摘要
随着人们对现代控制系统可靠性和安全性要求的提高,容错控制技术的研究在实际工程中已被广泛关注,许多方法得到有效发展,并取得成功的应用。Delta算子作为连续系统和离散系统的统一模型描述形式,具有其自身的优点。因此将Delta算子和容错控制结合起来进行研究将是一个较新的研究方向。本文对区域极点约束的Delta算子系统容错控制问题进行研究,将连续和离散系统容错控制的相关结果统一纳入到Delta算子框架。取得主要成果如下:
(1)研究圆形区域极点配置的Delta算子不确定系统鲁棒容错控制问题。针对在状态矩阵和输入矩阵均存在不确定性时的Delta算子系统,导出在执行器失效情况下Delta算子系统鲁棒D稳定的充分条件;利用线性矩阵不等式(LMI)方法,给出了Delta算子系统的鲁棒容错控制器设计方法。基于LMI的可行解,得到状态反馈控制律的参数化表示。
(2)研究圆形区域极点约束下Delta算子描述的结构不确定性系统鲁棒容错镇定问题。基于Riccati方程导出Delta算子系统存在结构不确定性和执行器故障的情况下,将闭环系统极点配置到指定圆盘,确保系统鲁棒容错镇定的充分条件;运用LMI方法,给出系统在区域极点约束下鲁棒容错控制器存在的充分条件,并通过求解LMI得到鲁棒容错控制器的设计。数值算例说明了该方法的有效性。
(3)研究Delta算子线性系统在区域极点配置下的H_∞容错控制问题。基于LMI和Delta算子界实引理,给出了在执行器失效情况下Delta算子系统D稳定H_∞容错控制的充要条件,从而把区域极点约束下H_∞容错控制器的设计问题化为求解Riccati不等式。
(4)研究Delta算子不确定线性系统在区域极点配置下的鲁棒H_∞容错控制问题。利用LMI方法,导出了Delta算子系统鲁棒容错控制器存在的充分条件,确保Delta算子系统存在不确定性和执行器故障的情况下依然满足区域极点约束和H_∞范数界约束;并可通过求解LMI得到鲁棒容错控制器的设计。仿真示例表明了该算法的可行性。
(5)研究Delta算子不确定线性系统在圆形区域极点约束下的H_∞可靠控制问题。在考虑更一般、更实际的执行器连续故障模型的基础上,运用LMI方法,给出在区域极点约束下Delta算子不确定系统H_∞可靠控制器的存在条件。通过求解LMI完成状态反馈控制器的设计。
With the increased requirement on the high reliability and safety of modern control systems, research to fault tolerant control has attracted a lot of attention in engineering practice, where a number of effective methods have been developed and successfully applied. The delta operator, as a unified method of the continuous-time systems and discrete-time systems, which is used in the fault tolerant control is a new theme. So, the problems of fault-tolerant control for the delta operator formulated systems with pole assignment are studied in this thesis. The proposed results can unify previous related conclusions of continuous time and discrete time systems with fault-tolerant control into the delta framework. The main conclusions of this thesis are as following:
(1) The robust fault-tolerant control problem of delta operator uncertain systems with circular regional pole assignment is considered, which the addressed uncertainties are in both state matrix and input matrix. A sufficient condition of robust D-stability for delta operator systems with actuator failures is presented. In terms of a linear matrix inequality (LMI) approach, the design method of the robust fault-tolerant controller is derived. When this LMI is feasible, the parameterized representation of the desired state feedback controller is also provided.
(2) The robust fault-tolerant stabilization problem of circular regional pole constraints for delta operator formulated systems with structured uncertainty is studied. A sufficient condition of robust fault-tolerant stabilization is derived using Riccati equations for the delta operator systems with structured uncertainty and actuator failure when allocating the closed-loop poles into a specified circular disk. In terms of a LMI approach, a sufficient condition for the existence of a robust fault-tolerant controller with regional pole assignment is presented. Then the controller can be designed through solving LMI. A numerical example is given to show the effectiveness of the proposed method.
(3)The H_∞fault-tolerant control problem of delta operator linear systems with regional pole assignment is considered. A sufficient and necessary condition of D-stable H_∞fault-tolerant for delta operator systems with actuator failures is presented by using the LMI theory and the delta operator bounded real lemma. The design of H_∞fault-tolerant controller with circular pole constraints is transformed into solving a Riccati inequality.
(4) The robust H_∞fault-tolerant control problem of circular regional poleassignment for delta operator uncertain linear systems is studied. In terms of a LMI approach, a sufficient condition for the existence of a robust fault-tolerant controller for the delta operator systems is presented, which can assure that the delta operator systems satisfy an regional pole constraints and H_∞-norm bound constraint in the event of uncertainty and actuator failures. Then the controller can be designed through solving LMI. A numerical simulation shows the feasibility of the developed algorithms.
(5) The H_∞reliable control problem is studied for the delta operator uncertain linear system with regional pole constraints. Based on a more practical and general model of actuator failure, an existed condition of the delta operator uncertain system with regional pole constraints is given via the LMI approach. A state feedback controller is designed by solving LMIs.
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