基于等价标准型的脉冲不能控广义系统高阶滑模控制

Descriptor systems appear in many fields, such as power systems, chemical process and constrained robots. It is assumed that descriptor systems are impulse controllable in the existing sliding mode control methods of descriptor systems. The main reason is that the existence of the singular derivative-term matrix makes the design of the sliding modes very difficult and complicated. In addition, since the states of impulse uncontrollable descriptor systems contain the high-order derivatives of the control inputs, the smoothness of the sliding mode controllers is required to make the system states continuous, which will further increase the difficulty of the design of the sliding mode controllers. This project aims to use the canonical forms to study the design problems of the high-order sliding mode controllers for impulse uncontrollable descriptor systems. Firstly, by establishing the canonical form of impulse uncontrollable descriptor systems, the sliding modes will be given in an explicit form which will facilitate the design. Then a state feedback high-order sliding mode controller is designed by respectively combining the high-order sliding mode control technique with the unit vector control method and the reaching law method to ensure the continuity of the states of the resulting closed-loop systems. Furthermore, when the system states are not accessible, the static output feedback high-order sliding mode control problem and the observer-based high-order sliding mode control problem will be further studied. The results of this project are of great importance for the development of sliding mode control theory of descriptor systems and the enhancement of control performance of practical systems.

广义系统广泛存在于电力系统、化学过程以及受限机器人等领域。目前，广义系统的滑模控制方法多数针对脉冲能控的广义系统进行研究，主要原因是奇异导数项矩阵的出现使得滑动模态的设计问题变得非常困难和复杂。此外，由于脉冲不能控广义系统的状态含有控制输入的高阶导数项，滑模控制器需要充分光滑才能保证系统状态的连续性，这进一步增加了控制器设计的难度。本项目针对脉冲不能控的广义系统，研究基于等价标准型的高阶滑模控制问题。拟从构建系统的等价标准型出发，利用滑动模态的具体形式给出其设计方法，进而通过将高阶滑模控制技术与单位向量控制方法、趋近率方法分别结合设计新型的状态反馈高阶滑模控制器来保证闭环系统状态的连续性；在此基础上，针对系统状态不可测的情况，将进一步研究静态输出反馈高阶滑模控制问题，以及基于观测器的高阶滑模控制问题。本项目的开展对完善现有的广义系统滑模控制理论以及提高实际系统的控制性能有着重要的意义。

本项目提出了基于等价标准型的高阶滑模控制技术来解决脉冲不能控广义系统的滑模控制问题。针对脉冲不能控广义系统滑动模态难以设计的问题，构建了系统的等价标准型来求解滑动模态的具体形式，从而给出了一种基于等价标准型的设计方法。考虑到脉冲不能控广义系统对滑模控制器的光滑性需求，提出了高阶滑模控制方法来保证闭环系统状态的连续性。利用等价标准型和高阶滑模控制技术，分别给出了广义高阶滑模观测器、基于降阶观测器的高阶滑模控制器与基于滑模观测器的高阶滑模控制器的设计方法，并证明了由脉冲不能控广义系统、观测器与高阶滑模控制器所组成闭环系统满足分离性原理。此外，还将线性广义系统中的高阶滑模控制方法向T-S模糊广义系统做了对应的拓广，通过建立切换函数中参数与T-S模糊系统反馈控制增益之间的联系，提出了模糊切换函数的概念以及基于模糊切换函数的高阶滑模控制方法，降低了基于公共切换函数的滑模控制方法的保守性。基于等价标准型的高阶滑模控制方法和基于模糊切换函数的高阶滑模控制方法分别为广义系统滑模控制与T-S模糊系统滑模控制相关问题的研究开辟了新的途径，进一步完善了滑模控制理论。