Skip to main content

Advertisement

SpringerLink
Log in

Optimal fractional order adaptive controllers for AVR applications

  • Original Paper
  • Published:
Electrical Engineering Aims and scope Submit manuscript

Abstract

This work presents strategies for fractional order model reference adaptive control (FOMRAC) and fractional order proportional–integral–derivative control (FOPID) applied to an automatic voltage regulator (AVR). The paper focuses on tuning the gains and orders of the FOPID controller and the gains and orders adaptive laws of the FOMRAC controller, with the goal of minimizing non-linear and high dimensionality objective functions, using sequential quadratic programming (SQP), particle swarm optimization (PSO), and genetic algorithms (GA). Two models used for AVR have been studied and reported in the literature and are the bases of the three case studies reported in this paper. To analyze the advantages and disadvantages of the proposed MRAC, comparisons are made with the previous results, i.e. with the results obtained by a PID controller and an MRAC controller optimized by GA. We demonstrate through some performance criteria that fractional order controllers optimized by the PSO algorithm improve the behavior of the controlled system, specifically the robustness with respect to model uncertainties, and improvements with respect to the speed convergence of the signals.

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
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

References

  1. Aguila-Camacho N, Duarte-Mermoud MA (2013) Fractional adaptive control for an automatic voltage regulator. ISA Trans 52(6):807–15

    Article  Google Scholar 

  2. Andersson G, Bel CA, Cañizares C (2009) Frequency and Voltage Control. In: Gómez-Expósito A, Conejo A (eds) Electric energy systems: analysis and operation, Chap. 9. CRC Press, Burgos Province, pp 355–399

  3. Anwar MN, Pan S (2014) A frequency domain design of PID controller for an AVR system. J Zhejiang Univ Sci C 15(4):293–299

    Article  Google Scholar 

  4. Betts JT, Frank PD (1994) A sparse nonlinear optimization algorithm. J Optim Theory Appl 82(3):519–541

    Article  MathSciNet  MATH  Google Scholar 

  5. Boggs PT (1996) Sequential Quadratic Programming. Ph.D. thesis, Departments of Mathematics and Operations Research-University of North Carolina

  6. Chapman SJ (2006) Máquinas Eléctricas 2006, tercera, ed edn. British Aerospace Australia, Australia

    Google Scholar 

  7. Chatterjee A, Mukherjee V, Ghoshal S (2009) Velocity relaxed and craziness-based swarm optimized intelligent PID and PSS controlled AVR system. Int J Electr Power Energy Syst 31(7–8):323–333

    Article  Google Scholar 

  8. Conceicao I (2008) Quantum Gaussian particle swarm optimization approach for PID controller design in AVR system. In: Proceedings International Conference on Systems, Man and Cybernetics vol 2, pp 3708–3713

  9. dos Santos Coelho L (2009) Tuning of PID controller for an automatic regulator voltage system using chaotic optimization approach. Chaos Solitons Fractals 39(4):1504–1514

    Article  Google Scholar 

  10. Eldersveld SK (1991) Large-scale sequential quadratic programming algorithms. Ph.D. thesis, Department of Operations Research-Stanford University, Stanford

  11. Gaing ZL (2004) A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans Energy Convers 19(2):384–391

    Article  Google Scholar 

  12. Gallegos J, Duarte-Mermoud MA (2016) Mixed order robust adaptive control for general linear time invariant systems. J Frankl Inst (2016) (submitted to)

  13. Gozde H, Taplamacioglu M (2011) Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system. J Frankl Inst 348(8):1927–1946

    Article  MATH  Google Scholar 

  14. Kennedy J, Eberhart R (1995) Particle swarm optimization. IEEE 95:1942–1948

    Google Scholar 

  15. Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier B.V, San Diego

    MATH  Google Scholar 

  16. Kundur P (1994) Power system stability and control. Palo Alto, California

    Google Scholar 

  17. Ladaci S, Charef A (2009) Robust fractional adaptive control based on the strictly positive realness condition. Int J Appl Math Comput Sci 19(1):69–76

    Article  MathSciNet  MATH  Google Scholar 

  18. Ladaci S, Charef A, Loiseau JJ (2006) On fractional adaptive control. Nonlinear Dyn 43(4):365–378

    Article  MathSciNet  MATH  Google Scholar 

  19. Math Work: fmincon SQP Algorithm (2014). https://www.mathworks.com/

  20. MathWork: Genetic Algorithm (2014). https://www.mathworks.com/

  21. Mukherjee V, Ghoshal S (2007) Comparison of intelligent fuzzy based AGC coordinated PID controlled and PSS controlled AVR system. Int J Electr Power Energy Syst 29(9):679–689

    Article  Google Scholar 

  22. Mukherjee V, Ghoshal S (2007) Intelligent particle swarm optimized fuzzy PID controller for AVR system. Electric Power Syst Res 77(12):1689–1698

    Article  Google Scholar 

  23. Narendra KS, Annaswamy AM (2005) Stable adaptative systems. Dover Publications Inc., Mineola

    MATH  Google Scholar 

  24. Ordóñez-Hurtado RH (2012) Aplicación de la técnica PSO a la determinación de funciones de Lyaunov cuadráticas comunes y a sistemas adaptables basados en modelos de error. Ph.D. thesis, Departamento de Ingeniería Eléctrica, Universidad De Chile

  25. Oustaloup A (1991) La commande CRONE: commande robuste d’ordre non entier. Hermes, USA

    MATH  Google Scholar 

  26. Pan I, Das S (2012) Chaotic multi-objective optimization based design of fractional order PI\(\lambda \text{ D }\mu \) controller in AVR system. Int J Electr Power Energy Syst 43(1):393–407

    Article  Google Scholar 

  27. Pan I, Das S (2013) Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization. Int J Electr Power Energy Syst 51:106–118

    Article  Google Scholar 

  28. Panda S, Sahu B, Mohanty P (2012) Design and performance analysis of PID controller for an automatic voltage regulator system using simplified particle swarm optimization. J Frankl Inst 349(8):2609–2625

    Article  MathSciNet  MATH  Google Scholar 

  29. Sahu BK, Mohanty PK, Panda S, Kar SK, Mishra N (2012) Design and comparative performance analysis of PID controlled automatic voltage regulator tuned by many optimizing liaisons. In: Proceedings of the 2012 International Conference on Advances in Power Conversion and Energy Technologies (APCET), pp 1–6. IEEE

  30. Sfaihi B, Boubaker O (2004) Full order observer design for linear systems with unknown inputs. In: IEEE International Conference on Industrial Technology. IEEE ICIT’04, vol 3, no 5, pp 1233–1238

  31. Shi Y, Eberhart R (1999) Empirical study of particle swarm optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), pp 1945–1950

  32. Tang Y, Cui M, Hua C, Li L, Yang Y (2012) Optimum design of fractional order PI\(\lambda \)D\(\mu \) controller for AVR system using chaotic ant swarm. Expert Syst Appl 39(8):6887–6896

    Article  Google Scholar 

  33. Valério D (2005) Ninteger v. 2.3 Fractional control toolbox for MatLab. https://www.mathworks.com/

  34. Valério D, da Costa JS (2004) Ninteger: a non-integer control toolbox for MatLab. In: Proceedings of the First IFAC Workshop on Fractional Differentiation and Applications. Bordeaux, France, pp 208–213

  35. Vinagre BM, Petras I, Podlubny I, Chen YQ (2002) Using fractional order adjustment rules and fractional order reference models in model reference adaptive control. Nonlinear Dyn 29(1–4):269–279

    Article  MathSciNet  MATH  Google Scholar 

  36. Wildi T (2007) Máquinas Eléctricas y Sistemas De Potencia. Pearson ed edn, México

  37. Zamani M, Karimi-Ghartemani M, Sadati N, Parniani M (2009) Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Eng Pract 17(12):1380–1387

    Article  Google Scholar 

  38. Zhu H, Li L, Zhao Y, Guo Y, Yang Y (2009) CAS algorithm-based optimum design of PID controller in AVR system. Chaos Solitons Fractals 42(2):792–800

    Article  Google Scholar 

Download references

Acknowledgements

This work has been supported by CONICYT Chile, under the grants FB0809 Advanced Mining Technology Center, FONDECYT Regular 1120453 Improvements of Adaptive Systems Performance by using Fractional Order Observers and Particle Swarm Optimization and FONDECYT Regular 1150488 Fractional Error Models in Adaptive Control and Applications. The third author would like to thank besides the support of CONICYT/FONDECYT Postdoctorado No. 3140604.

Author information

Authors and Affiliations

  1. Electrical Engineering Department, University of Chile, Av. Tupper 2007, Santiago, Chile

    Marco E. Ortiz-Quisbert, Manuel A. Duarte-Mermoud & Freddy Milla

  2. Advanced Mining Technology Center (AMTC), University of Chile, Av. Tupper 2007, Santiago, Chile

    Marco E. Ortiz-Quisbert, Manuel A. Duarte-Mermoud & Freddy Milla

  3. Department of Electrical Engineering, CINVESTAV-IPN, Av. IPN 2508, Mexico City, D.F., Mexico

    Rafael Castro-Linares

  4. School of Electrical Engineering, Pontificia Universidad Católica de Valparaíso, Av. Brasil 2147, Valparaiso, Chile

    Gastón Lefranc

Authors
  1. Marco E. Ortiz-Quisbert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuel A. Duarte-Mermoud
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Freddy Milla
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rafael Castro-Linares
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Gastón Lefranc
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Manuel A. Duarte-Mermoud.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ortiz-Quisbert, M.E., Duarte-Mermoud, M.A., Milla, F. et al. Optimal fractional order adaptive controllers for AVR applications. Electr Eng 100, 267–283 (2018). https://doi.org/10.1007/s00202-016-0502-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00202-016-0502-2

Keywords

Search

Navigation