LMI的线性不稳定系统的研究.docVIP

摘 要 在实际的控制中几乎不可能准确地建立控制对象的数学模型，通过对象降阶近似，线性化近似，忽略难以建模的动态特性，以及系统工作环境变化、测量误差、系统参数老化和各种干扰等因素的近似处理，会使所得到的对象和实际的对象存在一定的差距。鲁棒控制理论就是基于这种实际背景产生和发展的。 本文主要研究线性系统的方法，包括(LMI)和Lyapunov稳定性理论线性不确定系统的状态反馈控制器设计Riccati方程或Riccati不等式的复杂性，以及有大量的参数和正定矩阵需要预先调整的缺点，最后结合实例应用Simulink仿真验证所得结论，取得较好的控制效果。 关键词：不确定性；线性矩阵不等式；鲁棒控制；状态反馈 Abstract It is almost impossible to obtain an accurate mathematics model for the practical control. The model under which the controller is designed is usually different to the real plant owing to model reduction, linearization approximations, dynamics which is difficult to model, the change of the operating environment, measurement errors, system parameter aging, immeasurable disturbances, and so on. There are some differences between the plant acquired and the real one. The emergence and the development of the robust control theory is just in such environment. The work of this thesis mainly studies the stabilization of the linear uncertain systems, and control method, including linear matrix inequality theory and Lyapunov stability theory, to research stabilization of linear uncertain systems and design the device of state feedback. Include: analysis and control of state uncertainty linearity system, system and control matrix with uncertainty item linearity system, uncertainty time-delay system, and design of the state-feedback controller with memory of uncertainty time-delay system. We express the robust unflappability, and achieve the controller by the LMIs. These methods mentioned above avoid the complexity of Riccati equations or inequalities, and conquer the defects of pre-adjusting a large number of parameters and positive matrix. At last, we acquire the conclusion by Simulink and test the result, getting the favorable control effect. Key words: uncertainty; linear matrix inequality (LMI); robust control; state feedback 目 录 第1章 概 述 1 1.1 研究背景 1 1.2 状态反馈鲁棒控制器相关概念 2 1.3 系统的不确定性 3 1.4 线性矩阵不等式方法 6 1.5 控制系统MATLAB软件及仿真 8 1.6 本文主要研究内容 11 第2章 基本定理及引理 12 2.1