Flatness-based Nonlinear Anti-sloshing Control of Liquid Containers
Main Article Content
Abstract
The movement of the liquid inside the container, known as sloshing, is usually undesired. Thus, there is the necessity to keep under control the peaks that the liquid free-surface exhibits during motion. This paper aims at providing a solution for suppressing sloshing liquid in horizontally moving cylindrical container. After introducing equivalent discrete models based on a mass-spring-damper system introduced by the literature (non-linear model), the identification and utilization of flat outputs is presented to generate rest-to-rest trajectories in sloshing liquid systems, which is ensure the equilibrium of the sloshing height at both initial and final points. Moreover, a sliding-mode controller is described to solve the trajectory tracking problem. The effectiveness of the proposed approach is demonstrated through numerical simulations comparisons with a model predictive controller (MPC). This research contributes to the advancement of control techniques for anti-sloshing technology systems, enabling enhanced stability, performance, and safety in various engineering applications.
Keywords
sloshing, flat output, rest-to-rest trajectory, sliding-mode control, model predictive control
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
[1] Bauer, H (1966). Nonlinear mechanical model for the description of propellant sloshing. AIAA J, 4, 1662-1668. https://doi.org/10.2514/3.3752
[2] Guagliumi, L., Berti, A., Monti, E., Carricato, M., A simple model-based method for sloshing estimation in liquid transfer in automatic machines. IEEE Access (2021). https://doi.org/10.1109/ACCESS.2021.3113956
[3] Guagliumi, L., Berti, A., Monti, E., Carricato, M. Antisloshing trajectories for high-acceleration motions in automatic machines. J. Dyn. Syst. Meas. Control. (2022) https://doi.org/10.1115/1.4054224
[4] Di Leva, R., Carricato, M., Gattringer, H., Muller, A. Time-optimal trajectory planning for anti-sloshing 2-dimensional motions of an industrial robot. 2021 20th IEEE International Conference on Advanced Robotics (ICAR), pp. 32-37. (2021) https://doi.org/10.1109/ICAR53236.2021.9659383
[5] Guagliumi, L., Berti, A., Monti, E., Carricato, M., A software application for fast liquid-sloshing simulation. The 4th International Conference of IFToMM Italy. (2022) https://doi.org/10.1007/978-3-031-10776-4_94
[6] M. Fliess, J. Levine, Ph. Martin, P. Rouchon. Flatness and defect of nonlinear systems: introductory theory and applications. Internat. J. Control, 61, 1327-1361. (1995) https://doi.org/10.1080/00207179508921959
[7] Fliess, M., Levine, J., Martin, P. and Rouchon, P., A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems. IEEE Transactions on Automatic Control, 44, 922-937. (1999) https://doi.org/10.1109/9.763209
[8] M. Fliess, R. Marquez (2000). Continuous-time linear predictive control and flatness: a module-theoretic setting with examples, Int. J. Control, 73 (7), 606-623. https://doi.org/10.1080/002071700219452
[9] G. D. Forney Jr., Minimal bases of rational vector spaces with applications to multivariable linear systems, SIAM J. Control, 13 (3), 493-520. (1975). https://doi.org/10.1137/0313029
[10] L. Bitauld, M. Fliess, J. Levine, A flatness-based control synthesis of linear systems and application to windshield wipers. Proceedings of the ECC’97, paper no. 628, Brussels. (1997). https://doi.org/10.23919/ECC.1997.7082475
[11] J. Levine and D. V. Nguyen, Flat output characterization for linear systems using polynomial matrices. Systems and control Letters, 48:69-75. (2003). https://doi.org/10.1016/S0167-6911(02)00257-8
[12] Edwards, C., & Spurgeon, S., Sliding mode control: Theory and applications. London: Taylor & Francis. (1998). https://doi.org/10.1201/9781498701822
[13] T. V. I. Utkin, Variable structure system with sliding mode. IEEE Trans. Autom. Control, vol. 22, no. 2, pp. 212-227. (1977). https://doi.org/10.1109/TAC.1977.1101446
[14] R. A. DeCarlo, S. H. Zak, and G. P. Matthews, Variable structure control of nonlinear multivariable systems: A Tutorial. Proc.IEEE, vol. 76, no. 3, pp. 212-232. (March 1988) https://doi.org/10.1109/5.4400
[15] J. Y. Hung, W. Gao, and J. C. Hung, Variable structure control: A Survey. IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 2-22. (1993). https://doi.org/10.1109/41.184817
[16] G. M. Bone and S. Ning, Experimental comparison of position tracking control algorithms for pneumatic cylinder actuators. IEEE/ASME Trans Mechatronics, vol. 12, no. 5, pp. 557-561. (2007). https://doi.org/10.1109/TMECH.2007.905718
[17] S. Bashash and N. Jalili, Robust adaptive control of coupled parallel piezo-flexural nanopositioning stages, IEEE/ASME Trans Mechatronics, vol. 14, no. 1, pp. 11-20. (2009). https://doi.org/10.1109/TMECH.2008.2006501
[18] M. V. Pekka Ronkanen, Pasi Kallio and H. N. Koivo, Displacement control of piezoelectric actuators using current and voltage. IEEE/ASME Trans.on Mechatronics, vol. 16, no. 1, pp. 160-166. (2011). https://doi.org/10.1109/TMECH.2009.2037914
[19] Lévine, J. Analysis and Control of Nonlinear Systems: A Flatness-Based Approach. Berlin: Springer. (2009).
[20] Raouf A. Ibrahim, Liquid Sloshing Dynamics: Theory and Applications, Cambridge: Cambridge University Press. (2005), https://doi.org/10.1017/CBO9780511536656
[21] Di Leva, R., Carricato, M., Gattringer, H., Müller, A., Sloshing dynamics estimation for liquid-filled containers under 2-dimensional excitation. In: Proceedings of the 10th ECCOMAS Thematic Conference on Multibody Dynamics, pp. 80-89. (2021). https://doi.org/10.3311/ECCOMASMBD2021-274
[2] Guagliumi, L., Berti, A., Monti, E., Carricato, M., A simple model-based method for sloshing estimation in liquid transfer in automatic machines. IEEE Access (2021). https://doi.org/10.1109/ACCESS.2021.3113956
[3] Guagliumi, L., Berti, A., Monti, E., Carricato, M. Antisloshing trajectories for high-acceleration motions in automatic machines. J. Dyn. Syst. Meas. Control. (2022) https://doi.org/10.1115/1.4054224
[4] Di Leva, R., Carricato, M., Gattringer, H., Muller, A. Time-optimal trajectory planning for anti-sloshing 2-dimensional motions of an industrial robot. 2021 20th IEEE International Conference on Advanced Robotics (ICAR), pp. 32-37. (2021) https://doi.org/10.1109/ICAR53236.2021.9659383
[5] Guagliumi, L., Berti, A., Monti, E., Carricato, M., A software application for fast liquid-sloshing simulation. The 4th International Conference of IFToMM Italy. (2022) https://doi.org/10.1007/978-3-031-10776-4_94
[6] M. Fliess, J. Levine, Ph. Martin, P. Rouchon. Flatness and defect of nonlinear systems: introductory theory and applications. Internat. J. Control, 61, 1327-1361. (1995) https://doi.org/10.1080/00207179508921959
[7] Fliess, M., Levine, J., Martin, P. and Rouchon, P., A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems. IEEE Transactions on Automatic Control, 44, 922-937. (1999) https://doi.org/10.1109/9.763209
[8] M. Fliess, R. Marquez (2000). Continuous-time linear predictive control and flatness: a module-theoretic setting with examples, Int. J. Control, 73 (7), 606-623. https://doi.org/10.1080/002071700219452
[9] G. D. Forney Jr., Minimal bases of rational vector spaces with applications to multivariable linear systems, SIAM J. Control, 13 (3), 493-520. (1975). https://doi.org/10.1137/0313029
[10] L. Bitauld, M. Fliess, J. Levine, A flatness-based control synthesis of linear systems and application to windshield wipers. Proceedings of the ECC’97, paper no. 628, Brussels. (1997). https://doi.org/10.23919/ECC.1997.7082475
[11] J. Levine and D. V. Nguyen, Flat output characterization for linear systems using polynomial matrices. Systems and control Letters, 48:69-75. (2003). https://doi.org/10.1016/S0167-6911(02)00257-8
[12] Edwards, C., & Spurgeon, S., Sliding mode control: Theory and applications. London: Taylor & Francis. (1998). https://doi.org/10.1201/9781498701822
[13] T. V. I. Utkin, Variable structure system with sliding mode. IEEE Trans. Autom. Control, vol. 22, no. 2, pp. 212-227. (1977). https://doi.org/10.1109/TAC.1977.1101446
[14] R. A. DeCarlo, S. H. Zak, and G. P. Matthews, Variable structure control of nonlinear multivariable systems: A Tutorial. Proc.IEEE, vol. 76, no. 3, pp. 212-232. (March 1988) https://doi.org/10.1109/5.4400
[15] J. Y. Hung, W. Gao, and J. C. Hung, Variable structure control: A Survey. IEEE Trans. Ind. Electron., vol. 40, no. 1, pp. 2-22. (1993). https://doi.org/10.1109/41.184817
[16] G. M. Bone and S. Ning, Experimental comparison of position tracking control algorithms for pneumatic cylinder actuators. IEEE/ASME Trans Mechatronics, vol. 12, no. 5, pp. 557-561. (2007). https://doi.org/10.1109/TMECH.2007.905718
[17] S. Bashash and N. Jalili, Robust adaptive control of coupled parallel piezo-flexural nanopositioning stages, IEEE/ASME Trans Mechatronics, vol. 14, no. 1, pp. 11-20. (2009). https://doi.org/10.1109/TMECH.2008.2006501
[18] M. V. Pekka Ronkanen, Pasi Kallio and H. N. Koivo, Displacement control of piezoelectric actuators using current and voltage. IEEE/ASME Trans.on Mechatronics, vol. 16, no. 1, pp. 160-166. (2011). https://doi.org/10.1109/TMECH.2009.2037914
[19] Lévine, J. Analysis and Control of Nonlinear Systems: A Flatness-Based Approach. Berlin: Springer. (2009).
[20] Raouf A. Ibrahim, Liquid Sloshing Dynamics: Theory and Applications, Cambridge: Cambridge University Press. (2005), https://doi.org/10.1017/CBO9780511536656
[21] Di Leva, R., Carricato, M., Gattringer, H., Müller, A., Sloshing dynamics estimation for liquid-filled containers under 2-dimensional excitation. In: Proceedings of the 10th ECCOMAS Thematic Conference on Multibody Dynamics, pp. 80-89. (2021). https://doi.org/10.3311/ECCOMASMBD2021-274