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Active disturbance rejection control of nonlinear SISO Lagrangian systems via endogenous injections and exogenous feedback for trajectory tracking

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Abstract

This article deals with a linear classical approach for the robust output reference trajectory tracking control of nonlinear SISO Lagrangian systems with a controllable (flat) tangent linearization around an operating equilibrium point. An endogenous injections and exogenous feedback (EIEF) approach is proposed, which is naturally equivalent to the generalized proportional integral control method and to a robust classical compensation network. It is shown that the EIEF controller is also equivalent, within a frequency domain setting demanding respect for the separation principle, to the reduced order observer based active disturbance rejection control approach. The proposed linear control approach is robust with respect to total disturbances and, thus, it is effective for the linear control of the nonlinear Lagrangian system. An illustrative nonlinear rotary crane Lagrangian system example, which is non-feedback linearizable, is presented along with digital computer simulations.

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References

  1. Arnold, V. (1989). Mathematical Methods of Classical Mechanics. 2nd ed. New York: Springer.

    Book  Google Scholar 

  2. Crouch, P. E., & van der Schaft, A. J. (1987). Variational and Hamiltonian Control Systems. Berlin: Springer.

    Book  Google Scholar 

  3. Sira-Ramírez, H. (2018). From flatness, GPI observers, GPI control and flat filters to observer-based ADRC. Control Theory and Technology, 16(4), 249–260. https://doi.org/10.1007/s11768-018-8134-x.

    Article  MathSciNet  Google Scholar 

  4. Han, J. (2009). From PID to active disturbance rejection control. IEEE Transactions on Industrial Electronics, 56(3), 900–906.

    Article  Google Scholar 

  5. Gao, Z., Huang, Y., & Han, J. (2001). An alternative paradigm for control system design. In Proceedings of the 40th IEEE Conference on Decision and Control (pp. 4578–4585). Orlando, Florida, USA.

  6. Xue, W., & Huang, Y. (2015). Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems. ISA Transactions, 58, 133–154.

    Article  Google Scholar 

  7. Sira-Ramírez, H., & Gao, Z. (2020). Flatness based ADRC control of Lagrangian systems: A moving crane. In Proceedings of the IFAC World Congress. Berlin, Germany.

  8. Brockett, R. W. (1970). Finite Dimensional Linear Systems. New York: Wiley.

    MATH  Google Scholar 

  9. Sira-Ramírez, H., & Aggrawal, S. (2004). Differentially Flat Systems. Boston: Marcel Dekker.

    Book  Google Scholar 

  10. Åström, K. J., & Murray, R. M. (2008). Feedback Systems: An Introduction for Scientists and Engineers. Princeton: Princeton University Press.

    Book  Google Scholar 

  11. Sira-Ramírez, H., Luviano-Juárez, A., Ramírez-Neira, M., & Zurita-Bustamante, W. E. (2017). Active Disturbance Rejection Control of Dynamic Systems. Oxford: Elsevier.

    Google Scholar 

  12. Fliess, M., Márquez, R., Delaleau, E., & Sira-Ramírez, H. (2002). Correcteurs proportionnels-intègraux généralisés. ESAIM, Control, Optimization and Calculus Variations, 7(1), 23–41.

    Article  Google Scholar 

  13. Zurita Bustamante, E. W., Sira-Ramírez, H., & Linares-Flores, J. (2018). An equivalence between the adrc and the flat filtering controllers: A case study in double buck converter. In Proceedings of the 14th IEEE International Conference on Power Electronics (pp. 188–193). Puebla, Mexico.

  14. Sira-Ramírez, H., Zurita-Bustamante, E. W., & Huang, C. (2020). Equivalence among flat filters, dirty derivative-based PID controllers, ADRC, and integral reconstructor-based sliding mode control. IEEE Transactions on Control Systems Technology, 28(5), 1696–1710.

    Article  Google Scholar 

  15. Fliess, M., Levine, J., Rouchon, P., & Martin, Ph. (1995). Flatness and defect of non-linear systems: Introductory theory and examples. International Journal of Control, 61(6), 1327–1361.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The work of M. A. Aguilar-Orduña and B. C. Gómez-León was supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) Mexico under Scholarship Grants no. 702805 and no. 1039577, respectively.

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Authors and Affiliations

  1. Department of Electrical Engineering Mechatronics Section, Cinvestav-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, CP 07300, CDMX, Mexico

    Hebertt Sira-Ramírez, Mario Andres Aguilar-Orduña & Brian C. Gómez-León

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  1. Hebertt Sira-Ramírez
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  2. Mario Andres Aguilar-Orduña
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  3. Brian C. Gómez-León
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Correspondence to Hebertt Sira-Ramírez.

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Sira-Ramírez, H., Aguilar-Orduña, M.A. & Gómez-León, B.C. Active disturbance rejection control of nonlinear SISO Lagrangian systems via endogenous injections and exogenous feedback for trajectory tracking. Control Theory Technol. 19, 113–126 (2021). https://doi.org/10.1007/s11768-021-00033-3

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  • DOI: https://doi.org/10.1007/s11768-021-00033-3

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