执行器带饱和约束与时滞的控制系统的全局镇定研究

Control systems with actuator saturation and time-delay can be used to describe many control objects in a large number of projects, and thus are of great importance in both theory and practice. For the multiple integrators system with only actuator saturation, by using a model transformation （Teel’s transformation）and a recursive design method with cancellation among state components, a class of nonlinear controllers were proposed to solve the corresponding global stabilization problem by Teel. However, when the actuator is also subjected to time-delay, the natural cancellation among state components based on the Teel’s transformation does not work, which results in some shortcomings, such as the analysis procedure of the controller design is very complex and difficult, the conditions which ensure the stability of the closed-loop system are much conservative, the dynamic response of the closed-loop system is poor, and so on. This project will study the global stabilization problem of the control systems with actuator saturation and time-delay, based on the principle investigator's preliminary studies. Different from the Teel’s transformation, this project will construct a novel model transformation containing time delays, by which, the systems will be transformed into new systems which contain time delays both in its input and states. Effective control methods will then be established to design controllers for the new systems by using their special structures and the natural cancellation among state components in the recursive design. Finally, the proposed methods will be applied to the design of quadrotor control systems, and it is expected to provide certain technical support and theoretical guarantee for the relevant engineering practice.

执行器带饱和约束与时滞的控制系统可以描述大量工程中的控制对象，具有重要的研究价值。当执行器仅受饱和非线性约束时，著名学者Teel基于一类模型变换（Teel变换）并利用具有状态相消特征的递归设计思想，提出了一种非线性控制器来全局镇定多积分器系统。但当执行器同时含有时滞时，基于Teel变换的状态相消特征不再适用，导致控制器设计分析过程非常复杂，稳定性条件保守性偏大，闭环系统的动态响应较差等。本项目针对执行器带饱和约束与时滞的控制系统，在申请人前期研究工作的基础上，研究其全局镇定问题。与Teel变换不同，本项目通过构造含有时滞的新型模型变换，将原系统转化为一类输入和状态同时含有时滞的新系统，并利用转化后的控制系统的特殊结构及递归设计过程中的状态相消特征，建立有效的控制器设计方法。最后，将所提出的全局镇定控制方法用于四旋翼无人机控制系统的设计，期望为相关的工程实践提供一定的技术支持和理论保证。

本项目针对执行器带饱和约束与时滞的控制系统开展全局镇定研究，取得的主要成果如下：1) 针对执行器带饱和约束的多积分器与多振荡器的全局镇定问题，建立了具有更少饱和函数以及基于动态饱和函数的新型非线性控制律，从而能够更充分地利用控制能量。同时在控制律设计中引入了一系列自由参数，能够极大的提升闭环系统的动态性能；2) 针对执行器带饱和约束与时滞的线性与非线性系统的全局镇定问题，分别从充分利用时滞特征信息和从消除时滞特征对控制律设计所产生的不利影响等两个方向出发，系统建立了一系列简单高效的非线性控制策略，同时给出了具有低保守性的稳定性条件；3) 针对执行器带饱和约束的四旋翼无人机系统的控制问题，分别提出了基于线性化模型以及基于非线性模型的全局镇定控制策略，同时给出了显式的稳定性条件，仿真结果验证了所提方法的有效性与优越性。此外，本项目还针对具有多个状态和输入时滞的控制系统的极点配置问题，设计了相应的控制器来实现极点配置；针对中立型时滞系统的强稳定性分析问题，利用KYP引理，建立了基于线性矩阵不等式的强稳定性判据。经过三年时间的研究，发表11篇学术论文，其中发表SCI期刊论文10篇，发表EI论文1篇。