The mathematical model that approximates the dynamics of the industrial process is essential for the efficient synthesis of control algorithms in industrial applications. The model of the process can be obtained according to the identification procedures in the open-loop, or in the closed-loop. In the open-loop, the identification methods are well known and offer good process approximation, which is not valid for the closed-loop identification, when the system provides the feedback output and doesn’t permit it to be identified in the open-loop. This paper offers an approach for experimental identification in the closed-loop, which supposes the approximation of the process with inertial models, with or without time delay and astatism. The coefficients are calculated based on the values of the critical transfer coefficient and period of the underdamped response of the closed-loop system with P controller, when system achieves the limit of stability. Finally, the closed-loop identification was verified by the computer simulation and the obtained results demonstrated, that the identification procedure in the closed-loop offers good results in process of estimation of the model of the process.
References
[1]
Park, M.S., Yang, D.H., Park, D.G. and Hong, S.K. (2003) An Experimental Study on the Closed-Loop System Identification by Observer/Controller Identification (OCID) Algorithm. Proceedings of 2003 IEEE Conference on Control Applications, Istanbul, 25 June 2003, 37-42.
[2]
Forssell, U. and Ljung, L. (1999) Closed-Loop Identification Revisited. Journal of IFAC Automatica, 35, 1215-1241. https://doi.org/10.1016/S0005-1098(99)00022-9
[3]
Hornsey, S. (2018) A Review of Relay Auto-Tuning Methods for the Tuning of PID-Type Controllers. An International Journal of Undergraduate Research, 11, 1-1.1.
[4]
O’Dwyer, A. (2009) Handbook of PI and PID Controller Tuning Rules. 3rd Edition, Imperial College Press, London. https://doi.org/10.1142/p575
[5]
Ertveldt, J., Sanchez-Medina, J., Jardon, Z., Hinderdael, M. and Guillaume, P. (2022) Experimental Identification of Process Dynamics for Real-Time Control of Directed Energy Deposition. Procedia CIRP, 111, 321-325.
https://doi.org/10.1016/j.procir.2022.08.031
[6]
Kalil, C., de Castro, M., Silva, D. and Cortez, C. (2021) Applying Graph Theory and Mathematical-Computational Modelling to Study a Neurophysiological Circuit. Open Journal of Modelling and Simulation, 9, 159-171.
https://doi.org/10.4236/ojmsi.2021.92011
[7]
Ebadat, A. (2017) Experiment Design for Closed-Loop System Identification with Applications in Model Predictive Control and Occupancy Estimation. Doctoral Thesis, KTH Royal Institute of Technology, Stockholm.
[8]
Linder, J. and Enqvist, M. (2017) Identification of Systems with Unknown Inputs Using Indirect Input Measurements. International Journal of Control, 90, 729-745.
https://doi.org/10.1080/00207179.2016.1222557
[9]
Herrera, J., Ibeas, A., De la Sen, M., Alcántara, S. and Alonso-Quesada, S. (2013) Identification and Control of Delayed Unstable and Integrative LTI MIMO Systems Using Pattern Search Methods. Advances in Difference Equations, 2013, 331.
https://doi.org/10.1186/1687-1847-2013-331
[10]
Acioli Júnior, G., João, B.M. and Santos, Barros, P.R. (2009) On Simple Identification Techniques for First-Order plus Time-Delay Systems. IFAC Proceedings, 42, 605-610. https://doi.org/10.3182/20090706-3-FR-2004.00100
[11]
Laskawski, M.S. and Kazala, R. (2018) Identification of Parameters of Inertial Models Using the Levenberg-Marquardt Method. Proceedings of the 2018th Conference on Electrotechnology: Processes, Models, Control and Computer Science (EPMCCS), Kielce, 12-14 November 2018, 1-5.
https://doi.org/10.1109/EPMCCS.2018.8596396
[12]
Muroi, H. and Adachi, Sh. (2015) Model Validation Criteria for System Identification in Time Domain. IFAC-Papers onLine, 48, 86-91.
https://doi.org/10.1016/j.ifacol.2015.12.105
[13]
Huang, B. and Shah, S.L. (1997) Closed-Loop Identification: A Two Step Approach. Journal of Process Control, 7, 425-438.
https://doi.org/10.1016/S0959-1524(97)00019-X
[14]
Tufa, L.D. and Ramasamy, M. (2011) Closed-Loop Identification of Systems with Uncertain Time Delays Using ARX-OBF Structure. Journal of Process Control, 21, 1148-1154. https://doi.org/10.1016/j.jprocont.2011.06.021
[15]
Van den Hof, P. (1997) Closed-Loop Identification. IFAC Proceedings Series, 3, 1547-1560. https://doi.org/10.1016/S1474-6670(17)43063-1
[16]
Wang, J.H. and Ramirez-Mendoza, R.A. (2020) The Practical Analysis for Closed-Loop System Identification. Cogent Engineering, 7, Article ID: 1796895.
https://doi.org/10.1080/23311916.2020.1796895
[17]
Sharma, S., Verma, B. and Padhy, P.K. (2022) Closed-Loop Identification of Stable and Unstable Processes with Time-Delay. Journal of the Franklin Institute, 359, 3313-3332. https://doi.org/10.1016/j.jfranklin.2022.03.006
[18]
Padma Sree, R. and Chidambaram, M. (2006) Improved Closed Loop Identification of Transfer Function Model for Unstable Systems. Journal of the Franklin Institute, 343, 152-160. https://doi.org/10.1016/j.jfranklin.2005.10.001
[19]
Kurek, J. (2013) Identification of Inertial Model for Astatic System. Proceedings of the 18th International Conference on Methods & Models in Automation & Robotics (MMAR), Miedzyzdroje, 26-29 August 2013, 692-695.
https://doi.org/10.1109/MMAR.2013.6669995
