Conference article

Efficient hybrid simulation of autotuning PI controllers

Alberto Leva
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy

Marco Bonvini
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy

Download article

Published in: Proceedings of the 8th International Modelica Conference; March 20th-22nd; Technical Univeristy; Dresden; Germany

Linköping Electronic Conference Proceedings 63:8, p. 56-63

Show more +

Published: 2011-06-30

ISBN: 978-91-7393-096-3

ISSN: 1650-3686 (print), 1650-3740 (online)


Autotuning methods are typically conceived as procedures; thus need simulating as digital blocks. However; when no autotuning is in progress; it is far more efficient to represent the tuned controller as a continuous-time system; to exploit variable-step integration. This manuscript presents the first nucleus of a Modelica library of autotuning controllers; where the problem just mentioned is tackled explicitly. The focus is here restricted to the PI structure; but the presented ideas are general.


Autotuning; PI control; hybrid systems’ simulation


[1] K.J. Åström and T. Hägglund. Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica; 20(5):645–651; 1984. doi: 10.1016/0005-1098(84)90014-1.

[2] K.J. Åström and T. Hägglund. Industrial adaptive controllers based on frequency response techniques. Automatica; 27(4):599–609; 1991. doi: 10.1016/0005-1098(91)90052-4.

[3] K.J. Åström and T. Hägglund. Advanced PID control. Instrument Society of America; Research Triangle Park; NY; 2006.

[4] A. Besançon-Voda and H. Roux-Buisson. Another version of the relay feedback experiment. Journal of Process Control; 7(4):303–308; 1997. doi: 10.1016/S0959-1524(97)00018-8.

[5] R.C. Dorf and H. Bishop. Modern control systems. Addison-Wesley; Reading; UK; 1995.

[6] M. Gevers. Identification for control: from the early achievements to the revival of experiment design. European Journal of Control; 11(4–5):335–352; 2005. doi: 10.3166/ejc.11.335-352.

[7] H. Hjalmarsson. From experiment design to closed-loop control. Automatica; 43:393–438; 2005. doi: 10.1016/j.automatica.2004.11.021.

[8] A. Leva. PID autotuning algorithm based on relay feedback. IEE Proceedings-D; 140(5):328–338; 1993.

[9] A. Leva. Simple model-based PID autotuners with rapid relay identification. In Proc. 16th IFAC World Congress; Praha; Czech Republic; 2005.

[10] A. Leva and F. Donida. Normalised expression and evaluation of pi tuning rules. In Proc. 17th IFAC World Congress; Seoul; Korea; 2008.

[11] A. Leva and F. Donida. Quality indices for the autotuning of industrial regulators. IET Control Theory & Applications; 3(21):170–180; 2009.

[12] A. Leva; S. Negro; and A.V. Papadopoulos. PI/PID autotuning with contextual model parametrisation. Journal of Process Control; 20(4):452–463; 2010. doi: 10.1016/j.jprocont.2010.01.005.

[13] A. Leva and L. Piroddi. Model-specific autotuning of classical regulator: a neural approach to structural identification. Control Engineering and Practice; 4(10):1381–1391; 1996. doi: 10.1016/0967-0661(96)00148-7.

[14] A. Leva and L. Piroddi. On the parameterisation of simple process models for the autotuning of industrial regulators. In 26th American Control Conference (to appear); New York (USA); 2007.

[15] Y. Li; K.H. Ang; and C.Y. Chong. Patents; software; and hardware for PID control—an overview and analysis of the current art. IEEE Control Systems Magazine; pages 42–54; february 2006.

[16] W.L. Luyben. Getting more information from relay feedback tests. Industrial & Engineering Chemistry Research; 40(20):4391–4402; 2001. doi: 10.1021/ie010142h.

[17] A. O’Dwyer. Handbook of PI and PID controller tuning rules. World Scientific Publishing; Singapore; 2003. doi: 10.1142/p277.

[18] R.C. Panda and C.C. Yu. Analytical expressions for relay feed back responses. Journal of Process Control; 13:489–501; 2003. doi: 10.1016/S0959-1524(02)00119-1.

[19] F.G. Shinskey. Process control: as taught versus as practiced. Industrial & Engineering Chemistry Research; 41(16):3745–3750; 2002. doi: 10.1021/ie010645n.

[20] T. Thyagarajan and C.C. Yu. Improved autotuning using the shape factor from relay feedback. Ind. Eng. Chem. Res.; 43:4425–4440; 2003. doi: 10.1021/ie011006f.

[21] C.C. Yu. Autotuning of PID controllers: relay feedback approach. Springer-Verlag; London; 1999. doi: 10.1007/978-1-4471-3636-1.

Citations in Crossref