基于数学建模的位置随动系统的最优控制研究

摘要

位置随动系统作为一种能够对未知输入变量进行精确控制的典型闭环控制系统，其根本任务就是实现执行机构对位置指令的准确跟踪，在机床运动位置和角度控制中起到重要作用。针对一个小功率直流电机型随动系统，进行数学建模研究，并用状态空间形式予以描述。基于该数学模型，设计出一个LQR最优控制器。仿真结果表明：所提出的控制方法具有超调量小、调节时间短、稳态精度高的性能优势。此外，该方法较为简单，易于工程实现。%As a typical close⁃loop control system, the basic task of the position servo system is to ensure the actuator can accu⁃rately track the position commands, and plays an important role in modern production process. Aiming at a servo system with small⁃power DC motor, the mathematical modeling was carried out, and subsequently the model was described by means of space⁃state ex⁃pression. Based on the model, a LQR optimal controller was designed. The simulation results show that, the proposed control scheme possesses some performance advantages, including smaller overshoot, shorter regulation time and higher stable accuracy. In addition, the scheme is simple and easy to be realized in engineering.