Ma Carlos, Chen Michael Z Q, Lam James, Cheung Kie Chung
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong.
ISA Trans. 2017 Sep;70:228-237. doi: 10.1016/j.isatra.2017.05.014. Epub 2017 Jun 12.
In the common practice of designing an attitude tracker for an aerospacecraft, one transforms the Newton-Euler rotation equations to obtain the dynamic equations of some chosen inertial frame based attitude metrics, such as Euler angles and unit quaternions. A Lyapunov approach is then used to design a controller which ensures asymptotic convergence of the attitude to the desired orientation. Although this design methodology is pretty standard, it usually involves singularity-prone coordinate transformations which complicates the analysis process and controller design. A new, singularity free error feedback method is proposed in the paper to provide simple and intuitive stability analysis and controller synthesis. This new body frame based method utilizes the concept of Euleraxis and angles to generate the smallest error angles from a body frame perspective, without coordinate transformations. Global tracking convergence is illustrated with the use of a feedback linearizing PD tracker, a sliding mode controller, and a model reference adaptive controller. Experimental results are also obtained on a quadrotor platform with unknown system parameters and disturbances, using a boundary layer approximated sliding mode controller, a PIDD controller, and a unit sliding mode controller. Significant tracking quality is attained.
在为航天器设计姿态跟踪器的常见做法中，人们会变换牛顿 - 欧拉旋转方程，以获得基于某些选定惯性系姿态度量（如欧拉角和单位四元数）的动力学方程。然后使用李雅普诺夫方法设计一个控制器，以确保姿态渐近收敛到期望的方向。尽管这种设计方法相当标准，但它通常涉及易于出现奇异性的坐标变换，这使得分析过程和控制器设计变得复杂。本文提出了一种新的无奇异误差反馈方法，以提供简单直观的稳定性分析和控制器综合。这种基于机体坐标系的新方法利用欧拉轴和角的概念，从机体坐标系的角度生成最小误差角，而无需坐标变换。使用反馈线性化PD跟踪器、滑模控制器和模型参考自适应控制器说明了全局跟踪收敛。在具有未知系统参数和干扰的四旋翼平台上，使用边界层近似滑模控制器、PIDD控制器和单位滑模控制器也获得了实验结果。实现了显著的跟踪质量。
