【作者】 赵于前；

【导师】 阳春华； 桂卫华；

【作者基本信息】 中南大学 ， 控制理论与控制工程， 2002， 硕士

【摘要】 结构奇异值μ方法是求解具有结构不确定性系统的很好方法，该方法可以改善鲁棒控制系统设计的保守性，并把鲁棒稳定性和鲁棒性能综合起来考虑；分散控制是解决复杂系统和大系统控制的一种有效方法，它可以减少信息的处理量，快速实现反馈控制，降低数据通讯的复杂性。 分散控制的关键问题是分散控制器的设计，一般的方法是用分散H_∞方法设计，但对具有结构不确定性的关联大系统，这一设计方法会带来保守性。为了克服保守性，本文将结构奇异值μ方法应用于分散控制器的设计，而在这一方面的研究目前还罕见于文献。 结构奇异值μ方法的关键问题是μ的求解，传统的方法是用D-K迭代法，但此方法是非凸性的，即不能求得全局最优解。为了克服这一方法的局限性，本文第三章将基于结构奇异值μ的分散状态反馈控制问题变换为分散标定H_∞控制问题，再将该问题转化为线性矩阵不等式(LMI)约束，然后用迭代LMI方法求解。但分散标定H_∞控制问题不能用于解决分散输出反馈控制，因为它存在非凸性约束，为了解决这个问题，本文第四章以二次稳定性理论为基础，提出分散强鲁棒H_∞性能准则，并以LMI的形式给出分散输出反馈控制器存在的充分条件，最后用交叉迭代算法求解。 应用结构奇异值方法，本文对状态反馈和输出反馈分别进行了讨论，并分别给出了仿真示例，其中一个就是在控制问题中经常遇到的由两个倒立摆组成的Benchmark问题。仿真结果表明，由文中方法所设计的控制器组成的反馈控制系统具有很好的鲁棒稳定性和鲁棒性能，从而表明该方法的可行性。更多还原

【Abstract】 The structured singular value V is an important analysis and design method to resolve the structured uncertainty system. Applying the method to design controllers can reduce the conservation of the robust control system, and also give consideration to both the robust stability and the robust performance of the control system. Decentralized control is an efficient design method for complex control system and industrial large-scale system. Applying the method can reduce the amount of disposal information and the complexity of data communication. And more, it can realize feedback control quickly.The central problem for decentralized control is to design the decentralized controllers. Generally, we solve the problem by decentralized H~ control method. But the solution is conserve for the structured uncertainty interconnected large-scale system. To reduce the conservation of the system, we apply the structured singular value u to design the decentralized controllers of the system, and the research in the field is rare at present.The structured singular V problems are quite hard to solve. The traditional algorithm is D-K iteration. But the n problems are not convex in general, and hence it is difficult to find a global optimal solution. For state feedback, we resolve this problem in chapter 3 by transferring the decentralized n problems into the decentralized scaled H- control problem, then solve the problem by ILMI optimization problems. But the method cannot be applied for decentralized output feedback because of its no convex restriction. We resolve this problem in chapter 4 by submitting decentralized strongly robust H- performance criterion based on the quadratic stability theorem, then give the sufficient conditions for the existence of decentralized output feedback controller in terms of LMIs, at last, we compute the LMIs by cross iteration algorithm.We consider both state feedback and output feedback based on the structured singular value theory. To validate the correctness of the algorithm, we gave two numerical examples in the paper. Via the curves of simulation, we can know the feedback control system, which is made of our designing controllers, is perfect in the robust stability and the robust performance. Thus, it shows that our algorithm is feasible.更多还原