Have a personal or library account? Click to login
Robust LFT-LPV H∞ Control of an Underactuated Inverted Pendulum on a Cart with Optimal Weighting Functions Selection by GA and ES Cover

Robust LFT-LPV H∞ Control of an Underactuated Inverted Pendulum on a Cart with Optimal Weighting Functions Selection by GA and ES

Open Access
|Mar 2021

References

  1. 1. Abbas H.S., Tóth R., Petreczky M., Meskin N., and Mohammadpour J. (2014), Embedding of nonlinear systems in a Linear Parameter-Varying representation, In: Proc. of IFAC World Congress, Cape Town, South Africa, 6907–6913.10.3182/20140824-6-ZA-1003.02506
  2. 2. Abdou L., and Soltani F. (2005), OS-CFAR and CMLD threshold optimization with genetic algorithms, In: Proc. of 3rd International Conference on Systems, Signals & Devices, Vol III Communication and Signal Processing, Sousse, Tunisia.
  3. 3. Abdou L., and Soltani F. (2008), OS-CFAR and CMLD threshold optimization in distributed systems using evolotionary strategies, Signal, Image and Video Processing, Vol. 2, No. 2, 155–167.
  4. 4. Alcalá E., Puig V., Quevedo J., and Rosolia U. (2020), Autonomous racing using Linear Parameter Varying-Model Predictive Control (LPV-MPC), Control Engineering Practice, Vol. 95, 104270.
  5. 5. Alfaro-Cid E., McGookin E.W., and Murray-Smith D.J. (2008), Optimisation of the weighting function of an H∞ controller using genetic algorithms and structured genetic algorithms, International Journal of Systems Science, Vol. 39, No. 4, 335–347.
  6. 6. Apkarian P., and Gahinet P. (1995), A convex characterization of gain-scheduled H∞ controller, IEEE Transactions on Automatic Control, Vol. 40, No. 7, 853–864.
  7. 7. Beaven R.W., Wright M.T., and Seaward D.R. (1996), Weighting function selection in the H∞ design process, Control Engineering Practice, Vol. 4, No. 7, 625–633.
  8. 8. Boubaker O. (2013), The inverted pendulum benchmark in nonlinear control theory: A survey, International Journal of Advanced Robotic Systems, Vol. 10, No. 5, 233–241.
  9. 9. Briat C. (2015), Linear Parameter-Varying and Time-Delay Systems: Analysis, Observation, Filtering & Control, Springer-Verlag, Heidelberg.10.1007/978-3-662-44050-6
  10. 10. Choukchou-Braham A., Cherki B., Djemaï M., and Busawon K. (2014a), Classification of Underactuated Mechanical Systems, In: Choukchou-Braham A., Cherki B., Djemaï M., and Busawon K. (eds.), Analysis and Control of Underactuated Mechanical Systems, Springer, London, 35–54.10.1007/978-3-319-02636-7_4
  11. 11. Choukchou-Braham A., Cherki B., Djemaï M., and Busawon K. (2014b), Control Design Schemes for Underactuated Mechanical Systems, In: Choukchou-Braham A., Cherki B., Djemaï M., and Busawon K. (eds.), Analysis and Control of Underactuated Mechanical Systems, Springer-Verlag, London, 55–91.10.1007/978-3-319-02636-7_5
  12. 12. Do A.L., Sename O., Dugard L., and Soualmi B. (2011), Multi-objective optimization by genetic algorithms in H∞/LPV control of semi-active suspension, In: Proc. of IFAC World Congress, Milano, Italy, 7162–7167.
  13. 13. El-Bardini M., and El-Nagar A.M. (2014), Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system, ISA Transactions, Vol. 53, 732–743.
  14. 14. Fiacchini M., Viguria A., Cano R., Prieto A., Rubio F.R., Aracil J., and Canudas-de-Wit C. (2006), Design and experimentation of a personal pendulum vehicle, In: Proc. of Portuguese Conference on Automatic Control, Lisbona, Portugal.
  15. 15. Hansen N., Arnold D.V., and Auger A. (2015), Evolution Strategies, In: Kacprzyk J., and Pedrycz W. (eds.), Springer Handbook of Computational Intelligence, Springer, Heidelberg, 871–898.10.1007/978-3-662-43505-2_44
  16. 16. Hasseni S., and Abdou L. (2017), Robust LPV control applied to a personal pendulum vehicle, In: Proc. of International Conference on Sciences and Techniques of Automatic Control and Computer Engineering, Monastir, Tunisia, 6–11.10.1109/STA.2017.8314871
  17. 17. Hasseni S., and Abdou L. (2018), Integral backstepping/LFT-LPV H∞ control for the trajectory tracking of a quadcopter, In: Proc. of International Conference on Systems and Control, Valencia, Spain, 348–353.
  18. 18. Hasseni S., and Abdou L. (2020), Robust LPV control for attitude stabilization of a quadrotor helicopter under input saturations, Advances in Technology Innovation, Vol. 5, No. 2, 98–111.
  19. 19. Hjartarson A., Seiler P., and Packard A. (2015), LPV Tools: a toolbox for modeling, analysis and synthesis of parameter varying control systems, IFAC PapersOnLine, Vol. 48, No. 26, 136–145.
  20. 20. Holland J.H. (1992), Adaptation in Natural and Artificial Systems, MIT Press, MA, USA.10.7551/mitpress/1090.001.0001
  21. 21. Hu J., Bohn C., and Wu H.R. (2000), Systematic H∞ weighting function selection and its application to the real-time control of a vertical take-off aircraft, Control Engineering Practice, Vol. 8, No. 3, 241–252.
  22. 22. Iwasaki T., and Shibata G. (2001), LPV system analysis via quadratic separator for uncertain implicit system. IEEE Transactions on Automatic Control, Vol. 46, No. 10, 1195–1208.
  23. 23. Li S., Jiang S., and Pan F. (2019), Event-triggered fault detection for networked LPV systems, Circuits, Systems, and Signal Processing, Vol. 38, No. 7, 2992–3019.
  24. 24. Liu T.J., Du X., Sun X.M., Richter H., and Zhu F. (2019), Robust tracking control of aero-engine rotor speed based on switched LPV model, Aerospace Science and Technology, Vol. 91, 382–390.
  25. 25. Liu Z., Theilliol D., Gu F., He Y., Yang L., and Han J. (2017), State feedback controller design for affine parameter-dependent LPV systems, IFAC PapersOnLine, Vol. 50, No. 1, 9760–9765.
  26. 26. López-Estrada F.R., Ponsart J.C., Theilliol D., Zhang Y., and Astorga-Zaragoza C.M. (2016), LPV model-based tracking control and robust sensor fault diagnosis for a quadrotor UAV, Journal of Intelligent & Robotic Systems, Vol. 84, 163–177.
  27. 27. Nguyen A.T., Chevrel P., and Claveau F. (2020), LPV static output feedback for constrained direct tilt control of narrow tilting vehicles, IEEE Transactions on Control Systems Technology, Vol. 28, No. 2, 661–670.
  28. 28. Ohhira T., and Shimada A. (2017), Model predictive control for an Inverted pendulum robot with time-varying, IFAC PapersOnLine, Vol. 50, No. 1, 776–781.
  29. 29. Packard A. (1994), Gain scheduling via linear fractional transformations, Systems and Control Letters, Vol. 22, No. 2, 79-92.
  30. 30. Park M.S., and Chwa D. (2009), Swing-up and stabilization control of inverted-pendulum systems via coupled sliding-mode control method, IEEE Transactions on Industrial Electronics, Vol. 56, No. 9, 3541–3555.
  31. 31. Prasad L.B., Tyagi B., and Gupta H.O. (2014), Optimal control of nonlinear inverted pendulum system using PID controller and LQR: Performance analysis without and with disturbance input, International Journal of Automation and Computing, Vol. 11, No. 6, 661–670.
  32. 32. Raffo G.V., Ortega M.G., and Rubio F.R. (2007), Nonlinear H∞ Control Applied to the Personal Pendulum Car, In: Proc. of European Control Conference, Kos, Greece, 2065–2070.
  33. 33. Rechenberg I. (1973), Evolutionstrategie: Optimieruna Technischer Systeme nach Prinzipien der Biologischen Evolution, Frommann-Holzboog-Verlag, Stuttgart, Germany.
  34. 34. Robert D., Sename O., and Simon D. (2010), An H∞ LPV design for sampling varying controllers: experimentation with a T-inverted pendulum, IEEE Transactions on Control Systems Technology, Vol. 18, No. 3, 741–749.
  35. 35. Rotondo D., Cristofaro A., Johansen T.A., Nejjari F., and Puig V. (2018), Diagnosis of icing and actuator faults in UAVs using LPV unknown input observers, Journal of Intelligent & Robotic Systems, Vol. 91, No. 3–4, 651–665.
  36. 36. Rudra S., Barai R.K., and Maitra M. (2017), Block Backstepping Control of the Underactuated Mechanical Systems, In: Rudra S., Barai R.K., and Maitra M. (eds.), Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems, Springer-Verlag, Singapore, 31–52.10.1007/978-981-10-1956-2_3
  37. 37. Salhi S., Aouani N., and Salhi S. (2015), LPV affine modeling, analysis and simulation of DFIG based wind energy conversion system, In: Proc. of International Conference on Modelling, Identification and Control, Sousse, Tunisia.10.1109/ICMIC.2015.7409385
  38. 38. Scherer C.W. (2001), LPV control and full block multipliers, Automatica, Vol. 37, No. 3, 361–375.
  39. 39. Seto D., and Baillieul J. (1994), Control problem in super-articulated mechanical systems, IEEE Transactions on Automatic Control, Vol. 39, No. 14, 2442–2453.
  40. 40. Shamma J., and Athans M. (1991), Gain scheduling: potential hazards and possible remedies, In: Proc. of American Control Conference, Boston, USA, 516–521.10.23919/ACC.1991.4791421
  41. 41. Siradjuddin I., Amalia Z., Setiawan B., Ronilaya F., Rohadi E., Setiawan A., Rahmad C., and Adhisuwignjo S. (2018), Stabilising a cart inverted pendulum with an augmented PID control scheme, MATEC Web of Conference, Vol. 197, 11013.
  42. 42. Skogestad S., and Postlethwaite I. (2003), Multivariable Feedback Control, Analysis and Design, John Wiley & Sons, Chichester.
  43. 43. Tasoujian S., Salavati S., Franchek M.A., and Grigoriadis K.M. (2020), Robust delay-dependent LPV synthesis for blood pressure control with real-time Bayesian parameter estimation, IET Control Theory & Applications, Vol. 14, No. 10, 1334–1345.
  44. 44. Vu V.T., Sename O., Dugard L., and Gaspar P. (2017), Multi objective H∞ active-roll bar control for heavy vehicles, IFAC Paper-sOnLine, Vol. 50, No. 1, 13802–13807.
  45. 45. Wright A. (1991), Genetic Algorithms for Real Parameter Optimization, Morgan Kaufmann, San Mateo, California.10.1016/B978-0-08-050684-5.50016-1
  46. 46. Wu F. (2001), A generalized LPV system analysis and control synthesis framework, International Journal of Control, Vol. 74, No. 9, 745–759.
  47. 47. Wu F., Yang X., Packard A., and Becker G. (1996), Induced L2 norm control for LPV systems with bounded parameter variation rates, International Journal of Robust and Nonlinear Control, Vol. 6, No. 9-10, 983–998.
  48. 48. Xu F., Tan J., Wang Y., Wang X., Liang B., and Yuan B. (2019), Robust fault detection and set-theoretic UIO for discrete-time LPV systems with state and output equations scheduled by inexact scheduling variables, IEEE Transactions on Automatic Control, Vol. 64, No. 12, 4982–4997.
  49. 49. Yang D., Wang Y., and Chen Z. (2020), Robust fault diagnosis and fault tolerant control for PEMFC system based on an augmented LPV observer, International Journal of Hydrogen Energy, Vol. 45, No. 24, 13508–13522.
  50. 50. Yeo B.K., and Lu Y. (1999), Array failure correction with a genetic algorithm, IEEE Transactions on Antennas and Propagation, Vol. 47, No. 7, 823–828.
  51. 51. Younis W., and Abdelati M. (2009), Design and implementation of an experimental Segway model, AIP Conference Proceedings, Vol. 1107, 350–354.
  52. 52. Zhou K., and Doyle J.C. (1998), Essentials of Robust Control, Prentice Hall, Upper Saddle River, NJ.
DOI: https://doi.org/10.2478/ama-2020-0027 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 186 - 197
Submitted on: Mar 23, 2019
Accepted on: Jan 18, 2021
Published on: Mar 8, 2021
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2021 Seif-El-Islam Hasseni, Latifa Abdou, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.