Skip to main content
Top
Published in: Soft Computing 14/2018

27-05-2017 | Methodologies and Application

Optimal fractional order PID for a robotic manipulator using colliding bodies design

Authors: Reza Mohammadi Asl, Elham Pourabdollah, Milad Salmani

Published in: Soft Computing | Issue 14/2018

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, an optimal fractional order PID controller is presented. An evolutionary algorithm, named colliding bodies optimization, is applied to tune the proposed controller. For this purpose, the algorithm is changed and developed to an adaptive version, in which it can update itself by the time. This feature helps it to converge in a shorter time comparing with the basic one. The proposed optimal controller is utilized to control different systems. Firstly, it is used to control different typical transfer functions, which some of them have time delay. Then, in order to show the proficiency of the proposed fractional order controller, it is applied to control a robotic manipulator. The comparative results of the designed optimal controller are given to show its effectiveness.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Aghababa MP (2015) Fractional modeling and control of a complex nonlinear energy supply-demand system. Complexity 20(6):74–86MathSciNetCrossRef Aghababa MP (2015) Fractional modeling and control of a complex nonlinear energy supply-demand system. Complexity 20(6):74–86MathSciNetCrossRef
go back to reference Balasubramaniam P, Muthukumar P, Ratnavelu K (2015) Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system. Nonlinear Dyn 80(1–2):249–267MathSciNetCrossRefMATH Balasubramaniam P, Muthukumar P, Ratnavelu K (2015) Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system. Nonlinear Dyn 80(1–2):249–267MathSciNetCrossRefMATH
go back to reference Bingül Z, Karahan O (2011) A fuzzy logic controller tuned with PSO for 2 dof robot trajectory control. Expert Syst Appl 38(1):1017–1031CrossRef Bingül Z, Karahan O (2011) A fuzzy logic controller tuned with PSO for 2 dof robot trajectory control. Expert Syst Appl 38(1):1017–1031CrossRef
go back to reference Bouchekara H, Chaib A, Abido M, El-Sehiemy R (2016) Optimal power flow using an improved colliding bodies optimization algorithm. Appl Soft Comput 42:119–131CrossRef Bouchekara H, Chaib A, Abido M, El-Sehiemy R (2016) Optimal power flow using an improved colliding bodies optimization algorithm. Appl Soft Comput 42:119–131CrossRef
go back to reference Caponetto R, Dongola G, Fortuna L, Petráš I (2010) Modeling and control applications. World Scientific, Singapore Caponetto R, Dongola G, Fortuna L, Petráš I (2010) Modeling and control applications. World Scientific, Singapore
go back to reference Debbarma S, Saikia LC, Sinha N (2014) Solution to automatic generation control problem using firefly algorithm optimized i\(\lambda \)d\(\mu \) controller. ISA Trans 53(2):358–366CrossRef Debbarma S, Saikia LC, Sinha N (2014) Solution to automatic generation control problem using firefly algorithm optimized i\(\lambda \)d\(\mu \) controller. ISA Trans 53(2):358–366CrossRef
go back to reference Gude JJ, Kahoraho E (2010) Modified Ziegler–Nichols method for fractional PI controllers. In: 2010 IEEE conference on emerging technologies and factory automation (ETFA), IEEE, pp 1–5 Gude JJ, Kahoraho E (2010) Modified Ziegler–Nichols method for fractional PI controllers. In: 2010 IEEE conference on emerging technologies and factory automation (ETFA), IEEE, pp 1–5
go back to reference Hassanzadeh I, Alizadeh G, Hashemzadeh F, Kharrati H (2011) Performance tuning for robot manipulators using intelligent robust controller. Proc Inst Mech Eng Part I J Syst Control Eng 225(3):385–392CrossRef Hassanzadeh I, Alizadeh G, Hashemzadeh F, Kharrati H (2011) Performance tuning for robot manipulators using intelligent robust controller. Proc Inst Mech Eng Part I J Syst Control Eng 225(3):385–392CrossRef
go back to reference Kankashvar M, Kharrati H, Mohammadi Asl R, Sadeghiani A (2015) Designing PID controllers for a five-bar linkage robot manipulator using BBO algorithm. In: 2015 6th international conference on modeling, simulation, and applied optimization (ICMSAO), pp 1–6 Kankashvar M, Kharrati H, Mohammadi Asl R, Sadeghiani A (2015) Designing PID controllers for a five-bar linkage robot manipulator using BBO algorithm. In: 2015 6th international conference on modeling, simulation, and applied optimization (ICMSAO), pp 1–6
go back to reference Kaveh A, Mahdavi V (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27CrossRef Kaveh A, Mahdavi V (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27CrossRef
go back to reference Khooban MH, Sha-Sadeghi M, Niknam T, Blaabjerg F (2016) Analysis, control and design of speed control of electric vehicles delayed model: multi-objective fuzzy fractional-order pi\(\lambda \)d\(\mu \) controller. IET science, measurement and technology Khooban MH, Sha-Sadeghi M, Niknam T, Blaabjerg F (2016) Analysis, control and design of speed control of electric vehicles delayed model: multi-objective fuzzy fractional-order pi\(\lambda \)d\(\mu \) controller. IET science, measurement and technology
go back to reference Khubalkar S, Chopade A, Junghare A, Aware M, Das S (2016) Design and realization of stand-alone digital fractional order PID controller for buck converter fed DC motor. Circuits Syst Signal Process 35(6):2189–2211CrossRef Khubalkar S, Chopade A, Junghare A, Aware M, Das S (2016) Design and realization of stand-alone digital fractional order PID controller for buck converter fed DC motor. Circuits Syst Signal Process 35(6):2189–2211CrossRef
go back to reference Korkmaz M, Aydoğdu Ö, Doğan H (2012) Design and performance comparison of variable parameter nonlinear PID controller and genetic algorithm based PID controller. In: 2012 international symposium on innovations in intelligent systems and applications (INISTA) IEEE, pp 1–5 Korkmaz M, Aydoğdu Ö, Doğan H (2012) Design and performance comparison of variable parameter nonlinear PID controller and genetic algorithm based PID controller. In: 2012 international symposium on innovations in intelligent systems and applications (INISTA) IEEE, pp 1–5
go back to reference Lee CH, Chang FK (2010) Fractional-order PID controller optimization via improved electromagnetism-like algorithm. Expert Syst Appl 37(12):8871–8878CrossRef Lee CH, Chang FK (2010) Fractional-order PID controller optimization via improved electromagnetism-like algorithm. Expert Syst Appl 37(12):8871–8878CrossRef
go back to reference Liu L, Pan F, Xue D (2015) Variable-order fuzzy fractional PID controller. ISA Trans 55:227–233CrossRef Liu L, Pan F, Xue D (2015) Variable-order fuzzy fractional PID controller. ISA Trans 55:227–233CrossRef
go back to reference Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61CrossRef Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61CrossRef
go back to reference Mishra P, Kumar V, Rana K (2015) A fractional order fuzzy PID controller for binary distillation column control. Expert Syst Appl 42(22):8533–8549CrossRef Mishra P, Kumar V, Rana K (2015) A fractional order fuzzy PID controller for binary distillation column control. Expert Syst Appl 42(22):8533–8549CrossRef
go back to reference Mohammadi Asl R, Hashemzadeh F, Badamchizadeh MA (2015) A new adaptive neural network based observer for robotic manipulators. In: 2015 3rd RSI international conference on robotics and mechatronics (ICROM), pp 663–668 Mohammadi Asl R, Hashemzadeh F, Badamchizadeh MA (2015) A new adaptive neural network based observer for robotic manipulators. In: 2015 3rd RSI international conference on robotics and mechatronics (ICROM), pp 663–668
go back to reference Mohammadi Asl R, Shabbouei Hagh Y, Palm R (2017) Robust control by adaptive non-singular terminal sliding mode. Eng Appl Artif Intell 59:205–217CrossRef Mohammadi Asl R, Shabbouei Hagh Y, Palm R (2017) Robust control by adaptive non-singular terminal sliding mode. Eng Appl Artif Intell 59:205–217CrossRef
go back to reference Monje CA, Chen Y, Vinagre BM, Xue D, Feliu-Batlle V (2010) Fractional-order systems and controls: fundamentals and applications. Springer, BerlinCrossRefMATH Monje CA, Chen Y, Vinagre BM, Xue D, Feliu-Batlle V (2010) Fractional-order systems and controls: fundamentals and applications. Springer, BerlinCrossRefMATH
go back to reference Muthukumar P, Balasubramaniam P, Ratnavelu K (2016) T–S fuzzy predictive control for fractional order dynamical systems and its applications. Nonlinear Dyn 86:1–13CrossRefMATH Muthukumar P, Balasubramaniam P, Ratnavelu K (2016) T–S fuzzy predictive control for fractional order dynamical systems and its applications. Nonlinear Dyn 86:1–13CrossRefMATH
go back to reference Nobarian MS, Mohammadi Asl R, Nemati M, Hashemzadeh F (2016) Optimal \( {L_1} \) control for linear time-delayed systems using GSA algorithm. In: 2016 4th international conference on control, instrumentation, and automation (ICCIA), pp 111–115 Nobarian MS, Mohammadi Asl R, Nemati M, Hashemzadeh F (2016) Optimal \( {L_1} \) control for linear time-delayed systems using GSA algorithm. In: 2016 4th international conference on control, instrumentation, and automation (ICCIA), pp 111–115
go back to reference Pal PS, Kar R, Mandal D, Ghoshal S (2015) An efficient identification approach for stable and unstable nonlinear systems using colliding bodies optimization algorithm. ISA Trans 59:85–104CrossRef Pal PS, Kar R, Mandal D, Ghoshal S (2015) An efficient identification approach for stable and unstable nonlinear systems using colliding bodies optimization algorithm. ISA Trans 59:85–104CrossRef
go back to reference Pan M, Zheng L, Liu F, Zhang X (2016) Modeling heat transport in nanofluids with stagnation point flow using fractional calculus. Appl Math Model 40:8974–8984MathSciNetCrossRef Pan M, Zheng L, Liu F, Zhang X (2016) Modeling heat transport in nanofluids with stagnation point flow using fractional calculus. Appl Math Model 40:8974–8984MathSciNetCrossRef
go back to reference Panda S (2011) Robust coordinated design of multiple and multi-type damping controller using differential evolution algorithm. Int J Electr Power Energy Syst 33(4):1018–1030CrossRef Panda S (2011) Robust coordinated design of multiple and multi-type damping controller using differential evolution algorithm. Int J Electr Power Energy Syst 33(4):1018–1030CrossRef
go back to reference Podlubny I (1994) Fractional-order systems and fractional-order controllers. Inst Exp Phys Slovak Acad Sci Kosice 12(3):1–18 Podlubny I (1994) Fractional-order systems and fractional-order controllers. Inst Exp Phys Slovak Acad Sci Kosice 12(3):1–18
go back to reference Shabbouei Hagh Y, Mohammadi Asl R, Cocquempot V (2017) A hybrid robust fault tolerant control based on adaptive joint unscented kalman filter. ISA Trans 66:262–274CrossRef Shabbouei Hagh Y, Mohammadi Asl R, Cocquempot V (2017) A hybrid robust fault tolerant control based on adaptive joint unscented kalman filter. ISA Trans 66:262–274CrossRef
go back to reference Sharma R, Gaur P, Mittal A (2015) Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload. ISA Trans 58:279–291CrossRef Sharma R, Gaur P, Mittal A (2015) Performance analysis of two-degree of freedom fractional order PID controllers for robotic manipulator with payload. ISA Trans 58:279–291CrossRef
go back to reference Valério D, da Costa JS (2006) Tuning of fractional PID controllers with Ziegler–Nichols-type rules. Sig Process 86(10):2771–2784CrossRefMATH Valério D, da Costa JS (2006) Tuning of fractional PID controllers with Ziegler–Nichols-type rules. Sig Process 86(10):2771–2784CrossRefMATH
go back to reference Vyawahare VA, Nataraj P (2013) Fractional-order modeling of neutron transport in a nuclear reactor. Appl Math Model 37(23):9747–9767MathSciNetCrossRef Vyawahare VA, Nataraj P (2013) Fractional-order modeling of neutron transport in a nuclear reactor. Appl Math Model 37(23):9747–9767MathSciNetCrossRef
go back to reference Wang B, Li SE, Peng H, Liu Z (2015) Fractional-order modeling and parameter identification for lithium-ion batteries. J Power Sources 293:151–161CrossRef Wang B, Li SE, Peng H, Liu Z (2015) Fractional-order modeling and parameter identification for lithium-ion batteries. J Power Sources 293:151–161CrossRef
go back to reference Xu B, Chen D, Zhang H, Wang F (2015) Modeling and stability analysis of a fractional-order francis hydro-turbine governing system. Chaos Solitons Fract 75:50–61MathSciNetCrossRefMATH Xu B, Chen D, Zhang H, Wang F (2015) Modeling and stability analysis of a fractional-order francis hydro-turbine governing system. Chaos Solitons Fract 75:50–61MathSciNetCrossRefMATH
go back to reference Xu Y, Zhou J, Xue X, Fu W, Zhu W, Li C (2016) An adaptively fast fuzzy fractional order pid control for pumped storage hydro unit using improved gravitational search algorithm. Energy Convers Manag 111:67–78CrossRef Xu Y, Zhou J, Xue X, Fu W, Zhu W, Li C (2016) An adaptively fast fuzzy fractional order pid control for pumped storage hydro unit using improved gravitational search algorithm. Energy Convers Manag 111:67–78CrossRef
go back to reference Zhang DL, Ying-Gan T, Xin-Ping G (2014) Optimum design of fractional order PID controller for an avr system using an improved artificial bee colony algorithm. Acta Autom Sin 40(5):973–979MathSciNet Zhang DL, Ying-Gan T, Xin-Ping G (2014) Optimum design of fractional order PID controller for an avr system using an improved artificial bee colony algorithm. Acta Autom Sin 40(5):973–979MathSciNet
Metadata
Title
Optimal fractional order PID for a robotic manipulator using colliding bodies design
Authors
Reza Mohammadi Asl
Elham Pourabdollah
Milad Salmani
Publication date
27-05-2017
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 14/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2649-9

Other articles of this Issue 14/2018

Soft Computing 14/2018 Go to the issue

Premium Partner