制器实现微小跟踪误差以达到系统具有高性能的效果。
Controlling time delay systems with uncertainty is of significant values in control theory and application. This dissertation derives robust controller for continuous and/or discrete time systems with time-varying delays. We apply industrial communication network to light disposition systems, and design robust controller for the networked control systems and ATM communication networks. The main results and contributions of this dissertation are as follows:
(1) For a class of linear systems with uncertain parameters and unknown time varying delay in control input, a robust memoryless controller, guaranteeing asymptotic stabilization, is derived in terms of a linear matrix inequality (LMI) depending on the size of time delay and on the size of delay derivative. When the states of the time delay systems are not all measurable, an observer is constructed to estimate the states. If a linear matrix inequality (LMI) is solvable, the gains of the controller and observer can be obtained from the solution of the LMI. The observer and controller are also dependent on the size of time delay and on the size of delay derivative.
(2) A new robust H∞ control method is presented for the discrete systems with parameter uncertainty and time-delayed uncertainty. When a matrix inequality is satisfied, based on the modified Lyapunov function, the system without unknown disturbance can be quadratically stabilized under static state feedback control. Furthermore, when another matrix inequality is satisfied, the system with unknown disturbance can be quadratically stabilized with a disturbance attenuation γ under static state feedback control by an innovative passive control method. If a linear matrix inequality (LMI) is solvable, the gains of the memoryless feedback controller can be obtained from the solution of the LMI, and the state of system is asymptotically tracking to the designed reference signal.
(3) When subsystems are connected by network, there exist time delays and asynchronism. We propose a new robust H∞ control method based on the Algorithm
Riccati Inequality (ARI) and/or Linear Matrix Inequality (LMI) approach for the robust control of the systems. The uncertainty of time delays is converted to the uncertainty of the parameter matrix, and the states are transformed to the augmented states to eliminate the effect of the asynchronism. When there is no disturbance, the closed-loop system can be quadratically stabilized by the static state feedback. When the system is affected by unknown disturbance, the closed-loop system can be quadratically stabilized within a disturbance attenuation γ. For the high-speed communication networks with one bottleneck node and multiple sources, the exponential tracking performance of each source rate to the relevant bandwidth allocation fairness, as well as the queue length to the reference, shows the effective utilization of the networks subject to low loss rates. When the available bandwidth is constant, based on LMI and delay time-derivative dependent control methods, a robust controller is designed to achieve exponential tracking stability. The controller needn’t tune the parameters, and computing complex is comparatively low. When the available bandwidth, i.e., available throughput capacity, of bottleneck is time varying and unknown, a robust controller is designed to achieve small tracking error guaranteeing high performance. Upon the results of four LMIs, which can be solved simultaneously, we can get the gain of the controller.
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