Stabilization of the Inertia Wheel Inverted Pendulum by Advanced IDA-PBC Based Controllers: Comparative Study and Real-Time Experiments

Authors

Afef Hfaiedh, Ahmed Chemori, Afef Abdelkrim

Abstract

Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) is a popular control scheme, for the stabilization of underactuated mechanical systems, formulated in Port-Controlled Hamiltonian (PCH) structure. However, robustness enhancement of this control approach towards external disturbances remains an challenging and an open problem. In this paper, an experimental comparative study between two different IDA-PBC approaches is proposed. The first controller is a nonlinear Proportional Integral IDA-PBC, while the second one is a model reference adaptive IDA - PBC. To evaluate the effectiveness of both controllers, various real-time experimental scenarios have been conducted for the stabilization of the inertia wheel inverted pendulum. For the sake of a fair comparison, different performance-evaluation criteria have been proposed to quantify the control performance in terms of convergence and energy consumption. The results show a better performance of the nonlinear Proportional Integral IDA - PBC controller compared to the model reference adaptive IDA - PBC controller.

Citation

Journal: 2020 17th International Multi-Conference on Systems, Signals & Devices (SSD)
Year: 2020
Volume:
Issue:
Pages: 753–760
Publisher: IEEE
DOI: 10.1109/ssd49366.2020.9364159

BibTeX

@inproceedings{Hfaiedh_2020,
  title={{Stabilization of the Inertia Wheel Inverted Pendulum by Advanced IDA-PBC Based Controllers: Comparative Study and Real-Time Experiments}},
  DOI={10.1109/ssd49366.2020.9364159},
  booktitle={{2020 17th International Multi-Conference on Systems, Signals &amp; Devices (SSD)}},
  publisher={IEEE},
  author={Hfaiedh, Afef and Chemori, Ahmed and Abdelkrim, Afef},
  year={2020},
  pages={753--760}
}

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References

Andary, S., Chemori, A. & Krut, S. Estimation-based disturbance rejection in control for limit cycle generation on inertia wheel inverted pendulum testbed. 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems 1302–1307 (2009) doi:10.1109/iros.2009.5354120 – 10.1109/iros.2009.5354120
Andary, S., Chemori, A. & Krut, S. Stable limit cycle generation for underactuated mechanical systems, application: Inertia wheel inverted pendulum. 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems 526–531 (2008) doi:10.1109/iros.2008.4650994 – 10.1109/iros.2008.4650994
Khraief Haddad, N., Belghith, S., Gritli, H. & Chemori, A. From Hopf Bifurcation to Limit Cycles Control in Underactuated Mechanical Systems. Int. J. Bifurcation Chaos 27, 1750104 (2017) – 10.1142/s0218127417501048
Gritli, H., Khraief, N., Chemori, A. & Belghith, S. Self-generated limit cycle tracking of the underactuated inertia wheel inverted pendulum under IDA-PBC. Nonlinear Dyn 89, 2195–2226 (2017) – 10.1007/s11071-017-3578-y
González, H., Duarte-Mermoud, M. A., Pelissier, I., Travieso-Torres, J. C. & Ortega, R. A novel induction motor control scheme using IDA-PBC. J. Control Theory Appl. 6, 59–68 (2008) – 10.1007/s11768-008-7193-9
Ramírez, H., Sbarbaro, D. & Ortega, R. On the control of non-linear processes: An IDA–PBC approach. Journal of Process Control 19, 405–414 (2009) – 10.1016/j.jprocont.2008.06.018
Aoues, S., Matignon, D. & Alazard, D. Control of a flexible spacecraft using discrete IDA-PBC design. IFAC-PapersOnLine 48, 188–193 (2015) – 10.1016/j.ifacol.2015.10.237
Gómez-Estern, F. & Van der Schaft, A. J. Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems. European Journal of Control 10, 451–468 (2004) – 10.3166/ejc.10.451-468
Viola, G., Ortega, R., Banavar, R., Acosta, J. A. & Astolfi, A. Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes. IEEE Trans. Automat. Contr. 52, 1093–1099 (2007) – 10.1109/tac.2007.899064
Ryalat, M. & Laila, D. S. IDA-PBC for a class of underactuated mechanical systems with application to a rotary inverted pendulum. 52nd IEEE Conference on Decision and Control 5240–5245 (2013) doi:10.1109/cdc.2013.6760713 – 10.1109/cdc.2013.6760713
Santibanez, V., Kelly, R. & Sandoval, J. Control of the Inertia Wheel Pendulum by Bounded Torques. Proceedings of the 44th IEEE Conference on Decision and Control 8266–8270 doi:10.1109/cdc.2005.1583500 – 10.1109/cdc.2005.1583500
Tiefensee, F., Monaco, S. & Normand-Cyrot, D. IDA-PBC under sampling for port-controlled hamiltonian systems. Proceedings of the 2010 American Control Conference 1811–1816 (2010) doi:10.1109/acc.2010.5531444 – 10.1109/acc.2010.5531444
Ryalat, M., Laila, D. S. & Torbati, M. M. Integral IDA-PBC and PID-like control for port-controlled Hamiltonian systems. 2015 American Control Conference (ACC) 5365–5370 (2015) doi:10.1109/acc.2015.7172178 – 10.1109/acc.2015.7172178
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, 1000–1016 (2016) – 10.1002/rnc.3615
Andary, S. & Chemori, A. A dual model-free control of non-minimum phase systems for generation of stable limit cycles. IEEE Conference on Decision and Control and European Control Conference 1387–1392 (2011) doi:10.1109/cdc.2011.6160704 – 10.1109/cdc.2011.6160704
Krafes, S., Chalh, Z. & Saka, A. A Review on the Control of Second Order Underactuated Mechanical Systems. Complexity 2018, (2018) – 10.1155/2018/9573514
Ghommam, J. & Chemori, A. Adaptive RBFNN finite-time control of normal forms for underactuated mechanical systems. Nonlinear Dyn 90, 301–315 (2017) – 10.1007/s11071-017-3662-3
Spong, M. W. Underactuated mechanical systems. Lecture Notes in Control and Information Sciences 135–150 doi:10.1007/bfb0015081 – 10.1007/bfb0015081
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. International Journal of Control 91, 2657–2672 (2017) – 10.1080/00207179.2017.1331378
Zayane-Aissa, C., Laleg-Kirati, T.-M. & Chemori, A. Control of a perturbed under-actuated mechanical system. 2015 IEEE Conference on Control Applications (CCA) 294–299 (2015) doi:10.1109/cca.2015.7320644 – 10.1109/cca.2015.7320644
van der schaft, Port-controlled hamiltonian systems: Towards a theory for control and design of nonlinear physical systems. Journal of the Society of Instrument and Control Engineers (2000)
Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
Ryalat, M. & Laila, D. S. A Robust IDA-PBC Approach for Handling Uncertainties in Underactuated Mechanical Systems. IEEE Trans. Automat. Contr. 63, 3495–3502 (2018) – 10.1109/tac.2018.2797191
Choukchou-Braham, A., Cherki, B., Djemaï, M. & Busawon, K. Analysis and Control of Underactuated Mechanical Systems. (Springer International Publishing, 2014). doi:10.1007/978-3-319-02636-7 – 10.1007/978-3-319-02636-7
Rodriguez, H., Ortega, R., Escobar, G. & Barabanov, N. A robustly stable output feedback saturated controller for the boost DC-to-DC converter. Systems & Control Letters 40, 1–8 (2000) – 10.1016/s0167-6911(99)00113-9
Andary, S., Chemori, A. & Krut, S. Control of the Underactuated Inertia Wheel Inverted Pendulum for Stable Limit Cycle Generation. Advanced Robotics 23, 1999–2014 (2009) – 10.1163/016918609x12529279062438
haddad, Sta-bilization of inertia wheel inverted pendulum by model reference adaptive ida-pbc: From simulation to real-time experiments. 2015 3rd International Conference on Control Engineering & Information Technology (CEIT) (2015)
Spong, M. W., Corke, P. & Lozano, R. Nonlinear control of the Reaction Wheel Pendulum. Automatica 37, 1845–1851 (2001) – 10.1016/s0005-1098(01)00145-5
Haddad, N. K., Chemori, A. & Belghith, S. External disturbance rejection in IDA-PBC controller for underactuated mechanical systems: From theory to real time experiments. 2014 IEEE Conference on Control Applications (CCA) 1747–1752 (2014) doi:10.1109/cca.2014.6981565 – 10.1109/cca.2014.6981565
Andary, S., Chemori, A., Benoit, M. & Sallantin, J. A dual model-free control of underactuated mechanical systems, application to the inertia wheel inverted pendulum. 2012 American Control Conference (ACC) 1029–1034 (2012) doi:10.1109/acc.2012.6315492 – 10.1109/acc.2012.6315492
Freidovich, L. B. et al. Shaping stable periodic motions of inertia wheel pendulum: theory and experiment. Asian Journal of Control 11, 548–556 (2009) – 10.1002/asjc.135
hfaiedh, Rise controller for class I underactuated mechanical systems: Design and real-time experiments. The 3rd International Conference on Electromechanical Engineering (ICEE’2018) (2018)
Aguilar-Avelar, C., Rodríguez-Calderón, R., Puga-Guzmán, S. & Moreno-Valenzuela, J. Effects of nonlinear friction compensation in the inertia wheel pendulum. J Mech Sci Technol 31, 4425–4433 (2017) – 10.1007/s12206-017-0843-4