Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (2): 728-737.doi: 10.13229/j.cnki.jdxbgxb20191174

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Adaptive fractional PIλDμ sliding mode control method for speed control of spherical robot

Ting ZHOU(),Yu-gong XU,Bin WU()   

  1. School of Mechanical，Electronic and Control Engineering，Beijing Jiaotong University，Beijing 100044，China
  • Received:2019-12-23 Online:2021-03-01 Published:2021-02-09
  • Contact: Bin WU E-mail:14116373@bjtu.edu.cn;bwu@bjtu.edu.cn

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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 PIλDμstructure 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 PIλDμ 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

CLC Number: 

  • TP242.3

Fig.1

Diagram of spherical robot dynamical model in linear motion"

Table 1

Parameters of four controllers"

控制器参数取值
FO-PID ASMCλ11=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 ASMCλ11=0.7,λ12=12,η=2,ζ=2,k=6,w=5,ε=0.5
FO-PI ASMCλ11=2,λ12=12,η=2,ζ=2,k=6,w=5,α=0.1,ε=0.5
FO-PD ASMCλ11=2,λ12=12,η=2,ζ=2,k=6,w=5,α=0.1,ε=0.5

Fig.2

Velocity of shell response curves comparison among different controllers"

Table 2

Performance of three controllers without uncertain parameters"

控制器超调量 /%调节 时间/s稳态 误差/%恢复稳态 时间/s
FO-PID ASMC18.31.201.6
IO-PI ASMC40.53.901.8
FO-PI ASMC37.23.201.1

Fig.3

Curves of each second layer sliding mode surfaces S"

Fig.4

Curves of estimation of rolling friction"

Fig.5

Velocity of shell response curves comparison among different controllers with uncertain parameters"

Fig.6

Velocity of shell response curves when parameter λ11 changes"

Fig.7

Velocity of shell response curves when parameter λ12 changes"

Fig.8

Velocity of shell response curves when parameter α changes"

Fig.9

Velocity of shell response curves when parameter β changes"

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