球形机器人的自适应分数阶PI^(λ)D^(μ)滑模速度控制方法  

Adaptive fractional PI^(λ)D^(μ) sliding mode control method for speed control of spherical robot

作　　者：周挺 徐宇工[1] 吴斌[1] ZHOU Ting;XU Yu-gong;WU Bin(School of Mechanical,Electronic and Control Engineering,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]北京交通大学机械与电子控制工程学院,北京100044

出　　处：《吉林大学学报（工学版）》2021年第2期728-737,共10页Journal of Jilin University:Engineering and Technology Edition

基　　金：中央高校基本科研业务费专项项目(2019JBM408)。

摘　　要：为解决传统分层滑模控制方法应用于球形机器人速度控制中会出现调节时间长、超调量大的问题,通过在滑模面内引入微分环节并结合分数阶微积分,提出一种具有分数阶PI^(λ)D^(μ)结构的滑模面,并给了该滑模面渐近稳定的参数选取条件。基于该分数阶PI^(λ)D^(μ)滑模面设计了球形机器人直线运动速度控制器,并通过自适应算法实现了对未知滚动摩擦阻力的实时估计。仿真结果表明:相比传统分层滑模控制方法,本文自适应分数阶滑模控制方法能有效减少控制过程中的超调,并且具有更短的调节时间,能对未知滚动摩擦阻力进行准确的估计,在存在系统参数摄动的情况下具有更好的鲁棒性。The traditional hierarchical sliding mode control method applied directly to the spherical robot speed control will cause a long adjustment time and a large overshoot,which is hard to meet the requirements in practical application. In this paper,a new sliding surface with fractional order PI^(λ)D^(μ)structure is proposed by introducing a derivative element and fractional order calculus. The asymptotic stability condition of the sliding surface is given. Based on the new fractional PI^(λ)D^(μ)sliding surface,a velocity controller for the linear motion of the spherical robot is designed. Furthermore,an adaptive law is used to estimate the unknown rolling friction. The simulation results show that the new adaptive fractional sliding mode controller designed in this paper presents a better control performance and stronger robustness compared to the conventional one. Besides,the new controller can accurately estimate the unknown rolling friction.

关 键 词：控制理论 分数阶滑模 球形机器人 速度控制 自适应控制 

分 类 号：TP242.3[自动化与计算机技术—检测技术与自动化装置]