Abstract
This paper presents a methodology to solve the problem of robustification of Interconnection and Dam** Assignment-Passivity Based Control (IDA-PBC) scheme for the case of under-actuated systems with inertia matrix dependent of the unactuated coordinates. Specifically, we analyze the robustness of the IDA-PBC strategy with respect to constant external disturbances. This algorithm requires adding an integral action with a particular change of coordinates in an outer-loop to the IDA-PBC strategy to reject constant external disturbances. The asymptotic stability of the proposed controller despite constant external disturbances is proved using the closed-loop Hamiltonian as a Lyapunov candidate function and LaSalle’s invariance principle. Finally, as a proof of concept, we have applied the proposed robust IDA-PBC strategy to an Unmanned Aerial vehicle that transports a payload suspended by a cable, which is a class of underactuated system with inertia matrix dependent of the unactuated coordinate. Satisfactory results in numerical experiments demonstrate the applicability of the method.
Similar content being viewed by others
Data availability
This manuscript has no associated data.
References
Ortega, R., Spong, M.W., Gómez-Estern, F., Blankenstein, G.: Stabilization of a class of underactuated mechanical systems via interconnection and dam** assignment. IEEE Trans. Autom. Control 47(8), 1218–1233 (2002)
Ortega, R., Van Der Schaft, A., Maschke, B., Escobar, G.: Interconnection and dam** assignment passivity-based control of port-controlled hamiltonian systems. Automatica 38(4), 585–596 (2002)
Gómez-Estern, F., Van der Schaft, A.J.: Physical dam** in ida-pbc controlled underactuated mechanical systems. Eur. J. Control. 10(5), 451–468 (2004)
Ortega, R., Garcia-Canseco, E.: Interconnection and dam** assignment passivity-based control: A survey. Eur. J. Control. 10(5), 432–450 (2004)
Donaire, A., Junco, S.: On the addition of integral action to port-controlled hamiltonian systems. Automatica 45(8), 1910–1916 (2009)
Ortega, R., Romero, J.G.: Robust integral control of port-hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Syst. Control Lett. 61(1), 11–17 (2012)
Deng, M., Bu, N.: Robust control for nonlinear systems using passivity-based robust right coprime factorization. IEEE Trans. Autom. Control 57(10), 2599–2604 (2012)
**, L., Yu, S., Du, J.: Adaptive and integral control of pmsm with uncertainties and disturbances in the port-controlled hamiltonian framework. In: Proceedings of the 32nd Chinese Control Conference, pp. 1081–1086. IEEE (2013)
Romero, J.G., Donaire, A., Ortega, R.: Robust energy sha** control of mechanical systems. Syst. Control Lett. 62(9), 770–780 (2013)
Haddad, N.K., Chemori, A., Belghith, S.: External disturbance rejection in IDA-PBC controller for underactuated mechanical systems: From theory to real-time experiments. In: 2014 IEEE conference on control applications (CCA), pp. 1747–1752. IEEE (2014)
Ryalat, M., Laila, D.S., Torbati, M.M.: Integral IDA-PBC and PID-like control for port-controlled hamiltonian systems. In: 2015 American Control Conference (ACC), pp. 5365–5370. IEEE (2015)
Haddad, N.K., Chemori, A., Belghith, S.: Robustness enhancement of IDA-PBC controller in stabilising the inertia wheel inverted pendulum: theory and real-time experiments. Int. J. Control 91(12), 2657–2672 (2018)
Donaire, A., Romero, J.G., Ortega, R., Siciliano, B., Crespo, M.: Robust IDA-PBC for underactuated mechanical systems subject to matched disturbances. Int. J. Robust Nonlinear Control 27(6), 1000–1016 (2017)
Ryalat, M., Laila, D.S.: A robust IDA-PBC approach for handling uncertainties in underactuated mechanical systems. IEEE Trans. Autom. Control 63(10), 3495–3502 (2018)
Donaire, A., Romero, J.G., Ortega, R.: Correction to the paper “A robust IDA-PBC approach for handling uncertainties in underactuated mechanical systems”. ar**v preprint ar**v:1909.04856 (2019)
Acosta, J.Á., Sanchez, M., Ollero, A.: Robust control of underactuated aerial manipulators via IDA-PBC. In: 53rd IEEE Conference on Decision and Control, pp. 673–678. IEEE (2014)
Souza, C., Raffo, G.V., Castelan, E.B.: Passivity-based control of a quadrotor UAV. IFAC Proc. Vol. 47(3), 3196–3201 (2014)
Bouzid, Y., Siguerdidjane, H., Bestaoui, Y., Zareb, M.: Energy-based 3D autopilot for VTOL UAV under guidance & navigation constraints. J. Intell. Rob. Syst. 87(2), 341–362 (2017)
Guerrero-Sánchez, M.E., Abaunza, H., Castillo, P., Lozano, R., García-Beltrán, C.D.: Quadrotor energy-based control laws: a unit-quaternion approach. J. Intell. Rob. Syst. 88(2), 347–377 (2017)
Guerrero-Sánchez, M.E., Mercado-Ravell, D.A., Lozano, R., García-Beltrán, C.D.: Swing-attenuation for a quadrotor transporting a cable-suspended payload. ISA Trans. 68, 433–449 (2017)
Guerrero-Sánchez, M.E., Hernández-González, O., Lozano, R., García-Beltrán, C.D., Valencia-Palomo, G., López-Estrada, F.R.: Energy-based control and LMI-based control for a quadrotor transporting a payload. Mathematics 7(11), 1090 (2019)
Guerrero-Sánchez, M.E., Lozano, R., Castillo, P., Hernández-González, O., García-Beltrán, C., Valencia-Palomo, G.: Nonlinear control strategies for a UAV carrying a load with swing attenuation. Appl. Math. Model. 91, 709–722 (2020)
Funding
This work has been supported by Tecnológico Nacional de México grant number 9992.21-P. Additional funding was provided by Conacyt under the program Cátedras Patrimoniales Projects 88 and 2759.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Guerrero-Sánchez, M.E., Hernández-González, O., Valencia-Palomo, G. et al. Robust IDA-PBC for under-actuated systems with inertia matrix dependent of the unactuated coordinates: application to a UAV carrying a load. Nonlinear Dyn 105, 3225–3238 (2021). https://doi.org/10.1007/s11071-021-06776-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-021-06776-7