预设性能控制算法对机械臂运动控制的改进

PD控制是在工业生产过程控制中，应用比较广泛，结构最简单的控制策略之一。传统的PD控制侧重于控制系统的稳态性能，而对系统的动态性能（包括超调量和收敛速度等）控制不够，如果想要提高响应速度就会使超调量变大，加剧响应振荡；如果想要超调量小，可能又会使响应速度变慢。响应速度与超调量似乎是一对比较矛盾的性能参数，单纯使用传统的PD控制，很难做到提高响应速度的同时降低超调量。所谓预设性能控制，指的是控制误差的收敛速度及超调量满足预先设定的条件，同时把控制误差收敛到一个预先指定的比较小的区域内。本文将PD控制与预设性能控制相结合，利用简单的PD控制结构和以对数形式误差变换为基础的预设性能函数来设计机械臂运动控制器, 该控制器在设计的过程中可以预先设定稳态误差，而不像传统的PD控制器要通过多次的参数整定及调试后才能逐步减少控制误差。因此本文提出的控制算法设计过程比较简洁方便，具有比较精确的控制精度和比较快的响应速度，同时还能把超调量控制在合理的范围内。通过空间三关节机械臂的建模仿真分析，改进后的预设性能PD控制与传统PD控制相比较，响应速度提高了40%左右，超调量减少了10%左右。通过4自由度Dobot机械臂的样机实验分析，改进后的预设性能PD控制与传统PD控制相比较，响应速度提高了20%左右，超调量减少了5%左右，因此该算法对控制系统动态响应性能的改善是比较明显的。

Improved Motion Control of Manipulator by Prescribed Performance Control Algorithm

PD control was widely used in the control of industrial production process, and it was also one of the control strategies with the simplest structure. It focused on the steady-state performance of the control system, but there was not enough attention paid on the dynamic performance (including the overshoot and the convergence speed, etc.) of the system. Therefore, if the response speed was improved in the traditional PD control, the overshoot would increase and the oscillation response would be intensified. If a small overshoot was wanted, the response speed might be slow down. It seemed that the response speed and overshoot to be parameters of contradictory performance. It was difficult to improve response speed and reduce overshoot by using traditional PD control alone. The prescribed performance control meant that the tracking error should converge to a predefined small residual set, with convergence rate no less than a prespecified value. This paper combined PD control with the prescribed performance control to design the manipulator motion controller using simple PD control structure and the prescribed performance function based on error transform of logarithmic form. The steady-state error can be preset in the design process of the controller, while the control error of traditional ID controller can only be gradually reduced after multiple parameters setting and debugging. Therefore, in this paper, the design process of the control algorithm proposed was simple and convenient, with more accurate control precision and faster response speed. At the same time, the control algorithm can control the overshoot within a reasonable range. By the analysis of modeling and simulation of spatial three joints manipulator, the results showed that the prescribed performance PD control had the advantage of 40% faster response and 10% less overshoot comparing with the traditional PD control. By the prototype experimental analysis of the 4-Dof Dobot manipulator, the results showed that the prescribed performance PD control had the advantage of 20% faster response and 5% less overshoot comparing with the traditional PD control, which made it obvious for the improvement of the dynamic response performance of the control system.