“Model-Free PI/PID Controller Tuning of Higher Order Nonlinear Dynamic Systems”
Authors: Christer Dalen and David Di Ruscio,Affiliation: University of South-Eastern Norway
Reference: 2019, Vol 40, No 4, pp. 199-211.
Keywords: model-free, process control, PI/PID control, subspace system identification, nonlinear
Abstract: This paper concerns model-free PI/PID controller tuning of possible (nonlinear) higher order systems. The method can be considered as a three-step procedure. The first step is to persistently excite the system in open loop and identify the dynamic model using a subspace identification method. The second step is to approximate the model to an integrator plus time delay or double integrator plus time delay dynamic model. The third step is to compute the PI/PID controller parameters. The proposed method/theory is verified on some motivated nonlinear higher order dynamic models.
PDF (831 Kb)
DOI: 10.4173/mic.2019.4.2References:
[1] Aastrom, K. and Haegglund, T. (1995). Aastrom, K, and Haegglund, T. PID Controllers: Theory, Design, and Tuning. Instrument Society of America. .
[2] Dalen, C. and DiRuscio, D. (2016). Dalen, C, and DiRuscio, D. Model-Free Predictive Anti-Slug Control of a Well-Pipeline-Riser. Modeling, Identification and Control. 37(1):41--52. doi:10.4173/mic.2016.1.4
[3] Dalen, C. and DiRuscio, D. (2018). Dalen, C, and DiRuscio, D. A Novel Process-Reaction Curve Method for Tuning PID Controllers. Modeling, Identification and Control, 2018. 39(4):273--291. doi:10.4173/mic.2018.4.4
[4] Dalen, C. and DiRuscio, D. (2018). Dalen, C, and DiRuscio, D. A Semi-Heuristic Process-Reaction Curve PID Controller Tuning Method. Modeling, Identification and Control, 2018. 39(1):37--43. doi:10.4173/mic.2018.1.4
[5] Dalen, C. and DiRuscio, D. (2018). Dalen, C, and DiRuscio, D. PI Controller Tuning Based on Integrating Plus Time Delay Models: Performance Optimal tuning. Algorithms, 2018. 11(4). .
[6] Dalen, C., DiRuscio, D., and Nilsen, R. (2015). Dalen, C, , DiRuscio, D., and Nilsen, R. Model-free optimal anti-slug control of a well-pipeline-riser in the K-Spice/LedaFlow simulator. Modeling, Identification and Control. 36(3):179--188. doi:10.4173/mic.2015.3.5
[7] 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
[8] DiRuscio, D. (2009). DiRuscio, D, A Bootstrap Subspace Identification Method: Comparing Methods for Closed Loop Subspace Identification by Monte Carlo Simulations. Modeling, Identification and Control. 30(4):203--222. doi:10.4173/mic.2009.4.2
[9] 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
[10] 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
[11] Dong, H.-R., Jin, S., and Hou, Z.-S. (2015). Dong, H, -R., Jin, S., and Hou, Z.-S. Model free adaptive control for automatic car parking systems. 2015. 2015:1769--1774. .
[12] Fliess, M. and Join, C. (2009). Fliess, M, and Join, C. Model-free control and intelligent PID controllers: towards a possible trivialization of nonlinear control? In 15th IFAC Symposium on System Identification (SYSID 2009). IFAC, Saint-Malo, France. .
[13] Fliess, M. and Join, C. (2013). Fliess, M, and Join, C. Model-free control. International Journal of Control. 86(12):2228--2252. doi:10.1080/00207179.2013.810345
[14] Fossen, T.I. and Perez, T. (2004). Fossen, T, I. and Perez, T. Marine Systems Simulator (MSS). 2004. https://github.com/cybergalactic/MSS. .
[15] Hou, Z.-S. and Wang, Z. (2013). Hou, Z, -S. and Wang, Z. From model-based control to data-driven control: Survey, classification and perspective. Information Sciences. 235:3--35. doi:10.1016/j.ins.2012.07.014
[16] K-Spice. (0). K-Spice, K-Spice version 2.11 2015. kongsberg.com/k-spice. .
[17] LedaFlow. (0). LedaFlow, LedaFlow version 1.7. 2015. kongsberg.com/ledaflow. .
[18] Ljung, L. (1999). Ljung, L, System Identification (2nd ed.): Theory for the User. Prentice Hall PTR, Upper Saddle River, NJ, USA. .
[19] MATLAB. (2016). MATLAB, Version 9.1.0.441655 (R2016b). The MathWorks Inc., Natick, Massachusetts, USA. Control System Toolbox, Version 9.3. Optimization Toolbox, Version 6.2. .
[20] Mracek, C. and Cloutier, J. (1997). Mracek, C, and Cloutier, J. Missile longitudinal autopilot design using the state-dependent riccati equation method. Guidance, Navigation, and Control Conference. pages 1--6. .
[21] Schmidt, Z., Brill, J.P., and Beggs, H.D. (1979). Schmidt, Z, , Brill, J.P., and Beggs, H.D. Choking can eliminate severe pipeline slugging. Oil & Gas J.. (12):230--238. .
[22] 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. .
[23] Skogestad, S. (2003). Skogestad, S, Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control. 13(4):291--309. doi:10.1016/S0959-1524(02)00062-8
[24] Soederstroem, T. and Stoica, P. (1989). Soederstroem, T, and Stoica, P. System Identification. Prentice-Hall international series in systems and control engineering. Prentice-Hall. .
[25] Wang, J., Zhang, Y., Jin, X., and Su, H. (2018). Wang, J, , Zhang, Y., Jin, X., and Su, H. A Recursive Tuning Approach for the Model-Free PIDController Design. IFAC-PapersOnLine, 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control PID 2018. 51(4):143--147. doi:10.1016/j.ifacol.2018.06.116
[26] Ziegler, J.G. and Nichols, N.B. (1942). Ziegler, J, G. and Nichols, N.B. Optimum Settings for Automatic Controllers. Trans. American Society of Mechanical Engineers. 64:759--768. .
BibTeX:
@article{MIC-2019-4-2,
title={{Model-Free PI/PID Controller Tuning of Higher Order Nonlinear Dynamic Systems}},
author={Dalen, Christer and Di Ruscio, David},
journal={Modeling, Identification and Control},
volume={40},
number={4},
pages={199--211},
year={2019},
doi={10.4173/mic.2019.4.2},
publisher={Norwegian Society of Automatic Control}
};