球形机器人的自适应分数阶PIλDμ滑模速度控制方法

doi:10.13229/j.cnki.jdxbgxb20191174

摘要/Abstract

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^λD^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^λD^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。

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

Abstract:

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^λD^μstructure 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^λD^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.

Key words: control theory, fractional sliding mode, spherical robot, speed control, adaptive control

中图分类号:

TP242.3

周挺,徐宇工,吴斌. 球形机器人的自适应分数阶PI^λD^μ滑模速度控制方法[J]. 吉林大学学报(工学版), 2021, 51(2): 728-737.

Ting ZHOU,Yu-gong XU,Bin WU. Adaptive fractional PI^λD^μ sliding mode control method for speed control of spherical robot[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(2): 728-737.

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控制器	参数取值
FO-PID ASMC	λ₁₁=2,λ₂=12,λ₁₂=0.5,η=2,ζ=2,k=6,w=5,α=0.1,β=0.1,ε=0.5
IO-PI ASMC	λ₁₁=0.7,λ₁₂=12,η=2,ζ=2,k=6,w=5,ε=0.5
FO-PI ASMC	λ₁₁=2,λ₁₂=12,η=2,ζ=2,k=6,w=5,α=0.1,ε=0.5
FO-PD ASMC	λ₁₁=2,λ₁₂=12,η=2,ζ=2,k=6,w=5,α=0.1,ε=0.5

控制器	超调量 /%	调节时间/s	恢复稳态时间/s
FO-PID ASMC	18.3	1.2	1.6
IO-PI ASMC	40.5	3.9	1.8
FO-PI ASMC	37.2	3.2	1.1