Skip to main content

Advertisement

SpringerLink
Log in

An expert 2DOF fractional order fuzzy PID controller for nonlinear systems

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This work presents a generic two-degree-of-freedom fractional order fuzzy PI-D (2DOF FOFPI-D) controller dedicated to a class of nonlinear systems. The control law for proposed scheme is derived from basic 2DOF fractional order PID controller in discrete domain. Expert intelligence is embedded in overall derived control law by utilizing formula-based fuzzy design methodology. The controller structure comprises of fractional order fuzzy PI (FOFPI) and fractional order derivative filter to handle multiple issues and provides flexibility in design and self-tuning control feature. Further, the proposed scheme is compared with its integer order counterpart and 2DOF PI-D controller for coupled nonlinear 2-link robotic arm in real operating environment. The parameters of designed controllers are optimally tuned using multi-objective non-dominated sorting genetic algorithm-II for attaining low variation in control effort and error index. Intensive simulation studies are performed to analyze trajectory tracking, model uncertainty, disturbance due to cogging, sensor noise and noise as well as disturbance rejection simultaneously. Results demonstrate the superior performance of 2DOF FOFPI-D controller as compared to other designed controllers in the facets of different operating conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Miccio M, Cosenza B (2014) Control of a distillation column by type-2 and type-1 fuzzy logic PID controllers. J Process Control 24(5):475–484

    Article  Google Scholar 

  2. Precup R-E, Preitl S, Petriu EM, Tar JK, Tomescu ML, Pozna C (2009) Generic two-degree-of-freedom linear and fuzzy controllers for integral processes. J Frankl Inst 346(10):980–1003

    Article  MathSciNet  MATH  Google Scholar 

  3. Malki HA, Li H, Chen G (1994) New design and stability analysis of fuzzy proportional-derivative control systems. IEEE Trans Fuzzy Syst 2(4):245–254

    Article  Google Scholar 

  4. Misir D, Malki HA, Guanrong C (1996) Design and analysis of a fuzzy proportional–integral–derivative controller. Fuzzy Sets Syst 79(3):297–314

    Article  MathSciNet  MATH  Google Scholar 

  5. Malki HA, Misir D, Feigenspan D, Guanrong C (1997) Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads. IEEE Trans Control Syst Technol 5(3):371–378

    Article  Google Scholar 

  6. Sooraksa P, Chen G (1998) Mathematical modeling and fuzzy control of a flexible-link robot arm. Math Comput Model 27(6):73–93

    Article  MATH  Google Scholar 

  7. Li W, Chang X, Wahl FM, Farrell J (2001) Tracking control of a manipulator under uncertainty by FUZZY P + ID controller. Fuzzy Sets Syst 122(1):125–137

    Article  MathSciNet  MATH  Google Scholar 

  8. Er MJ, Sun YL (2001) Hybrid fuzzy proportional-integral plus conventional derivative control of linear and nonlinear systems. IEEE Trans Ind Electron 48(6):1109–1117

    Google Scholar 

  9. Tang KS, Kim Fung M, Guanrong C, Kwong S (2001) An optimal fuzzy PID controller. IEEE Trans Ind Electron 48(4):757–765

    Article  Google Scholar 

  10. Tang W, Chen G, Lu R (2001) A modified fuzzy PI controller for a flexible-joint robot arm with uncertainties. Fuzzy Sets Syst 118(1):109–119

    Article  MathSciNet  Google Scholar 

  11. Ying H, Siler W, Buckley JJ (1990) Fuzzy control theory: a nonlinear case. Automatica 26(3):513–520

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen G, Pham TT (2000) Introduction to fuzzy sets, fuzzy logic, and fuzzy control systems. CRC Press, Boca Raton

    Book  Google Scholar 

  13. Mohan V, Rani A, Singh V (2017) Robust adaptive fuzzy controller applied to double inverted pendulum. J Intell Fuzzy Syst 32(5):3669–3687

    Article  Google Scholar 

  14. Kumar A, Kumar V (2017) Hybridized ABC-GA optimized fractional order fuzzy pre-compensated FOPID control design for 2-DOF robot manipulator. AEU Int J Electron Commun 79(Supplement C):219–233

    Article  Google Scholar 

  15. Kumar A, Kumar V (2018) Performance analysis of optimal hybrid novel interval type-2 fractional order fuzzy logic controllers for fractional order systems. Expert Syst Appl 93(Supplement C):435–455

    Article  Google Scholar 

  16. Sharma R, Gaur P, Mittal A (2016) Design of two-layered fractional order fuzzy logic controllers applied to robotic manipulator with variable payload. Appl Soft Comput 47:565–576

    Article  Google Scholar 

  17. Das S, Pan I, Das S (2013) Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time. ISA Trans 52(4):550–566

    Article  Google Scholar 

  18. Das S, Pan I, Das S, Gupta A (2012) A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices. Eng Appl Artif Intell 25(2):430–442

    Article  Google Scholar 

  19. Kumar V, Rana KPS, Kumar J, Mishra P (2016) Self-tuned robust fractional order fuzzy PD controller for uncertain and nonlinear active suspension system. Neural Comput Appl. https://doi.org/10.1007/s00521-016-2774-x

    Article  Google Scholar 

  20. Jesus IS, Barbosa RS (2015) Genetic optimization of fuzzy fractional PD + I controllers. ISA Trans 57:220–230

    Article  Google Scholar 

  21. Haji VH, Monje CA (2017) Fractional order fuzzy-PID control of a combined cycle power plant using Particle Swarm Optimization algorithm with an improved dynamic parameters selection. Appl Soft Comput 58:256–264

    Article  Google Scholar 

  22. Zamani A-A, Tavakoli S, Etedali S, Sadeghi J (2017) Adaptive fractional order fuzzy proportional–integral–derivative control of smart base-isolated structures equipped with magnetorheological dampers. J Intell Mater Syst Struct. https://doi.org/10.1177/1045389X17721046

    Article  Google Scholar 

  23. Pan I, Korre A, Das S, Durucan S (2012) Chaos suppression in a fractional order financial system using intelligent regrouping PSO based fractional fuzzy control policy in the presence of fractional Gaussian noise. Nonlinear Dyn 70(4):2445–2461

    Article  MathSciNet  Google Scholar 

  24. Pan I, Das S (2016) Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO. ISA Trans 62:19–29

    Article  Google Scholar 

  25. Sharma R, Rana KPS, Kumar V (2014) Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator. Expert Syst Appl 41(9):4274–4289

    Article  Google Scholar 

  26. Kumar V, Rana K (2017) Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload. J Frankl Inst 354(2):993–1022

    Article  MathSciNet  MATH  Google Scholar 

  27. Das S, Pan I, Das S (2013) Fractional order fuzzy control of nuclear reactor power with thermal-hydraulic effects in the presence of random network induced delay and sensor noise having long range dependence. Energy Convers Manag 68:200–218

    Article  Google Scholar 

  28. 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 

  29. Kumar V, Rana K, Mishra P (2016) Robust speed control of hybrid electric vehicle using fractional order fuzzy PD and PI controllers in cascade control loop. J Frankl Inst 353(8):1713–1741

    Article  MathSciNet  MATH  Google Scholar 

  30. Araki M, Taguchi H (2003) Two-degree-of-freedom PID controllers. Int J Control Autom Syst 1:401–411

    Google Scholar 

  31. 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 

  32. Pachauri N, Singh V, Rani A (2017) Two degree of freedom PID based inferential control of continuous bioreactor for ethanol production. ISA Trans 68:235

    Article  Google Scholar 

  33. Ghosh A, Rakesh Krishnan T, Tejaswy P, Mandal A, Pradhan JK, Ranasingh S (2014) Design and implementation of a 2-DOF PID compensation for magnetic levitation systems. ISA Trans 53(4):1216–1222

    Article  Google Scholar 

  34. Debbarma S, Saikia LC, Sinha N (2014) Automatic generation control using two degree of freedom fractional order PID controller. Int J Electr Power Energy Syst 58:120–129

    Article  Google Scholar 

  35. Li M, Zhou P, Zhao Z, Zhang J (2016) Two-degree-of-freedom fractional order-PID controllers design for fractional order processes with dead-time. ISA Trans 61:147–154

    Article  Google Scholar 

  36. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  37. Kumar V, Rana K (2016) Some investigations on hybrid fuzzy IPD controllers for proportional and derivative kick suppression. Int J Autom Comput 13(5):516–528

    Article  Google Scholar 

  38. Lipták BG (2013) Process control: instrument engineers’ handbook. Butterworth-Heinemann, Oxford

    Google Scholar 

  39. Gopal M (2002) Control systems: principles and design. Tata McGraw-Hill Education, New York

    Google Scholar 

  40. Goodrich C, Peterson AC (2016) Discrete fractional calculus. Springer, Berlin

    MATH  Google Scholar 

  41. Lubich C (1986) Discretized fractional calculus. SIAM J Math Anal 17(3):704–719

    Article  MathSciNet  MATH  Google Scholar 

  42. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

  43. Kumar S, Saxena R, Singh K (2017) Fractional Fourier transform and fractional-order calculus-based image edge detection. Circuits Syst Signal Process 36(4):1493–1513

    Article  Google Scholar 

  44. Tsirimokou G, Psychalinos C, Elwakil A (2017) Current-mode fractional-order filters. In: Gan W-S, Kuo C-CJ, Zheng ThF, Barni M (eds) Design of CMOS analog integrated fractional-order circuits. SpringerBriefs in electrical and computer engineering. Springer, Berlin, pp 41–54

    Chapter  Google Scholar 

  45. Oldham K, Spanier J (1974) The fractional calculus theory and applications of differentiation and integration to arbitrary order. Elsevier, Amsterdam

    MATH  Google Scholar 

  46. Chen Y, Petras I, Xue D (2009) Fractional order control-a tutorial. pp 1397–1411. https://doi.org/10.1109/ACC.2009.5160719

  47. Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press, Cambridge

    MATH  Google Scholar 

  48. Pan I, Das S (2012) Chaotic multi-objective optimization based design of fractional order PIλDμ controller in AVR system. Int J Electr Power Energy Syst 43(1):393–407

    Article  Google Scholar 

  49. Chen Z, Yuan X, Ji B, Wang P, Tian H (2014) Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II. Energy Convers Manag 84:390–404

    Article  Google Scholar 

  50. Ayala HVH, dos Santos Coelho L (2012) Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator. Expert Syst Appl 39(10):8968–8974

    Article  Google Scholar 

  51. Esfe MH, Razi P, Hajmohammad MH, Rostamian SH, Sarsam WS, Arani AAA, Dahari M (2017) Optimization, modeling and accurate prediction of thermal conductivity and dynamic viscosity of stabilized ethylene glycol and water mixture Al2O3 nanofluids by NSGA-II using ANN. Int Commun Heat Mass Trans 82:154–160

    Article  Google Scholar 

  52. Craig JJ (2005) Introduction to robotics: mechanics and control. Pearson Prentice Hall, Upper Saddle River

    Google Scholar 

  53. De Wit CC, Praly L (2000) Adaptive eccentricity compensation. IEEE Trans Control Syst Technol 8(5):757–766

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology, University Of Delhi, New Delhi, 110078, India

    Vijay Mohan, Himanshu Chhabra, Asha Rani & Vijander Singh

Authors
  1. Vijay Mohan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Himanshu Chhabra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Asha Rani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vijander Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vijay Mohan.

Ethics declarations

Conflict of interest

All authors declare that he/she has no conflict of interest.

Ethical approval

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohan, V., Chhabra, H., Rani, A. et al. An expert 2DOF fractional order fuzzy PID controller for nonlinear systems. Neural Comput & Applic 31, 4253–4270 (2019). https://doi.org/10.1007/s00521-017-3330-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-017-3330-z

Keywords

Search

Navigation