Evaluation of the PI\(^\lambda \) Controllers Tuned by Differential Evolution

  • João Pedro Caseiro Oliveira
  • Edson Antonio BatistaEmail author
  • Ruben Barros Godoy
  • Cristiano Quevedo Andrea


This manuscript proposes a way to tune fractional-order proportional–integral controllers, to synthesize them in hardware and to evaluate them by using hardware-in-the-loop technique. In order to validate the tuned controllers, it was imposed to control a plant where two loops of control were necessary. The obtained results showed satisfactory performance for both designed controllers and proved that fractional calculus can be implemented on high-performance digital processors. Controllers were implemented on the Altera DE2-115 cyclone IV EP4CE115 board.


PI\(^\lambda \) controller Differential evolution FPGA 



  1. Biswas, A., Das, S., Abraham, A., & Dasgupta, S. (2009). Design of fractional-order PI\(\lambda \)D\(\mu \) controllers with an improved differential evolution. Engineering Applications of Artificial Intelligence, 22(2), 343–350.Google Scholar
  2. Carlson, G., & Halijak, C. (1964). Approximation of fractional capacitors \((1/s)(1/n)\) by a regular Newton process. IEEE Transactions on Circuit Theory, 11(2), 210–213.Google Scholar
  3. Chareff, A., Sun, H. H., Tsao, Y. Y., & Onaral, B. (1992). Fractal system as represented by singularity function. IEEE Transactions on Automatic Control, 37(9), 1465–1470.MathSciNetzbMATHCrossRefGoogle Scholar
  4. Chen, Y., Petras, I., & Xue, D. (2009). Fractional order control—A tutorial. In 2009 American Control Conference, St. Louis, MO (pp. 1397–1411).Google Scholar
  5. Feliu-Batlle, V., Rivas-Perez, R., Sanchez-Rodrigues, L., & Ruiz-Torija, M. (2009). Robust fractional-order PI controller implemented on a laboratory hydraulic. Journal of Hydraulic Engineering, 135(4), 271–282.CrossRefGoogle Scholar
  6. Godoy, R. B., Pinto, J. O. P., Canesin, C. A., Coelho, E. A. A., & Pinto, A. M. A. C. (2012). Differential-evolution-based optimization of the dynamic response for parallel operation of inverters with no controller interconnection. IEEE Transactions on Industrial Electronics, 59(7), 2859–2866.CrossRefGoogle Scholar
  7. Ingalalli, A., Satheesh, H., & Kande, M. (2016). Platform for hardware in loop simulation. In 2016 International Symposium on Power Electronics, Electrical Drives. Automation and Motion (SPEEDAM) (vol. 351, pp. 41–46).Google Scholar
  8. Ismail, M. M., & Hassan, M. A. M. (2015). Control of shunt active filter based on fractional order PID controller. 17th International Middle-East Power System Conference (MEPCON’15) Mansoura University, Egypt.Google Scholar
  9. Maiti, D., Chakraborty, M., Acharya, A., & Konar, A. (2008). Design of a fractional-order self-tuning regulator using optimization algorithms. In 2008 11th International Conference on Computer and Information Technology, Khulna (pp. 470–475).Google Scholar
  10. Matsuda, K., & Fujii, H. (1993). H\(_\infty \) optimized wave-absorbing control: Analytical and experimental results. Journal of Guidance, Control, and Dynamics, 16(6), 1146–1153.zbMATHGoogle Scholar
  11. Munkhammar, J. (2004). Riemann–Liouville fractional derivatives and the Taylor–Riemann Series, 7. Uppsala: Uppsala University.Google Scholar
  12. Ortigueira, M. D., & Tenreiro, M. J. A. (2015). What is a fractional derivative? Journal of Computational Physics, 293, 4–13.MathSciNetzbMATHCrossRefGoogle Scholar
  13. Oustaloup, A., Levron, F., Mathieu, B., & Manot, F. M. (2000). Frequency-band complex noninteger differentiator: Characterization and synthesis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(1), 25–39.Google Scholar
  14. Praboo, N. N., & Bhada, P. K. (2013). Simulation work on fractional order PI control strategy for speed control of DC motor based on stability boundary locus methods. International Journal of Engineering Trends and Technology (IJETT), 4(8), 3403–3409.Google Scholar
  15. Qu, L., Hu, H., & Huang, Y. (2010). Fractional order PID controller based on particle swarm optimization implemented with FPGA. In 2010 International Conference on Artificial Intelligence and Computational Intelligence (AICI), Sanya (pp. 165–169).Google Scholar
  16. Shamseldin, M. A., Sallam, M., Bassiuny, A. H., & Ghany, A. M. A. (2019). A novel self-tuning fractional order PID control based on optimal model reference adaptive system. International Journal of Power Electronics and Drive Systems, 10(1), 230–241.Google Scholar
  17. Souza, F. P. (2000). Power factor correction for low power installations using active filters. Doctoral thesis, Federal University of Santa Catarina, Florianópolis, 210p.Google Scholar
  18. Storn, R., & Price, K. (1997). Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11, 341–359.MathSciNetzbMATHCrossRefGoogle Scholar
  19. Tehrani, K. A., Amirahmadi, A., Rafiei, S. M. R., Griva, G., Barrandon, L., Hamzaoui, M., Rasoanarivo, I., & Sargos, F. M. (2010). Design of fractional order PID controller for boost converter based on Multi-Objective optimization. In 2010 14th International Power Electronics and Motion Control Conference (EPE/PEMC), (pp. T3-179–T3-185).Google Scholar
  20. Tenti, P., Paredes, H. K. M., & Mattavelli, P. (2011). Conservative power theory, a framework to approach control and accountability issues in smart microgrids. IEEE Transactions on Power Electronics, 26(3), 664–673.CrossRefGoogle Scholar
  21. Zhao, C., & Zhang, X. (2008). The application of fractional order PID controller to position servomechanism. 7th World Congress on Intelligent Control and Automation (pp. 3380–3383).Google Scholar
  22. Zheng, W., Wang, X., & Pi, Y. (2015). Study of the fractional order proportional integral controller for PMSM based on differential evolution algorithm. In 2015 IEEE Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), Chongqing (pp. 201–205).Google Scholar

Copyright information

© Brazilian Society for Automatics--SBA 2019

Authors and Affiliations

  1. 1.Faculty of Engineering, Architecture and Urban Planning and GeographyFederal University of Mato Grosso do SulCampo GrandeBrazil

Personalised recommendations