“Subspace System Identification of a Pilot Tunnel System of a Combined Sewage System”

Authors: Yongjie Wang and Finn Haugen,
Affiliation: University of South-Eastern Norway
Reference: 2023, Vol 44, No 2, pp. 69-82.

Keywords: Urban drainage systems, subspace system identification, drainage tunnel, model-based control, Saint-Venant equations

Abstract: This paper presents an investigation into the potential use of subspace identification methods (SIMs) for model-based control of urban drainage systems (UDS) that play a crucial role in collecting and transporting stormwater runoff and domestic sewage to Water Resource Recovery Facilities (WRRF) in urban areas. To evaluate the feasibility of level control using model-based algorithms in UDS, a pilot tunnel system was constructed. Three linear state-space models were identified using the system identification toolbox in MATLAB and an open-source module in Python named SIPPY. The study finds that the identified models can predict the system output with acceptable accuracy thus for model-based control of the system. The findings of this study aim to contribute to the development of more efficient and effective control strategies for UDS.

PDF PDF (3430 Kb)        DOI: 10.4173/mic.2023.2.3

[1] AakreHaugen, F. (2018). Simulations and real applications of PI and MPC averaging level control in a water resource recovery facility, In Proceedings of The 59th Conference on Simulation and Modelling (SIMS 59), 26-28 September 2018, Oslo Metropolitan University, Norway. pages 297--302. doi:10.3384/ecp18153297
[2] Armenise, G., Vaccari, M., DiCapaci, R.B., and Pannocchia, G. (2018). An Open-Source System Identification Package for Multivariable Processes, In 2018 UKACC 12th International Conference on Control (CONTROL). IEEE, Sheffield, pages 152--157. doi:10.1109/CONTROL.2018.8516791
[3] Breckpot, M., Agudelo, O.M., and DeMoor, B. (2012). Model Predictive Control applied to a river system with two reaches, In 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). IEEE, Maui, HI, USA, pages 4549--4554. doi:10.1109/CDC.2012.6426501
[4] Cen, L., Xi, Y., and Li, D. (2010). Aggregation-based model predictive control of open channel networks, In Proceedings of the 29th Chinese Control Conference. IEEE, pages 3170--3175. https://ieeexplore.ieee.org/abstract/document/5572239.
[5] Chanson, H. (2004). Hydraulics of open channel flow, Elsevier. doi:10.1016/B978-0-7506-5978-9.X5000-4
[6] DiRuscio, D. (1997). Subspace system identification: Theory and applications, Lecture notes, Telemark University College, Porsgrunn, Norway, 1997. http://davidr.no/iia2217/pensum/main_00.pdf.
[7] DiRuscio, D. (2001). Model predictive control and optimization, Lecture notes, System and Control Engineering Department of Technology Telemark University College. https://web01.usn.no/davidr/sce4106/syllabus/main_mpc.pdf.
[8] DiRuscio, D. and Foss, B. (1998). On state space model based predictive control, IFAC Proceedings Volumes. 31(11):301--306. Publisher: Elsevier. doi:10.1016/S1474-6670(17)44945-7
[9] García, C.E., Prett, D.M., and Morari, M. (1989). Model predictive control: Theory and practice—A survey, Automatica. 25(3):335--348. doi:10/br9kgh
[10] Igreja, J.M., Cadete, F.M., and Lemos, J.M. (2011). Application of distributed model predictive control to a water delivery canal, In 2011 19th Mediterranean Conference on Control & Automation (MED). IEEE, Corfu, Greece, pages 682--687. doi:10/fgwvjh
[11] Kamboh, S.A., Sarbini, I.N., Labadin, J., and Eze, M.O. (2016). Simulation of 2D Saint-Venant equations in open channel by using MATLAB, Journal of IT in Asia. 5(1):15--22. doi:10/ghcsm9
[12] Kurganov, A. and Levy, D. (2002). Central-Upwind Schemes for the Saint-Venant System, ESAIM: Mathematical Modelling and Numerical Analysis. 36(3):397--425. doi:10.1051/m2an:2002019
[13] Kurganov, A. and Petrova, G. (2007). A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System, Communications in Mathematical Sciences. 5(1):133--160. doi:10.4310/CMS.2007.v5.n1.a6
[14] Litrico, X. and Fromion, V. (2009). Modeling and control of hydrosystems, Springer, London. doi:10.1007/978-1-84882-624-3
[15] Ljung, L. (1998). System identification, In A.Procházka, J.Uhlíř, P.W.J. Rayner, and N.G. Kingsbury, editors, Signal analysis and prediction, pages 163--173. Birkhäuser Boston, Boston, MA. doi:10.1007/978-1-4612-1768-8_11
[16] Ljung, L. (1999). System identification: theory for the user, Prentice Hall information and system sciences series. Prentice Hall PTR, Upper Saddle River, NJ, 2nd ed edition. doi:10.1016/S0005-1098(01)00214-X
[17] Lund, N. S.V., Falk, A. K.V., Borup, M., Madsen, H., and SteenMikkelsen, P. (2018). Model predictive control of urban drainage systems: A review and perspective towards smart real-time water management, Critical Reviews in Environmental Science and Technology, 2018. 48(3):279--339. doi:10.1080/10643389.2018.1455484
[18] MathWorks. (2023). Loss Function and Model Quality Metrics, 2023. https://se.mathworks.com/help/ident/ug/model-quality-metrics.html.
[19] MATLAB. (2023). System Identification Toolbox version: 10, 0 (r2022b). 2023. https://www.mathworks.com.
[20] Muroi, H. and Adachi, S. (2015). Model Validation Criteria for System Identification in Time Domain, IFAC-PapersOnLine. 48(28):86--91. doi:10.1016/j.ifacol.2015.12.105
[21] Ocampo-Martinez, C., Puig, V., Cembrano, G., and Quevedo, J. (2013). Application of Predictive Control Strategies to the Management of Complex Networks in the Urban Water Cycle, IEEE Control Systems Magazine. 33(1):15--41. doi:10.1109/MCS.2012.2225919
[22] Pannocchia, G. and Calosi, M. (2010). A predictor form PARSIMonious algorithm for closed-loop subspace identification, Journal of Process Control. 20(4):517--524. doi:10.1016/j.jprocont.2010.01.004
[23] Qin, S.J. (2006). An overview of subspace identification, Computers & Chemical Engineering. 30(10-12):1502--1513. doi:10.1016/j.compchemeng.2006.05.045
[24] Qin, S.J., Lin, W., and Ljung, L. (2005). A novel subspace identification approach with enforced causal models, Automatica. 41(12):2043--2053. doi:10.1016/j.automatica.2005.06.010
[25] Qin, S.J. and Ljung, L. (2003). Closed-loop subspace identification with innovation estimation, IFAC Proceedings Volumes. 36(16):861--866. doi:10.1016/S1474-6670(17)34868-1
[26] SciPy.org. (2023). scipy, signal.dlsim. 2023. https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.dlsim.html.
[27] VanOverschee, P. and DeMoor, B. (1996). Subspace Identification for Linear Systems, Springer US, Boston, MA. doi:10.1007/978-1-4613-0465-4
[28] Xu, M., Negenborn, R., van Overloop, P., and vande Giesen, N. (2012). De Saint-Venant equations-based model assessment in model predictive control of open channel flow, Advances in Water Resources. 49:37--45. ZSCC: 0000029. doi:10/f4d992
[29] Xu, M., van Overloop, P., and vande Giesen, N. (2011). On the study of control effectiveness and computational efficiency of reduced Saint-Venant model in model predictive control of open channel flow, Advances in Water Resources. 34(2):282--290. doi:10.1016/j.advwatres.2010.11.009
[30] Yang, H.-C. and Chang, F.-J. (2005). Modelling combined open channel flow by artificial neural networks, Hydrological Processes. 19(18):3747--3762. doi:10.1002/hyp.5858

  title={{Subspace System Identification of a Pilot Tunnel System of a Combined Sewage System}},
  author={Wang, Yongjie and Haugen, Finn},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}