Limit cycle prediction of systems with fractional controllers and backlash

被引：10
作者：
Barbosa, Ramiro S. [1 ]
Machado, J. A. Tenreiro [1 ]
机构：
[1] Polytech Porto, GECAD Knowledge Engn & Decis Support Res Ctr, ISEP IPP Inst Engn, Rua Dr Antonio Bernardino de Almeida 431, P-4200072 Oporto, Portugal
来源：
JOURNAL OF VIBRATION AND CONTROL | 2017年 / 23卷 / 04期
关键词：
Fractional-order control; nonlinear systems; describing function; limit-cycle prediction; backlash; DERIVATIVES; CHAOS;
D O I：
10.1177/1077546315581572
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
This article investigates the limit cycle (LC) prediction of systems with backlash by means of the describing function (DF) when using discrete fractional-order (FO) algorithms. The DF is an approximate method that gives good estimates of LCs. The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.
引用
收藏
页码：587 / 603
页数：17
相关论文
共 44 条
  • [11] AXTELL M, 1990, PROC NAECON IEEE NAT, P563, DOI 10.1109/NAECON.1990.112826
  • [12] Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena
    Barbosa, Ramiro S.
    Machado, J. A. Tenreiro
    Galhano, Alexandra M.
    [J]. JOURNAL OF VIBRATION AND CONTROL, 2007, 13 (9-10) : 1407 - 1418
  • [13] Analysis of the van der pol oscillator containing derivatives of fractional order
    Barbosa, Ramiro S.
    Machado, J. A. Tenreiro
    Vinagre, B. M.
    Calderon, A. J.
    [J]. JOURNAL OF VIBRATION AND CONTROL, 2007, 13 (9-10) : 1291 - 1301
  • [14] Time domain design of fractional differintegrators using least-squares
    Barbosa, Ramiro S.
    Tenreiro Machado, J. A.
    Silva, Manuel F.
    [J]. SIGNAL PROCESSING, 2006, 86 (10) : 2567 - 2581
  • [15] Tuning of PID controllers based on Bode's ideal transfer function
    Barbosa, RS
    Machado, JAT
    Ferreira, IM
    [J]. NONLINEAR DYNAMICS, 2004, 38 (1-4) : 305 - 321
  • [16] Describing function analysis of systems with impacts and backlash
    Barbosa, RS
    Machado, JAT
    [J]. NONLINEAR DYNAMICS, 2002, 29 (1-4) : 235 - 250
  • [17] Continued fraction expansion approaches to discretizing fractional order derivatives - an expository review
    Chen, YQ
    Vinagre, BM
    Podlubny, I
    [J]. NONLINEAR DYNAMICS, 2004, 38 (1-4) : 155 - 170
  • [18] Chen YQ, 2002, IEEE T CIRCUITS-I, V49, P363, DOI 10.1109/81.989172
  • [19] Describing function of two masses with backlash
    Duarte, Fernando B.
    Machado, J. Tenreiro
    [J]. NONLINEAR DYNAMICS, 2009, 56 (04) : 409 - 413
  • [20] Fractional describing function of systems with Coulomb friction
    Duarte, Fernando B.
    Machado, J. Tenreiro
    [J]. NONLINEAR DYNAMICS, 2009, 56 (04) : 381 - 387
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