Tracking-error control via the relaxing port-Hamiltonian formulation: Application to level control and batch polymerization reactor

Authors

T. Sang Nguyen, N. Ha Hoang, Mohd Azlan Hussain, Chee Keong Tan

Abstract

In this paper, a tracking-error-based control design without feedback passivation stage is developed for the stabilization of physical and chemical nonlinear processes. To achieve control objectives, the system dynamics is first formulated under appropriate conditions as a relaxing (pseudo) port-Hamiltonian (PH) representation with some quadratic storage function, in which the positive semi-definite property of damping matrix may not be taken necessarily into account. Then, a reference trajectory expressed by a certain structure passing through a desired set-point (or containing an optimal profile) is suitably chosen. By adding a relevant damping injection, asymptotic and global convergence of error dynamics is guaranteed. Two case studies including the level control of a four-tank process of continuous time type and the optimal tracking of a batch polymerization reactor of discontinuous time type due to the nature of the process operation are used to illustrate the application and the effectiveness of the approach. Besides the control performance comparison with the conventional passivity-based control method and the robustness evaluation against disturbance and/or noise are included.

Keywords

Port-Hamiltonian formulation; Tracking-error method; Passivity-based control; Nonlinear system

Citation

• Journal: Journal of Process Control
• Year: 2019
• Volume: 80
• Issue:
• Pages: 152–166
• Publisher: Elsevier BV
• DOI: 10.1016/j.jprocont.2019.05.014

BibTeX

@article{Nguyen_2019,
  title={{Tracking-error control via the relaxing port-Hamiltonian formulation: Application to level control and batch polymerization reactor}},
  volume={80},
  ISSN={0959-1524},
  DOI={10.1016/j.jprocont.2019.05.014},
  journal={Journal of Process Control},
  publisher={Elsevier BV},
  author={Nguyen, T. Sang and Hoang, N. Ha and Hussain, Mohd Azlan and Tan, Chee Keong},
  year={2019},
  pages={152--166}
}

Download the bib file

References

• Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493
• Willems, J. C. Dissipative dynamical systems Part II: Linear systems with quadratic supply rates. Archive for Rational Mechanics and Analysis vol. 45 352–393 (1972) – 10.1007/bf00276494
• Brogliato, Dissipative system analysis and control. (2007)
• Van der Schaft, (2000)
• Ortega, Passivity-based control of nonlinear systems: a tutorial. (1997)
• Van der Schaft, Port-controlled Hamiltonian systems: towards a theory for control and design of nonlinear physical systems. SICE J. (2000)
• Ortega, (2013)
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Transactions on Automatic Control vol. 45 1498–1502 (2000) – 10.1109/9.871758
• Ortega, R., Jeltsema, D. & Scherpen, J. M. A. Power shaping: A new paradigm for stabilization of nonlinear RLC circuits. IEEE Transactions on Automatic Control vol. 48 1762–1767 (2003) – 10.1109/tac.2003.817918
• Jeltsema, D., Ortega, R. & M.A. Scherpen, J. An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems. Automatica vol. 40 1643–1646 (2004) – 10.1016/j.automatica.2004.04.007
• Favache, A. & Dochain, D. Power-shaping control of reaction systems: The CSTR case. Automatica vol. 46 1877–1883 (2010) – 10.1016/j.automatica.2010.07.011
• Favache, A., Dochain, D. & Winkin, J. J. Power-shaping control: Writing the system dynamics into the Brayton–Moser form. Systems & Control Letters vol. 60 618–624 (2011) – 10.1016/j.sysconle.2011.04.021
• Hoang, H., Couenne, F., Dochain, D. & Le Gorrec, Y. From Brayton-Moser formulation to Port Hamiltonian representation: the CSTR case study. IFAC Proceedings Volumes vol. 44 1628–1633 (2011) – 10.3182/20110828-6-it-1002.02464
• Hoang, Thermodynamics based stabilitization of CSTR networks. (2012)
• Sira-Ramirez, H. & Angulo-Nunez, M. I. Passivity-based control of nonlinear chemical processes. International Journal of Control vol. 68 971–996 (1997) – 10.1080/002071797223163
• Sira-Ramirez, H. A general canonical form for feedback passivity of nonlinear systems. International Journal of Control vol. 71 891–905 (1998) – 10.1080/002071798221623
• Riverol, C. Passivity-based control for a non-isothermal tank used in the production of pineapple syrup. Food Control vol. 12 373–378 (2001) – 10.1016/s0956-7135(01)00011-1
• Fossas, E., Ros, R. M. & Sira-Ramírez, H. Passivity-Based Control of a Bioreactor System. Journal of Mathematical Chemistry vol. 36 347–360 (2004) – 10.1023/b:jomc.0000044522.36742.4b
• Nguyen, N. T., Prodan, I. & Lefèvre, L. Flat trajectory design and tracking with saturation guarantees: a nano-drone application. International Journal of Control vol. 93 1266–1279 (2018) – 10.1080/00207179.2018.1502474
• Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Automatic Control vol. 36 1228–1240 (1991) – 10.1109/9.100932
• Sepulchre, R., Janković, M. & Kokotović, P. V. Constructive Nonlinear Control. Communications and Control Engineering (Springer London, 1997). doi:10.1007/978-1-4471-0967-9 – 10.1007/978-1-4471-0967-9
• Nguyen, Tracking error plus damping injection control of non-minimum phase processes. 10th Symposium on Advanced Control of Chemical Process (2018)
• Sbarbaro, D. & Ortega, R. Averaging level control: An approach based on mass balance. Journal of Process Control vol. 17 621–629 (2007) – 10.1016/j.jprocont.2007.01.005
• Johnsen, Interconnection and damping assignment passivity-based control of a four-tank system. (2007)
• ALTINTEN, A. & ERDOĞAN, S. TRACKING PERFORMANCE OF CONTROL METHODS. Chemical Engineering Communications vol. 181 21–36 (2000) – 10.1080/00986440008912813
• Altınten, A., Erdoğan, S., Hapoğlu, H. & Alpbaz, M. Control of a polymerization reactor by fuzzy control method with genetic algorithm. Computers & Chemical Engineering vol. 27 1031–1040 (2003) – 10.1016/s0098-1354(03)00073-5
• Hosen, M. A. et al. Performance analysis of three advanced controllers for polymerization batch reactor: An experimental investigation. Chemical Engineering Research and Design vol. 92 903–916 (2014) – 10.1016/j.cherd.2013.07.032
• Dörfler, F., Johnsen, J. K. & Allgöwer, F. An introduction to interconnection and damping assignment passivity-based control in process engineering. Journal of Process Control vol. 19 1413–1426 (2009) – 10.1016/j.jprocont.2009.07.015
• Ramírez, H., Sbarbaro, D. & Ortega, R. On the control of non-linear processes: An IDA–PBC approach. Journal of Process Control vol. 19 405–414 (2009) – 10.1016/j.jprocont.2008.06.018
• Hoang, N. H., Mai, T. P. & Dochain, D. On the relaxing dissipation of dissipative pseudo Hamiltonian models. IFAC-PapersOnLine vol. 48 1051–1056 (2015) – 10.1016/j.ifacol.2015.09.107
• Larsen, M., Janković, M. & Kokotović, P. V. Coordinated passivation designs. Automatica vol. 39 335–341 (2003) – 10.1016/s0005-1098(02)00237-6
• Hudon, N., Ha Hoang, N., Paulo García-Sandoval, J. & Dochain, D. Towards a potential-based analysis of reacting systems. IFAC-PapersOnLine vol. 48 141–143 (2015) – 10.1016/j.ifacol.2015.10.228
• Guay, M. & Hudon, N. Stabilization of Nonlinear Systems via Potential-Based Realization. IEEE Transactions on Automatic Control vol. 61 1075–1080 (2016) – 10.1109/tac.2015.2455671
• Hoang, N. H., Dochain, D., Couenne, F. & Le Gorrec, Y. Dissipative pseudo-Hamiltonian realization of chemical systems using irreversible thermodynamics. Mathematical and Computer Modelling of Dynamical Systems vol. 23 135–155 (2016) – 10.1080/13873954.2016.1237973
• Khalil, (2002)
• Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science vol. 89 223–234 (2013) – 10.1016/j.ces.2012.12.002
• Hoang, N. H. & Dochain, D. On the equivalence of storage functions in controlled thermodynamic systems. IFAC-PapersOnLine vol. 49 579–584 (2016) – 10.1016/j.ifacol.2016.07.405
• Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal vol. 47 1819–1831 (2001) – 10.1002/aic.690470813
• Eberard, D., Maschke, B. M. & van der Schaft, A. J. An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes. Reports on Mathematical Physics vol. 60 175–198 (2007) – 10.1016/s0034-4877(07)00024-9
• Hoang, H., Couenne, F., Jallut, C. & Le Gorrec, Y. The port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors. Journal of Process Control vol. 21 1449–1458 (2011) – 10.1016/j.jprocont.2011.06.014
• Crawford, C. R. & Moon, Y. S. Finding a positive definite linear combination of two Hermitian matrices. Linear Algebra and its Applications vol. 51 37–48 (1983) – 10.1016/0024-3795(83)90148-9
• Johansson, K. H. The quadruple-tank process: a multivariable laboratory process with an adjustable zero. IEEE Transactions on Control Systems Technology vol. 8 456–465 (2000) – 10.1109/87.845876
• Biswas, P. P., Srivastava, R., Ray, S. & Samanta, A. N. Sliding mode control of quadruple tank process. Mechatronics vol. 19 548–561 (2009) – 10.1016/j.mechatronics.2009.01.001
• Belhaj, W. & Boubaker, O. On MIMO PID Control of the quadruple-tank process via ILMIs Approaches : Minimum and Non-Minimum Case studies. IFAC Proceedings Volumes vol. 46 481–486 (2013) – 10.3182/20131218-3-in-2045.00083
• Åström, K. J. Limitations on Control System Performance. European Journal of Control vol. 6 2–20 (2000) – 10.1016/s0947-3580(00)70906-x
• Biswas, Backstepping control of polymerization reactor. (2013)
• Hvala, N., Aller, F., Miteva, T. & Kukanja, D. Modelling, simulation and control of an industrial, semi-batch, emulsion-polymerization reactor. Computers & Chemical Engineering vol. 35 2066–2080 (2011) – 10.1016/j.compchemeng.2011.05.016
• Melo, P. A., Biscaia, E. C., Jr. & Pinto, J. C. The bifurcation behavior of continuous free-radical solution loop polymerization reactors. Chemical Engineering Science vol. 58 2805–2821 (2003) – 10.1016/s0009-2509(03)00132-5
• Melo, P. A., Sampaio, J. G., Biscaia, E. C., Jr. & Pinto, J. C. Periodic oscillations in continuous free-radical solution polymerization reactors—a general approach. Chemical Engineering Science vol. 56 3469–3482 (2001) – 10.1016/s0009-2509(01)00023-9
• Altınten, A., Ketevanlioğlu, F., Erdoğan, S., Hapoğlu, H. & Alpbaz, M. Self-tuning PID control of jacketed batch polystyrene reactor using genetic algorithm. Chemical Engineering Journal vol. 138 490–497 (2008) – 10.1016/j.cej.2007.07.029
• Yüce, S., Hasaltun, A., Erdoğan, S. & Alpbaz, M. Temperature Control of a Batch Polymerization Reactor. Chemical Engineering Research and Design vol. 77 413–420 (1999) – 10.1205/026387699526395
• HAPOGLU, H., ÖZKAN, G. & ALPBAZ, M. OPTIMAL TEMPERATURE CONTROL IN A BATCH POLYMERIZATION REACTOR USING NONLINEAR GENERALIZED PREDICTIVE CONTROL. Chemical Engineering Communications vol. 183 155–185 (2000) – 10.1080/00986440008960507
• Ponnuswamy, S. R., Shah, S. L. & Kiparissides, C. A. Computer optimal control of batch polymerization reactors. Industrial & Engineering Chemistry Research vol. 26 2229–2236 (1987) – 10.1021/ie00071a010
• Ha Hoang, N., Couenne, F., Le Gorrec, Y., Chen, C. L. & Ydstie, B. E. Passivity-based nonlinear control of CSTR via asymptotic observers. Annual Reviews in Control vol. 37 278–288 (2013) – 10.1016/j.arcontrol.2013.09.007
• Hoang, N. H. & Dochain, D. A comment on thermodynamically consistent feasibility condition of asymptotic observers. Chemical Engineering Science vol. 199 258–274 (2019) – 10.1016/j.ces.2019.01.010