Observer design for a class of irreversible port Hamiltonian systems
In this paper we address the state estimation problem of a particular class of irreversible port Hamiltonian systems (IPHS), which are assumed to be partially observed. Our main contribution consists to design an observer such that the augmented system (plant + observer) is strictly passive. Under some additional assumptions, a Lyapunov function is constructed to ensure the stability of the coupled system. Finally, the proposed methodology is applied to the gas piston system model. Some simulation results are also presented.
[1] Duindam, V., Macchelli, A., Stramigioli, S., & Bruyninckx, H. (2009). Modeling and Control of Complex Physical Systems-The Port-Hamiltonian Approach. Springer-Verlag, Berlin, Germany.
[2] Maschke, B., Van der Schaft, A., & Breed- veld, P.C. (1992). An intrinsic Hamilton- ian formulation of network dynamics: Non- standard Poisson structures and gyrators. Journal of the Franklin Institute, 329(5), 923- 966.
[3] Van der Schaft, A., & Maschke, B. (1995).The Hamiltonian formulation of energy con- serving physical systems with external ports. Arch, fur Elektron, Ubertragungstech. 49(5-6), 362-371.
[4] Van der Schaft, A., & Jeltsema, D. (2014). Port-Hamiltonian Systems Theory: An Intro- ductory Overview. Foundations and Trends® in Systems and Control, 173-378.
[5] Dorfler, F., Johnsen, J., & Allg¨ower, F.(2009). An introduction to interconnection and damping assignment passivity-based con- trolin process engineering. Journal of Process Control, 19, 1413-1426.
[6] Hangos, K.M., Bokor, J., & Szederk´enyi, G.(2001). Hamiltonian view on process systems. AIChE Journal. 47, 1819-1831.
[7] Ramirez, H., Maschke, B., & Sbarbaro, D. (2013). Irreversible port-Hamiltonian sys- tems: A general formulation of irreversible processes with application to the CSTR.Chemical Engineering Science, 89(11), 223- 234.
[8] Biedermann, B., & Meurer, T. (2021). Ob- server design for a class of nonlinear systems combining dissipativity with interconnection and damping assignment. International Jour- nal of Robust and Nonlinear Control, 31(9), 4064-4080.
[9] Karagiannis, D., & Astolfi, A. (2005). Nonlin- ear observer design using invariant manifolds and applications. in Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 7775-7780.
[10] Shim, H., Seo, J.H., & Teel, A.R. (2003). Nonlinear observer design via passivation of error dynamics. Automatica, 39(5), 885-892.
[11] Venkatraman, A., & Van der Schaft, A.(2010). Full order observer design for a class of port Hamiltonian systems. Automatica, 46(3), 555-561.
[12] Zenfari, S., Laabissi, M., & Achhab, M.E.(2022). Proportional observer design for port Hamiltonian systems using the contraction analysis approach. International Journal of Dynamics and Control, 10(2), 403-408.
[13] Ramirez, H., Le Gorrec, Y., Maschke, B., & Couenne, F. (2016). On the passivity based control of irreversible processes: A port- Hamiltonian approach. Automatica, 64, 105- 111.
[14] Zenfari, S., Laabissi, M., & Achhab, M.E.(2019). Passivity Based Control method for the diffusion process. IFAC-PapersOnLine, 52(7), 80-84.
[15] Villalobos Aguilera,I. (2020). Passivity based control of irreversible port Hamiltonian sys- tem: An energy shaping plus damping in- jection approach. Master Thesis, Universidad T´ecnica Federico Santa Mar´ıa.
[16] Ramirez, H., Maschke, B., & Sbarbaro, D.(2013). Modelling and control of multi-energy systems: An irreversible port-Hamiltonian approach. European Journal of Control, 19(6), 513-520.
[17] Lieb, E.H., & Yngvason, J. (2013). The entropy concept for non-equilibrium states. Proceedings of the Royal Society A: Mathe- matical, Physical, and Engineering Sciences, 469.
[18] Byrnes, C.I., Isidori, A., & Willems, J.C.(1991). Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Au- tomatic Control, 36(11), 1228-1240.
[19] Van der Schaft, A. (2000). L2- gain and passivity techniques in nonlinear control. Springer, Berlin.
[20] Agarwal, P., & Choi, J. (2016). Fractional calculus operators and their image formulas. Journal of the Korean Mathematical Society, 53(5), 1183-1210.
[21] Baleanu, D., Sajjad, S.S., Jajarmi, A., & Defterli, O. (2021). The fractional dynamics of a linear triatomic molecule. Romanian Re- ports in Physics, 73, 105.
[22] Baleanu, D., Sajjad, S.S., Asad, J,H., Ja- jarmi, A., & Estiri, E. (2021). Hyperchaotic behaviors, optimal control, and synchroniza- tion of a nonautonomous cardiac conduction system. Advances in Difference Equations, 1, 1-24.
[23] Chu, Y.M., Ali Shah, N., Agarwal, P., Chung, J.D. (2021). Analysis of fractional multi-dimensional Navier-Stokes equation. Advances in Difference Equations, 91(2021).
[24] Jajarmi, A., Baleanu, K., Vahid, Z., & Mobayen, S. (2022). A general fractional for- mulation and tracking control for immuno- genictumor dynamics. Mathematical Methods in the Applied Sciences, 45(2), 667-680.
[25] Quresh, S., & Jan, R. (2021). Modeling of measles epidemic with optimized frac- tional order under Caputo differential opera- tor. Chaos, Solitons & Fractals, 145, 110766.
[26] Quresh, S., Chang, M.M., & Shaikh, A.A.(2021). Analysis of series RL and RC circuits with time-invariant source using truncated M, Atangana beta and conformable derivatives. Journal of Ocean Engineering and Science, 6(3), 217-227.
[27] Wang, B., Jahanshahi, H., Volos, C., Bekiros, S., Khan, M.A., Agarwal, P., & Aly, A.A. (2021). A new RBF neural network-based fault-tolerant active control for fractional time-delayed systems. Electron- ics. 10(12):1501.
[28] Yusuf, A., Qureshi, S., & Mustapha, U.T.(2022). Fractional Modeling for Improving Scholastic Performance of Students with Op- timal Control. International Journal of Ap- plied and Computational Mathematics, 8(1), 1-20.