“PD/PID controller tuning based on model approximations: Model reduction of some unstable and higher order nonlinear models”

Authors: Christer Dalen and David Di Ruscio,
Affiliation: University of South-Eastern Norway
Reference: 2017, Vol 38, No 4, pp. 185-197.

Keywords: PD and PID controllers, tuning, double integrating system, time delay, maximum time delay error, relative time delay margin, robustness, performance, Pareto Optimal

Abstract: A model reduction technique based on optimization theory is presented, where a possible higher order system/model is approximated with an unstable DIPTD model by using only step response data. The DIPTD model is used to tune PD/PID controllers for the underlying possible higher order system. Numerous examples are used to illustrate the theory, i.e. both linear and nonlinear models. The Pareto Optimal controller is used as a reference controller.

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DOI forward links to this article:
[1] Christer Dalen and David Di Ruscio (2018), doi:10.4173/mic.2018.1.4
[2] A. Hanif Halim and I. Ismail (2018), doi:10.1007/s00521-018-3588-9
[3] Christer Dalen and David Di Ruscio (2018), doi:10.4173/mic.2018.4.4
[4] Adri Senen, Titi Ratnasari, Yoakim Simamora, B. Warsito, Sudarno and T. Triadi Putranto (2020), doi:10.1051/e3sconf/202020215006
[1] Aastrom, K. and Haegglund, T. (1995). Aastrom, K, and Haegglund, T. PID Controllers: Theory, Design, and Tuning. Instrument Society of America. .
[2] Aastrom, K.J., Panagopoulos, H., and Haegglund, T. (1998). Aastrom, K, J., Panagopoulos, H., and Haegglund, T. Design of pi controllers based on non-convex optimization. Automatica. 34(5):585--601. doi:10.1016/S0005-1098(98)00011-9
[3] Balchen, J. (1958). Balchen, J, A Performance Index for Feedback Control Systems Based on the Fourier Transform of the Control Deviation. Acta polytechnica Scandinavica: Mathematics and computing machinery series. Norges tekniske vitenskapsakademi. .
[4] Boubaker, O. (2012). Boubaker, O, The inverted pendulum: A fundamental benchmark in control theory and robotics. 2012. pages 1--6. doi:10.1109/ICEELI.2012.6360606
[5] DiRuscio, D. (1996). DiRuscio, D, Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations. Modeling, Identification and Control. 17(3):193--230. doi:10.4173/mic.1996.3.3
[6] DiRuscio, D. (2009). DiRuscio, D, Closed and Open Loop Subspace System Identification of the Kalman Filter. Modeling, Identification and Control. 30(2):71--86. doi:10.4173/mic.2009.2.3
[7] DiRuscio, D. (2010). DiRuscio, D, On Tuning PI Controllers for Integrating Plus Time Delay Systems. Modeling, Identification and Control. 31(4):145--164. doi:10.4173/mic.2010.4.3
[8] DiRuscio, D. (2012). DiRuscio, D, Pi controller tuning based on integrating plus time delay models: Performance optimal tuning. 2012. In Proceedings of the IASTED Control and Applications Conference. Crete Greece June 18-21. .
[9] DiRuscio, D. and Dalen, C. (2017). DiRuscio, D, and Dalen, C. Tuning PD and PID Controllers for Double Integrating Plus Time Delay Systems. Modeling, Identification and Control. 38(2):95--110. doi:10.4173/mic.2017.2.4
[10] Fossen, T.I. and Perez, T. (2004). Fossen, T, I. and Perez, T. Marine Systems Simulator (MSS). 2004. http://www.marinecontrol.org, .
[11] Garpinger, O. and Haegglund, T. (2014). Garpinger, O, and Haegglund, T. Modeling for optimal pid design. 2014. pages 6929--6934. Preprints of the 19th World Congress. .
[12] Jahanshahi, E. and Skogestad, S. (2013). Jahanshahi, E, and Skogestad, S. Closed-loop model identification and pid/pi tuning for robust anti-slug control. IFAC Proceedings Volumes. 46(32):233 -- 240. 10th IFAC International Symposium on Dynamics and Control of Process Systems. doi:10.3182/20131218-3-IN-2045.00009
[13] Lee, J., Cho, W., and Edgar, T.F. (2014). Lee, J, , Cho, W., and Edgar, T.F. Simple analytic pid controller tuning rules revisited. Industrial & Engineering Chemistry Research. 53(13):5038--5047. 10.1021/ie4009919, doi:10.1021/ie4009919
[14] L’Ingenieur, S. I.P. (2005). L’Ingenieur, S, I.P. Comportement dynamique d'un vehicule auto-balance de type segway. Concours Centrale-Supélec. https://www.concours-centrale-supelec.fr/CentraleSupelec/2005/PSI/sujets/SI.pdf. In french. Accessed 01.05.17. .
[15] Ljung, L. (1999). Ljung, L, System Identification (2nd ed.): Theory for the User. Prentice Hall PTR, Upper Saddle River, NJ, USA. .
[16] MATLAB. (2016). MATLAB, Version (R2016b). The MathWorks Inc., Natick, Massachusetts, USA. Control System Toolbox, Version 9.3. Optimization Toolbox, Version 6.2. .
[17] Pareto, V. (1894). Pareto, V, Il massimo di utilità dato dalla libera concorrenza. Giornale degli Economisti,luglio, 1894b. pages 48--66. .
[18] SchmidtZ., J. P. .B., Brill. (1979). SchmidtZ, , J. P. .B., Brill. Choking can eliminate severe pipeline slugging. 1979. 312:230--238. .
[19] Seborg, D., Edgar, T., and Mellichamp, D. (1989). Seborg, D, , Edgar, T., and Mellichamp, D. Process Dynamics and Control. Number v. 1 in Chemical Engineering Series. Wiley. .
[20] Seborg, D., Edgar, T., and Mellichamp, D. (2004). Seborg, D, , Edgar, T., and Mellichamp, D. Process dynamics and control. Wiley series in chemical engineering. Wiley. .
[21] Shannon, C.E. (1949). Shannon, C, E. Communication in the presence of noise. Proceedings of the IRE. 37(1):10--21. doi:10.1109/JRPROC.1949.232969
[22] Silva, G., Datta, A., and Bhattacharyya, S. (2005). Silva, G, , Datta, A., and Bhattacharyya, S. PID Controllers for Time-Delay Systems. Control Engineering. Birkhauser Boston. .
[23] Skogestad, S. (2003). Skogestad, S, Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control. 13(13):291--309. doi:10.1016/S0959-1524(02)00062-8
[24] Skogestad, S., Havre, K., and Larsson, T. (2002). Skogestad, S, , Havre, K., and Larsson, T. Control limitations for unstable plants. IFAC Proceedings Volumes. 35(1):485 -- 490. 15th IFAC World Congress. doi:10.3182/20020721-6-ES-1901.00330
[25] Skogestad, S. and Postlethwaite, I. (1996). Skogestad, S, and Postlethwaite, I. Multivariable feedback control: analysis and design. Wiley. .
[26] Son, K.H. and Nomoto, K. (1982). Son, K, H. and Nomoto, K. On the Coupled Motion of Steering and Rolling of a High Speed Container Ship. Naval Architect of Ocean Engineering. 20:73--83. .
[27] Yocum, B. (1973). Yocum, B, Offshore Riser Slug Flow Avoidance: Mathematical Models for Design and Optimization. Society of Petroleum Engineers of AIME. .
[28] Ziegler, J. and Nichols, N.B. (1942). Ziegler, J, and Nichols, N.B. Optimum settings for automatic controllers. Trans. of the A.S.M.E.. 64(64):759--768. .

  title={{PD/PID controller tuning based on model approximations: Model reduction of some unstable and higher order nonlinear models}},
  author={Dalen, Christer and Di Ruscio, David},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}