메뉴 건너뛰기




Volumn 52, Issue 3, 2013, Pages 429-437

Design, implementation and application of distributed order PI control

Author keywords

Auto tuning; Distributed order; Fractional calculus; Genetic algorithm; Incremental distributed order controller

Indexed keywords

CALCULATIONS; DISCRETE EVENT SIMULATION; GENETIC ALGORITHMS; MACHINE DESIGN; ROBUST CONTROL; SIGNAL PROCESSING; TUNING; TWO TERM CONTROL SYSTEMS;

EID: 84876849621     PISSN: 00190578     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.isatra.2012.12.004     Document Type: Article
Times cited : (44)

References (81)
  • 2
    • 51249169579 scopus 로고
    • Mean fractional-order-derivatives differential equations and filters
    • M. Caputo Mean fractional-order-derivatives differential equations and filters Annali dell'Universita di Ferrara 41 1995 73 84
    • (1995) Annali dell'Universita di Ferrara , vol.41 , pp. 73-84
    • Caputo, M.1
  • 3
    • 0001342751 scopus 로고    scopus 로고
    • On the existence of the order domain and the solution of distributed order equations (Parts I, II)
    • 965-87
    • R.L. Bagley, and P.J. Torvik On the existence of the order domain and the solution of distributed order equations (Parts I, II) International Journal of Applied Mechanics 2 2000 865 882 965-87
    • (2000) International Journal of Applied Mechanics , vol.2 , pp. 865-882
    • Bagley, R.L.1    Torvik, P.J.2
  • 6
    • 0036650957 scopus 로고    scopus 로고
    • Variable order and distributed order fractional operators
    • DOI 10.1023/A:1016586905654, Fractional Order Calculus and Its Applications
    • C.F. Lorenzo, and T.T. Hartley Variable order and distributed order fractional operators Nonlinear Dynamics 29 1-4 2002 57 98 (Pubitemid 34945393)
    • (2002) Nonlinear Dynamics , vol.29 , Issue.1-4 , pp. 57-98
    • Lorenzo, C.F.1    Hartley, T.T.2
  • 8
    • 0036964107 scopus 로고    scopus 로고
    • A generalized model for the uniaxial isothermal deformation of a viscoelastic body
    • T.M. Atanackovic A generalized model for the uniaxial isothermal deformation of a viscoelastic body Acta Mechanica 159 2002 77 86
    • (2002) Acta Mechanica , vol.159 , pp. 77-86
    • Atanackovic, T.M.1
  • 9
    • 0142183629 scopus 로고    scopus 로고
    • On a distributed derivative model of a viscoelastic body
    • DOI 10.1016/j.crme.2003.08.003
    • T.M. Atanackovic On a distributed derivative model of a viscoelastic body Comptes Rendus Mecanique 331 2003 687 692 (Pubitemid 37314589)
    • (2003) Comptes Rendus - Mecanique , vol.331 , Issue.10 , pp. 687-692
    • Atanackovic, T.M.1
  • 11
    • 15544379185 scopus 로고    scopus 로고
    • A generalised fractional derivative approach to viscoelastic material properties measurement
    • DOI 10.1016/j.amc.2004.06.099, PII S0096300304003315, 12th International Workshop on Dynamics and Control
    • J.J. de Espindola, J.M. da Silva Neto, and E.M.O. Lopes A generalised fractional derivative approach to viscoelastic material properties measurement Applied Mathematics and Computation 164 2005 493 506 (Pubitemid 40402967)
    • (2005) Applied Mathematics and Computation , vol.164 , Issue.2 , pp. 493-506
    • De Espiindola, J.J.1    Da Silva Neto, J.M.2    Lopes, E.M.O.3
  • 15
  • 16
    • 78650021700 scopus 로고    scopus 로고
    • Nonlinear fractional derivative models of viscoelastic impact dynamics based on entropy elasticity and generalized Maxwell law
    • M. Fukunaga, and N. Shimizu Nonlinear fractional derivative models of viscoelastic impact dynamics based on entropy elasticity and generalized Maxwell law Computational and Nonlinear Dynamics 6 2 2011 021005
    • (2011) Computational and Nonlinear Dynamics , vol.6 , Issue.2 , pp. 021005
    • Fukunaga, M.1    Shimizu, N.2
  • 17
    • 0003896880 scopus 로고    scopus 로고
    • Fractional system identification an approach using continuous order-distributions
    • T.T. Hartley, and C.F. Lorenzo Fractional system identification an approach using continuous order-distributions NASA Technical Memorandum 1999 209640
    • (1999) NASA Technical Memorandum , pp. 209640
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 18
    • 0141892685 scopus 로고    scopus 로고
    • Fractional-order system identification based on continuous order-distributions
    • T.T. Hartley, and C.F. Lorenzo Fractional-order system identification based on continuous order-distributions Signal Processing 83 11 2003 2287 2300
    • (2003) Signal Processing , vol.83 , Issue.11 , pp. 2287-2300
    • Hartley, T.T.1    Lorenzo, C.F.2
  • 22
    • 79551493680 scopus 로고    scopus 로고
    • On distributed order integrator/differentiator
    • Y. Li, H. Sheng, and Y.Q. Chen On distributed order integrator/ differentiator Signal Processing 91 5 2011 1079 1084
    • (2011) Signal Processing , vol.91 , Issue.5 , pp. 1079-1084
    • Li, Y.1    Sheng, H.2    Chen, Y.Q.3
  • 23
    • 77957368251 scopus 로고    scopus 로고
    • On distributed order low pass filter, Mechatronics and embedded systems and applications (MESA)
    • Li Y, Sheng H, Chen YQ. On distributed order low pass filter, Mechatronics and embedded systems and applications (MESA). In: Proceedings of the 2010 IEEE/ASME international conference, vol. 15-17; 2010. p. 588-92.
    • (2010) Proceedings of the 2010 IEEE/ASME International Conference , vol.15-17 , pp. 588-592
    • Li, Y.1    Sheng, H.2    Chen, Y.Q.3
  • 25
    • 67149103784 scopus 로고    scopus 로고
    • Time distributed-order diffusion-wave equation. I. Volterra-type equation
    • Atanackovic TM, Pilipović S, Zorica D. Time distributed-order diffusion-wave equation. I. Volterra-type equation. In: Proceedings of the Royal Society A, vol. 465; 2009. p. 1869-91.
    • (2009) Proceedings of the Royal Society A , vol.465 , pp. 1869-1891
    • Atanackovic, T.M.1    Pilipović, S.2    Zorica, D.3
  • 26
    • 67149125441 scopus 로고    scopus 로고
    • Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations
    • Atanackovic TM, Pilipović S, Zorica D. Time distributed-order diffusion-wave equation. II. Applications of Laplace and Fourier transformations. In: Proceedings of the Royal Society A, vol. 465; 2009. p. 1893-917.
    • (2009) Proceedings of the Royal Society A , vol.465 , pp. 1893-1917
    • Atanackovic, T.M.1    Pilipović, S.2    Zorica, D.3
  • 27
    • 68649098514 scopus 로고    scopus 로고
    • Variable-order fractional differential operators in anomalous diffusion modeling
    • H. Sun, W. Chen, and Y.Q. Chen Variable-order fractional differential operators in anomalous diffusion modeling Physica A Statistical Mechanics and its Applications 388 21 2009 4586 4592
    • (2009) Physica A Statistical Mechanics and Its Applications , vol.388 , Issue.21 , pp. 4586-4592
    • Sun, H.1    Chen, W.2    Chen, Y.Q.3
  • 28
    • 73749087815 scopus 로고    scopus 로고
    • On mean square displacement behaviors of anomalous diffusions with variable and random orders
    • H. Sun, W. Chen, H. Sheng, and Y.Q. Chen On mean square displacement behaviors of anomalous diffusions with variable and random orders Physics Letters A 374 2010 906 910
    • (2010) Physics Letters A , vol.374 , pp. 906-910
    • Sun, H.1    Chen, W.2    Sheng, H.3    Chen, Y.Q.4
  • 35
    • 0000227056 scopus 로고    scopus 로고
    • Distributed order differential equations modelling dielectric induction and diffusion
    • M. Caputo Distributed order differential equations modelling dielectric induction and diffusion Fractional Calculus & Applied Analysis 4 4 2001 421 442
    • (2001) Fractional Calculus & Applied Analysis , vol.4 , Issue.4 , pp. 421-442
    • Caputo, M.1
  • 37
    • 34547102267 scopus 로고    scopus 로고
    • The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
    • DOI 10.1016/j.cam.2006.10.014, PII S0377042706006017
    • F. Mainardi, and G. Pagnini The role of the Fox-Wright functions in fractional sub-diffusion of distributed order Journal of Computational and Applied Mathematics 207 2 2007 245 257 (Pubitemid 47102000)
    • (2007) Journal of Computational and Applied Mathematics , vol.207 , Issue.2 , pp. 245-257
    • Mainardi, F.1    Pagnini, G.2
  • 38
    • 84555190064 scopus 로고    scopus 로고
    • Stability analysis of distributed order fractional differential equations
    • H.S. Najafi, A.R. Sheikhani, and A. Ansari Stability analysis of distributed order fractional differential equations Abstract and Applied Analysis 2011 175323 2011 12
    • (2011) Abstract and Applied Analysis , vol.2011 , pp. 12
    • Najafi, H.S.1    Sheikhani, A.R.2    Ansari, A.3
  • 40
    • 53449102089 scopus 로고    scopus 로고
    • Lévy flights in nonhomogeneous media distributed-order fractional equation approach
    • T. Srokowski Lévy flights in nonhomogeneous media distributed-order fractional equation approach Physical Review E 78 3 2008 031135
    • (2008) Physical Review e , vol.78 , Issue.3 , pp. 031135
    • Srokowski, T.1
  • 41
    • 77952873423 scopus 로고    scopus 로고
    • Existence and calculation of the solution to the time distributed order diffusion equation
    • T.M. Atanackovic, S. Pilipović, and D. Zorica Existence and calculation of the solution to the time distributed order diffusion equation Physica Scripta T 136 2009 014012
    • (2009) Physica Scripta T , vol.136 , pp. 014012
    • Atanackovic, T.M.1    Pilipović, S.2    Zorica, D.3
  • 42
    • 34748907169 scopus 로고    scopus 로고
    • The two forms of fractional relaxation of distributed order
    • DOI 10.1177/1077546307077468
    • F. Mainardi, A. Mura, R. Gorenflo, and M. Stojanovic The two forms of fractional relaxation of distributed order Journal of Vibration and Control 9 2007 1249 1268 (Pubitemid 47482811)
    • (2007) JVC/Journal of Vibration and Control , vol.13 , Issue.9-10 , pp. 1249-1268
    • Mainardi, F.1    Mura, A.2    Gorenflo, R.3    Stojanovic, M.4
  • 43
    • 37449011239 scopus 로고    scopus 로고
    • Distributed order calculus and equations of ultraslow diffusion
    • A.N. Kochubei Distributed order calculus and equations of ultraslow diffusion Journal of Mathematical Analysis and Applications 340 1 2008 252 281
    • (2008) Journal of Mathematical Analysis and Applications , vol.340 , Issue.1 , pp. 252-281
    • Kochubei, A.N.1
  • 44
    • 77957363180 scopus 로고    scopus 로고
    • Random walk models associated with distributed fractional order differential equations
    • S. Umarov, and S. Steinberg Random walk models associated with distributed fractional order differential equations Lecture Notes: Monograph Series 51 2006 117 127
    • (2006) Lecture Notes: Monograph Series , vol.51 , pp. 117-127
    • Umarov, S.1    Steinberg, S.2
  • 48
    • 33745759950 scopus 로고    scopus 로고
    • Intermediate processes and critical phenomena theory, method and progress of fractional operators and their applications to modern mechanics
    • M. Xu, and W. Tan Intermediate processes and critical phenomena theory, method and progress of fractional operators and their applications to modern mechanics Science in China Series G Physics Mechanics and Astronomy 49 3 2006 257 272
    • (2006) Science in China Series G Physics Mechanics and Astronomy , vol.49 , Issue.3 , pp. 257-272
    • Xu, M.1    Tan, W.2
  • 52
    • 80053927109 scopus 로고    scopus 로고
    • Viscoelastic behavior through fractional calculus: An easier method for best fitting experimental results
    • M.D. Paola, M. Pirrota, and A. Valenza Viscoelastic behavior through fractional calculus: an easier method for best fitting experimental results Mechanics of Materials 43 12 2011 799 806
    • (2011) Mechanics of Materials , vol.43 , Issue.12 , pp. 799-806
    • Paola, M.D.1    Pirrota, M.2    Valenza, A.3
  • 53
    • 84864341024 scopus 로고    scopus 로고
    • Exact mechanical models of fractional hereditary materials
    • M.D. Paola, and M. Zingales Exact mechanical models of fractional hereditary materials Journal of Rheology 56 5 2011 983 1004
    • (2011) Journal of Rheology , vol.56 , Issue.5 , pp. 983-1004
    • Paola, M.D.1    Zingales, M.2
  • 54
    • 2642547272 scopus 로고    scopus 로고
    • Experimental Lagrangian acceleration probability density function measurement
    • N. Mordant, A.M. Crawford, and E. Bodenschatz Experimental Lagrangian acceleration probability density function measurement Physica D Nonlinear Phenomena 193 1-4 2004 245 251
    • (2004) Physica D Nonlinear Phenomena , vol.193 , Issue.14 , pp. 245-251
    • Mordant, N.1    Crawford, A.M.2    Bodenschatz, E.3
  • 55
    • 0035931880 scopus 로고    scopus 로고
    • Fluid particle accelerations in fully developed turbulence
    • DOI 10.1038/35059027
    • A.L. Porta, G.A. Voth, A.M. Crawford, J. Alexander, and E. Bodenschatz Fluid particle accelerations in fully developed turbulence Nature 409 6823 2001 1017 1019 (Pubitemid 32204048)
    • (2001) Nature , vol.409 , Issue.6823 , pp. 1017-1019
    • La Porta, A.1    Voth, G.A.2    Crawford, A.M.3    Alexander, J.4    Bodenschatz, E.5
  • 56
    • 3042739081 scopus 로고    scopus 로고
    • Temporal statistics in high Rayleigh number convective turbulence
    • R. Camussi, and R. Verzicco Temporal statistics in high Rayleigh number convective turbulence European Journal of Mechanics B/Fluids 23 3 2004 427 442
    • (2004) European Journal of Mechanics B/Fluids , vol.23 , Issue.3 , pp. 427-442
    • Camussi, R.1    Verzicco, R.2
  • 65
    • 0242354999 scopus 로고    scopus 로고
    • Geometric and physical interpretation of fractional integration and fractional differentiation
    • I. Podlubny Geometric and physical interpretation of fractional integration and fractional differentiation Fractional Calculus and Applied Analysis 5 4 2002 367 386
    • (2002) Fractional Calculus and Applied Analysis , vol.5 , Issue.4 , pp. 367-386
    • Podlubny, I.1
  • 66
    • 33745869026 scopus 로고    scopus 로고
    • Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
    • I. Podlubny, and N. Heymans Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives Rheologica Acta 45 5 2006 765 772
    • (2006) Rheologica Acta , vol.45 , Issue.5 , pp. 765-772
    • Podlubny, I.1    Heymans, N.2
  • 68
    • 67650624466 scopus 로고    scopus 로고
    • Fractional-order feedback control of a dc motor
    • I. Petráš Fractional-order feedback control of a dc motor Journal of Electrical Engineering 60 3 2009 117 128
    • (2009) Journal of Electrical Engineering , vol.60 , Issue.3 , pp. 117-128
    • Petráš, I.1
  • 69
    • 41549148741 scopus 로고    scopus 로고
    • Tuning and auto-tuning of fractional order controllers for industry applications
    • DOI 10.1016/j.conengprac.2007.08.006, PII S0967066107001566
    • C.A. Monje, B.M. Vinagre, V. Feliu, and Y.Q. Chen Tuning and auto-tuning of fractional order controllers for industry applications Control Engineering Practice 16 7 2008 798 812 (Pubitemid 351470859)
    • (2008) Control Engineering Practice , vol.16 , Issue.7 , pp. 798-812
    • Monje, C.A.1    Vinagre, B.M.2    Feliu, V.3    Chen, Y.4
  • 70
    • 84857037252 scopus 로고    scopus 로고
    • Improved model reduction and tuning of fractional-order controllers for analytical rule extraction with genetic programming
    • S. Das, I. Pan, S. Das, and A. Gupta Improved model reduction and tuning of fractional-order controllers for analytical rule extraction with genetic programming ISA Transactions 51 2 2012 237 261
    • (2012) ISA Transactions , vol.51 , Issue.2 , pp. 237-261
    • Das, S.1    Pan, I.2    Das, S.3    Gupta, A.4
  • 71
    • 79955905595 scopus 로고    scopus 로고
    • Classical controller design techniques for fractional order case
    • C. Yeroglu, and N. Tan Classical controller design techniques for fractional order case ISA Transactions 50 3 2011 461 472
    • (2011) ISA Transactions , vol.50 , Issue.3 , pp. 461-472
    • Yeroglu, C.1    Tan, N.2
  • 79
    • 79955893889 scopus 로고    scopus 로고
    • On the selection of tuning methodology of fopid controllers for the control of higher order processes
    • S. Das, S. Saha, S. Das, and A. Gupta On the selection of tuning methodology of fopid controllers for the control of higher order processes ISA Transactions 50 3 2011 376 388
    • (2011) ISA Transactions , vol.50 , Issue.3 , pp. 376-388
    • Das, S.1    Saha, S.2    Das, S.3    Gupta, A.4
  • 80
    • 68949169312 scopus 로고    scopus 로고
    • On robust stability of linear time invariant fractional-order systems with real parametric uncertainties
    • K.A. Moornani, and M. Haeri On robust stability of linear time invariant fractional-order systems with real parametric uncertainties ISA Transactions 48 4 2009 484 490
    • (2009) ISA Transactions , vol.48 , Issue.4 , pp. 484-490
    • Moornani, K.A.1    Haeri, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.