Pragmatic Design Methods Using Adaptive Controller Structures for Mechatronic Applications with Variable Parameters and Working Conditions

  • Stefan PreitlEmail author
  • Radu-Emil Precup
  • Zsuzsa Preitl
  • Alexandra-Iulia Stînean
  • Claudia-Adina Dragoş
  • Mircea-Bogdan Rădac
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 55)


This chapter treats two pragmatic design methods for controllers dedicated to mechatronic applications working under variable conditions; for such applications adaptive structures of the control algorithms are of great interest. Basically, the design is based on two extensions of the modulus optimum method and of the symmetrical optimum method (SO-m): the Extended SO-m and the double parameterization of the SO-m (2p-SO-m). Both methods are introduced by the authors and they use PI(D) controllers that can ensure high control performance: increased value of the phase margins, improved tracking performance, and efficient disturbance rejection. A short and systematic presentation of the methods and digital implementation aspects using an adaptive structure of the algorithms for industrial applications are given. The application deals with a cascade speed control structure for a driving system with continuously variable parameters, i.e., electrical drives with variable reference input, variable moment of inertia and variable disturbance input.


Fuzzy Controller Controller Parameter Phase Margin Variable Reference Load Disturbance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Abbreviations


Symmetrical Optimum method


Modulus Optimum method


Extended Symmetrical Optimum method


Double parameterization of the SO-m


Two Degree of Freedom


Variable Moment of Inertia


Transfer function


Control algorithm


Continuously Variable Reference, Moment of Inertia and Load Disturbance

DC-m, BLDC-m

DC-motors, Brush-Less DC-motors


Mathematical Model


Control Structure


Cascade Control Structure



This work was supported by a grant in the framework of the Partnerships in priority areas—PN II program of the Romanian National Authority for Scientific Research ANCS, CNDI - UEFISCDI, project number PN-II-PT-PCCA-2011-3.2-0732, by a grant of the Romanian National Authority for Scientific Research, CNCS - UEFISCDI, project number PN-II-ID-PCE-2011-3-0109. Also, the work was partially supported by the strategic grant POSDRU ID 77265 (2010) of the Ministry of Labor, Family and Social Protection, Romania, co-financed by the European Social Fund—Investing in People.


  1. 1.
    Åström, K.J., Hägglund, T.: PID Controllers Theory: Design and Tuning. Instrument Society of America, Research Triangle Park, NC (1995)Google Scholar
  2. 2.
    Föllinger, O.: Regelungstechnik. Elitera Verlag, Berlin (1985)Google Scholar
  3. 3.
    Kessler, C.: Das symetrische Optimum. Regelungstechnik 6(11), 395–400 (1958)zbMATHGoogle Scholar
  4. 4.
    Kessler, C.: Das symetrische Optimum. Regelungstechnik 6(12), 432–436 (1958)Google Scholar
  5. 5.
    Loron, L.: Tuning of PID controllers by the non-symmetrical optimum method. Automatica 33(1), 103–107 (1997)CrossRefzbMATHGoogle Scholar
  6. 6.
    Preitl, S., Precup, R.-E.: An extension of tuning relations after symmetrical optimum method for PI and PID controllers. Automatica 35(10), 1731–1736 (1999)CrossRefzbMATHGoogle Scholar
  7. 7.
    Vrancic, D., Peng, Y., Strmcnik, S.: A new PID controller tuning method based on multiple integrations. Control Eng. Pract. 7(5), 623–633 (1999)CrossRefGoogle Scholar
  8. 8.
    Vrancic, D., Strmcnik, S., Juricic, D.: A magnitude optimum multiple integration tuning method for filtered PID controller. Automatica 37(9), 1473–1479 (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Preitl, Z.: Improving disturbance rejection by means of a double parameterization of the symmetrical optimum method. Sci. Bull. “Politehnica” Univ. Timisoara, Trans. Autom. Comput. Sci. 50(64), 25–34 (2005)Google Scholar
  10. 10.
    Preitl, Z.: Model Based Design Methods for Speed Control Applications. Editura Politehnica, Timisoara, Romania (2008)Google Scholar
  11. 11.
    Vrančić, D., Strmčnik, S., Kocijan, J., de Moura Oliveira, P.B.: Improving disturbance rejection of PID controllers by means of the magnitude optimum method. ISA Trans. 49(1), 47–56 (2010)Google Scholar
  12. 12.
    Papadopoulos, K.G., Mermikli, K., Margaris, N.I.: Optimal tuning of PID controllers for integrating processes via the symmetrical optimum criterion. In: Proceedings of 19th Mediterranean Conference on Control and Automation (MED 2012), Corfu, Greece, pp. 1289–1294 (2011)Google Scholar
  13. 13.
    Papadopoulos, K.G., Mermikli, K., Margaris, N.I.: On the automatic tuning of PID type controllers via the magnitude optimum criterion. In: Proceedings of 2012 IEEE International Conference on Industrial Technology (ICIT 2012), Athens, Greece, pp. 869–874 (2012)Google Scholar
  14. 14.
    Papadopoulos, K.G., Margaris, N.I.: Extending the symmetrical optimum criterion to the design of PID type-p control loops. J. Process Control 22(1), 11–25 (2012)CrossRefGoogle Scholar
  15. 15.
    Isermann, R.: Mechatronic Systems: Fundamentals. Springer, Berlin, Heidelberg, New York (2005)Google Scholar
  16. 16.
    Preitl, S., Precup, R.-E.: Cross optimization aspects concerning the extended symmetrical optimum method. Preprints of PID’00 IFAC Workshop, Terrassa, Spain, pp. 223–228 (2000)Google Scholar
  17. 17.
    Preitl, S., Precup, R.-E.: Linear and fuzzy control extensions of the symmetrical optimum method. In: Kolemisevska-Gugulovska, T., Stankovski, M.J. (eds.) Proceedings COSY 2011 of the Special International Conference on Complex Systems: Synergy of Control, Computing & Communication, Ohrid, Macedonia, 16–20 September. The ETAI Society, Skopje, MK, pp. 59–68 (2011)Google Scholar
  18. 18.
    Precup, R.-E., Preitl, S.: Development of some fuzzy controllers with non-homogenous dynamics with respect to the input channels meant for a class of systems. In: Proceedings of European Control Conference (ECC’99), Karlsruhe, Germany, paper index F56, 6 pp (1999)Google Scholar
  19. 19.
    Preitl, S., Precup, R.-E., Preitl, Z.: Control Structures and Algorithms, vols. 1 and 2. Editura Orizonturi Universitare, Timisoara, Romania (2009) (in Romanian)Google Scholar
  20. 20.
    Preitl, S., Precup, R.-E.: Development of TS fuzzy controllers with dynamics for low order benchmarks with time variable parameters. In: Proceedings of 5th International Symposium of Hungarian Researchers on Computational Intelligence, Budapest, Hungary, pp. 239–248 (2004)Google Scholar
  21. 21.
    Preitl, S., Preitl, Z., Precup, R.-E.: Low cost fuzzy controllers for classes of second-order systems. Preprints of 15th World Congress of IFAC (b’02), Barcelona, Spain, paper index 416, 6 pp (2002)Google Scholar
  22. 22.
    Precup, R.-E., Hellendoorn, H.: A survey on industrial applications of fuzzy control. Comput. Ind. 62(3), 213–226 (2011)CrossRefGoogle Scholar
  23. 23.
    Koch, C., Radler, O., Spröwitz, A., Ströhla, T., Zöppig, V.: Project course ‘Design mechatronic systems’. In: Proceedings of IEEE International Conference on Mechatronics (ICM 2006), Budapest, Hungary, pp. 69–72 (2006)Google Scholar
  24. 24.
    Hehenberger, P., Naderer, R., Schuler, C., Zeman, K.: Conceptual design of mechatronic systems as a recurring element of innovation processes. In: Proceedings of 4th IFAC Symposium on Mechatronic Systems (MECHATRONICS 2006), Heidelberg, Germany, pp. 342–347 (2006)Google Scholar
  25. 25.
    Pabst, I.: An approach for reliability estimation and control of mechatronic systems. In: Proceedings of 4th IFAC Symposium on Mechatronic Systems (MECHATRONICS 2006), Heidelberg, Germany, pp. 831–836 (2006)Google Scholar
  26. 26.
    Su, Y., Mueller, C.: Smooth reference trajectory generation for industrial mechatronic systems under torque saturation. In: Proceedings of 4th IFAC Symposium on Mechatronic Systems (MECHATRONICS 2006), Heidelberg, Germany, pp. 896–901 (2006)Google Scholar
  27. 27.
    Boldea, I.: Advanced electric drives. Ph.D. courses. “Politehnica” Univ. Timisoara, Timisoara, Romania (2010–2011)Google Scholar
  28. 28.
    Nasar, S.A., Boldea, I.: Electric Drives. Electric Power Engineering Series, 2nd edn. CRC Press, Boca Raton (2005)Google Scholar
  29. 29.
    Yedamale, P.: Brushless DC (BLDC) Motor Fundamentals. Application Note 885, Microchip Technology Inc., Chandler, AZ (2003)Google Scholar
  30. 30.
    Baldursson, S.: BLDC motor modelling and control—A Matlab/Simulink implementation. M.Sc. Thesis, Institutionen för Energi och Miljö, Göteborg, Sweden (2005)Google Scholar
  31. 31.
    Grimble, M.J., Hearns, G.: Advanced control for hot rolling mills. In: Frank, P.-M. (ed.) Advances in Control: Highlights of ECC’99, pp. 135–170. Springer, London (1999)Google Scholar
  32. 32.
    Stînean, A.-I., Preitl, S., Precup, R.-E., Dragoş, C.-A., Petriu, E., Rădac, M.-B.: Choosing a proper control structure for a mechatronic system with variable parameters. Preprints of 2nd IFAC Workshop on Convergence of Information Technologies and Control Methods with Power Systems (ICPS’13), Cluj-Napoca, Romania, paper index 29, 6 pp (2013)Google Scholar
  33. 33.
    Škrjanc, I., Blažič, S., Matko, D.: Direct fuzzy model-reference adaptive control. Int. J. Intell. Syst. 17(10), 943–963 (2002)CrossRefzbMATHGoogle Scholar
  34. 34.
    Baranyi, P., Tikk, D., Yam, Y., Patton, R.J.: From differential equations to PDC controller design via numerical transformation. Comput. Ind. 51(3), 281–297 (2003)CrossRefzbMATHGoogle Scholar
  35. 35.
    Zhao, J., Dimirovski, G.M.: Quadratic stability of a class of switched nonlinear systems. IEEE Trans. Autom. Control 49(4), 574–578 (2004)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Nakashima, T., Schaefer, G., Yokota, Y., Ishibuchi, H.: A weighted fuzzy classifier and its application to image processing tasks. Fuzzy Sets Syst. 158(3), 284–294 (2007)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Vaščák, J.: Approaches in adaptation of fuzzy cognitive maps for navigation purposes. In: Proceedings of 8th International Symposium on Applied Machine Intelligence and Informatics (SAMI 2010), Herl’any, Slovakia, pp. 31–36 (2010)Google Scholar
  38. 38.
    Lian, J., Zhao, J., Dimirovski, G.M.: Integral sliding mode control for a class of uncertain switched nonlinear systems. Eur. J. Control 16(1), 16–22 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Milojković, M., Nikolić, S., Danković, B., Antić, D., Jovanović, Z.: Modelling of dynamical systems based on almost orthogonal polynomials. Math. Comput. Modell. Dyn. Syst. 16(2), 133–144 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Tikk, D., Johanyák, Z.C., Kovács, S., Wong, K.W.: Fuzzy rule interpolation and extrapolation techniques: criteria and evaluation guidelines. J. Adv. Comput. Intell. Intell. Inf. 15(3), 254–263 (2011)Google Scholar
  41. 41.
    Angelov, P., Yager, R.: A new type of simplified fuzzy rule-based systems. Int. J. Gen Syst. 41(2), 163–185 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Triharminto, H.H., Adji, T.B., Setiawan, N.A.: 3D dynamic UAV path planning for interception of moving target in cluttered environment. Int. J. Artif. Intell. 10(S13), 154–163 (2013)Google Scholar
  43. 43.
    Wang, Y., Yang, Y., Zhao, Z.: Robust stability analysis for an enhanced ILC-based PI controller. J. Process Control 23(2), 201–214 (2013)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Stefan Preitl
    • 1
    Email author
  • Radu-Emil Precup
    • 1
  • Zsuzsa Preitl
    • 2
  • Alexandra-Iulia Stînean
    • 1
  • Claudia-Adina Dragoş
    • 1
  • Mircea-Bogdan Rădac
    • 1
  1. 1.Department of Automation and Applied Informatics“Politehnica” University of TimisoaraTimisoaraRomania
  2. 2.Siemens A.G.ErlangenGermany

Personalised recommendations