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

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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.

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References

  • Aghababa MP (2015) Fractional modeling and control of a complex nonlinear energy supply-demand system. Complexity 20(6):74–86

    Article  MathSciNet  Google Scholar 

  • 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):249–267

    Article  MathSciNet  MATH  Google Scholar 

  • Bingül Z, Karahan O (2011) A fuzzy logic controller tuned with PSO for 2 dof robot trajectory control. Expert Syst Appl 38(1):1017–1031

    Article  Google Scholar 

  • Bouchekara H, Chaib A, Abido M, El-Sehiemy R (2016) Optimal power flow using an improved colliding bodies optimization algorithm. Appl Soft Comput 42:119–131

    Article  Google Scholar 

  • Caponetto R, Dongola G, Fortuna L, Petráš I (2010) Modeling and control applications. World Scientific, Singapore

    Google Scholar 

  • 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):358–366

    Article  Google Scholar 

  • 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

  • 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):385–392

    Article  Google Scholar 

  • 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

  • Kaveh A, Mahdavi V (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27

    Article  Google Scholar 

  • 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

  • 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):2189–2211

    Article  Google Scholar 

  • 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

  • Lee CH, Chang FK (2010) Fractional-order PID controller optimization via improved electromagnetism-like algorithm. Expert Syst Appl 37(12):8871–8878

    Article  Google Scholar 

  • Liu L, Pan F, Xue D (2015) Variable-order fuzzy fractional PID controller. ISA Trans 55:227–233

    Article  Google Scholar 

  • Lu JG, Zhao YA (2016) Decentralized robust \( {H_{\infty }} \) control of fractional-order interconnected systems with uncertainties. Int J Control. doi:10.1080/00207179.2016.1201595

    Google Scholar 

  • Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  • Mishra P, Kumar V, Rana K (2015) A fractional order fuzzy PID controller for binary distillation column control. Expert Syst Appl 42(22):8533–8549

    Article  Google Scholar 

  • 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, Shabbouei Hagh Y, Palm R (2017) Robust control by adaptive non-singular terminal sliding mode. Eng Appl Artif Intell 59:205–217

    Article  Google Scholar 

  • Monje CA, Chen Y, Vinagre BM, Xue D, Feliu-Batlle V (2010) Fractional-order systems and controls: fundamentals and applications. Springer, Berlin

    Book  MATH  Google Scholar 

  • Muthukumar P, Balasubramaniam P, Ratnavelu K (2016) T–S fuzzy predictive control for fractional order dynamical systems and its applications. Nonlinear Dyn 86:1–13

    Article  MATH  Google Scholar 

  • 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

  • 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 59:85–104

    Article  Google Scholar 

  • Pan M, Zheng L, Liu F, Zhang X (2016) Modeling heat transport in nanofluids with stagnation point flow using fractional calculus. Appl Math Model 40:8974–8984

    Article  MathSciNet  Google Scholar 

  • 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):1018–1030

    Article  Google Scholar 

  • Perng JW, Chen GY, Hsu YW (2016) Fopid controller optimization based on SIWPSO-RBFNN algorithm for fractional-order time delay systems. Soft Comput. doi:10.1007/s00500-016-2050-0

    Google Scholar 

  • Podlubny I (1994) Fractional-order systems and fractional-order controllers. Inst Exp Phys Slovak Acad Sci Kosice 12(3):1–18

    Google Scholar 

  • Shabbouei Hagh Y, Mohammadi Asl R, Cocquempot V (2017) A hybrid robust fault tolerant control based on adaptive joint unscented kalman filter. ISA Trans 66:262–274

    Article  Google Scholar 

  • 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 58:279–291

    Article  Google Scholar 

  • Valério D, da Costa JS (2006) Tuning of fractional PID controllers with Ziegler–Nichols-type rules. Sig Process 86(10):2771–2784

    Article  MATH  Google Scholar 

  • Vyawahare VA, Nataraj P (2013) Fractional-order modeling of neutron transport in a nuclear reactor. Appl Math Model 37(23):9747–9767

    Article  MathSciNet  Google Scholar 

  • Wang B, Li SE, Peng H, Liu Z (2015) Fractional-order modeling and parameter identification for lithium-ion batteries. J Power Sources 293:151–161

    Article  Google Scholar 

  • 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 75:50–61

    Article  MathSciNet  MATH  Google Scholar 

  • 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 111:67–78

    Article  Google Scholar 

  • 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):973–979

    MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank Dr. Aniello Castiglione, and the reviewers for their helpful suggestions that have helped to have an improved version of the manuscript.

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Authors and Affiliations

  1. Control Engineering Department, Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran

    Reza Mohammadi Asl

  2. Information Technology Engineering Department, Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran

    Elham Pourabdollah & Milad Salmani

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  1. Reza Mohammadi Asl
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  2. Elham Pourabdollah
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  3. Milad Salmani
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Correspondence to Reza Mohammadi Asl.

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All authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by V. Loia.

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Mohammadi Asl, R., Pourabdollah, E. & Salmani, M. Optimal fractional order PID for a robotic manipulator using colliding bodies design. Soft Comput 22, 4647–4659 (2018). https://doi.org/10.1007/s00500-017-2649-9

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  • DOI: https://doi.org/10.1007/s00500-017-2649-9

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