Systematization of Analysis and Design of Robust Control Systems via IMC Parametrization

本研究计画透过IMC参数化，系统分析及设计鲁棒控制系统。(1)提出了多变量系统的状态空间-IMC参数化方法，并将其分为3部分。(2)在状态空间框架下推导了IMC参数化与Yula参数化的关系。结果表明，反馈矩阵与系统对参考输入的响应有关，观测器矩阵与系统对扰动的响应有关。(3)建立了伺服系统的IMC参数化方法。(4)针对基于单盘规格的鲁棒控制灵敏度低于常规鲁棒控制的2盘混合灵敏度问题，给出了该问题的求解方法。(5)阐明了当被控对象在虚轴附近含有稳定极点时，H∞控制对输入扰动的响应迟钝。在IMCP的基础上提出了突破方法。(6)提出了自适应IMC。(7)采用IMC参数化方法解决了时滞系统的2盘混合灵敏度问题。此外，通过引入Pade近似，大大扩大了鲁棒稳定范围。(8)提出了多变量系统的逆系统解耦方法用于IMC参数化设计。(9)鲁棒控制的系统设计，包括对无延迟和有延迟系统从PID控制到H∞控制。

This research project presents the systematic analysis and design of robust control systems via IMC parametrization as follows.(1)The state space -IMC parametrization for multivariable systems is proposed by dividing it into 3 parts.(2)The relation between IMC parametrization and Yula parametrization is derived in the framework of state space. It is shown that the feedback matrix is related to the responses to the reference inputs and the observer matrix is concerned with the responses to the disturbances.(3)The IMC parametrization for servo systems is established.(4)The solution to the 2 disk mixed sensitivity problem, which yields lower sensitivity than the conventional robust control based on the 1 disk specification, is presented.(5)It is clarified that the H infinity control suffers from sluggish responses to input disturbances if the plant contains stable poles near the imaginary axis. The breakthrough method is presented on the basis of IMCP.(6)The adaptive IMC is presented.(7) The 2 disk mixed sensitivity problem of lame delay systems is solved by using IMC parametrization. Furthermore, The robust stable range is considerably enlarged by introducing Pade approximation.(8)The inverse system and decoupling for multivariable systems are proposed for design of IMC parametrization.(9)The systamtic design of robust control which includes from PID control to H infinity control for delay-free and delayed systems.