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Multi-objective invasive weed optimization of the LQR controller

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Abstract

The Robogymnast is a triple link underactuated pendulum that mimics a human gymnast hanging from a horizontal bar. In this paper, two multi-objective optimization methods are developed using invasive weed optimization (IWO). The first method is the weighted criteria method IWO (WCMIWO) and the second method is the fuzzy logic IWO hybrid (FLIWOH). The two optimization methods were used to investigate the optimum diagonal values for the Q matrix of the linear quadratic regulator (LQR) controller that can balance the Robogymnast in an upright configuration. Two LQR controllers were first developed using the parameters obtained from the two optimization methods. The same process was then repeated, but this time with disturbance applied to the Robogymnast states to develop another set of two LQR controllers. The response of the controllers was then tested in different scenarios using simulation and their performance evaluated. The results show that all four controllers are able to balance the Robogymnast with varying accuracies. It has also been observed that the controllers trained with disturbance achieve faster settling time.

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References

  1. S. Takashiro, N. Yoshihiko. Analysis and control of underactuated mechanisms via the averaging method. In Proceedings of the 2nd Asian Control Conference, Springer, Seoul, Korea, vol. 1, pp. 273–276, 1997.

    Google Scholar 

  2. L. B. Prasad, B. Tyagi, H. O. Gupta. 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, pp. 661–670, 2014.

    Article  Google Scholar 

  3. K. J. AAström, K. Furuta. Swinging up a pendulum by energy control. Automatica, vol. 36, no. 2, pp. 287–295, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  4. G. A. Medrano-Cerda, E. E. Eldukhri, M. Cetin. Balancing and attitude control of double and triple inverted pendulums. Transactions of the Institute of Measurement and Control, vol. 17, no. 3, pp. 143–154, 1995.

    Article  Google Scholar 

  5. K. Furut, T. Ochiai, N. Ono. Attitude control of a triple inverted pendulum. International Journal of Control, vol. 39, no. 6, pp. 1351–1365, 1984.

    Article  MATH  Google Scholar 

  6. S. C. Brown, K. M. Passino. Intelligent control for an acrobot. Journal of Intelligent and Robotic Systems, vol. 18, no. 3, pp. 209–248, 1997.

    Article  MATH  Google Scholar 

  7. H. G. Kamil, E. E. Eldukhri, M. S. Packianather. Balancing control of robot gymnast based on discrete-time linear quadratic regulator technique. In Proceedings of the 2nd International Conference on Artificial Intelligence, Modelling and Simulation, IEEE, Madrid, Spain, pp. 137–142, 2014.

    Google Scholar 

  8. K. Deb. Multi-objective optimization. Search Methodologies, E. K. Burke, G. Kendall, Eds., New York, USA: Springer, pp. 403–449, 2014.

    Chapter  Google Scholar 

  9. Y. Li, J. C. Liu, Y. Wang. Design approach of weighting matrices for LQR based on multi-objective evolution algorithm. In Proceedings of International Conference on Information and Automation, IEEE, Changsha, China, pp. 1188–1192, 2008.

    Chapter  Google Scholar 

  10. S. A. Ghoreishi, M. A. Nekoui, S. O. Basiri. Optimal design of LQR weighting matrices based on intelligent optimization methods. International Journal of Intelligent Information Processing, vol. 2, no. 1, pp. 63–74, 2008.

    Google Scholar 

  11. S. Das, I. Pan, S. Das. Multi-objective LQR with optimum weight selection to design FOPID controllers for delayed fractional order processes. ISA Transactions, vol. 58, pp. 35–49, 2015.

    Article  Google Scholar 

  12. P. Khalaf, H. Richter, A. J. van den Bogert, D. Simon. Multi-objective optimization of impedance parameters in a prosthesis test robot. In Proceedings of ASME Dynamic Systems and Control Conference, ASME, Columbus, USA, 2015.

    Google Scholar 

  13. H. Q. Wang, L. Liao, D. Y. Wang, S. J. Wen, M. C. Deng. Improved artificial bee colony algorithm and its application in LQR controller optimization. Mathematical Problems in Engineering, vol. 2014, Article No. 695637, 2014.

    Google Scholar 

  14. H. A. Ismail, M. S. Packianather, R. I. Grosvenor, E. E. Eldhukri. The application of IWO in LQR controller design for the Robogymnast. In Proceedings of SAI Intelligent Systems Conference, IEEE, London, UK, pp. 274–279, 2015.

    Google Scholar 

  15. E. E. Eldukhri, D. T. Pham. Autonomous swing-up control of a three-link robot gymnast. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 224, no. 7, pp. 825–833, 2010.

    Google Scholar 

  16. S. Sehgal, S. Tiwari. LQR control for stabilizing triple link inverted pendulum system. In Proceedings of the 2nd International Conference on Power, Control and Embedded Systems, IEEE, Allahabad, India, pp. 1–5, 2012.

    Google Scholar 

  17. E. Lee, J. Perkins. Comparison of techniques for stabilization of a triple inverted pendulum. 2008.

    Google Scholar 

  18. R. T. Marler, J. S. Arora. Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization, vol. 26, no. 6, pp. 369–395, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  19. G. P. Rangaiah, A. Bonilla-Petriciolet. Multi-objective Optimization in Chemical Engineering: Developments and Applications, New York, USA: John Wiley and Sons, 2013.

    Book  Google Scholar 

  20. K. E. Parsopoulos, M. N. Vrahatis. Particle swarm optimization method in multiobjective problems. In Proceedings of ACM Symposium on Applied Computing, ACM, Madrid, Spain, pp. 603–607, 2002.

    Google Scholar 

  21. A. R. Mehrabian, C. Lucas. A novel numerical optimization algorithm inspired from weed colonization. Ecological Informatics, vol. 1, no. 4, pp. 355–366, 2006.

    Article  Google Scholar 

  22. M. R. Ghalenoei, H. Hajimirsadeghi, C. Lucas. Discrete invasive weed optimization algorithm: Application to cooperative multiple task assignment of UAVs. In Proceedings of the 28h Chinese Control Conference on Decision and Control, IEEE, Shanghai, China, pp. 1665–1670, 2009.

    Google Scholar 

  23. H. Madivada, C. S. P. Rao. An invasive weed optimization (IWO) approach for multi-objective job shop scheduling problems (JSSPs). International Journal of Mechanical Engineering and Technology (IJMET), vol. 3, no. 3, pp. 627–637, 2012.

    Google Scholar 

  24. Y. Y. Chai, L. M. Jia, Z. D. Zhang. Mamdani model based adaptive neural fuzzy inference system and its application. International Journal of Computational Intelligence, vol.5, no. 1, pp. 22–29, 2009.

    Google Scholar 

  25. A. Hamam, N. D. Georganas. A comparison of Mamdani and Sugeno fuzzy inference systems for evaluating the quality of experience of hapto-audio-visual applications. In Proceedings of the International Workshop on Haptic Audio Visual Environments and Games, IEEE, Ottawa, Canada, pp. 87–92, 2008.

    Google Scholar 

  26. H. Kamil. Intelligent Model-based Control of Complex Three-link Mechanisms, Ph.D. dissertation, Cardiff University, UK, 2015.

    Google Scholar 

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Acknowledgements

I would like to express the deepest gratitude to Majlis Amanah Rakyat (MARA) and German Malaysian Institute (GMI) for their sponsorship. Finally, I would like to thank my family and friends for their support.

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Authors and Affiliations

  1. Cardiff School of Engineering, Trevithick Building, The Parade 14-17, Cardiff South Glamorgan, CF24 3AA, UK

    Hafizul Azizi Ismail, Michael S. Packianather & Roger I. Grosvenor

  2. German Malaysian Institute, Jalan Ilmiah, Taman Universiti, Kajang, 43000, Selangor, Malaysia

    Hafizul Azizi Ismail

Authors
  1. Hafizul Azizi Ismail
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  2. Michael S. Packianather
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  3. Roger I. Grosvenor
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Correspondence to Hafizul Azizi Ismail.

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Recommended by Associate Editor De Xu

Hafizul Azizi Ismail received the B. Eng. (Hons) degree in mechatronics engineering from the International Islamic University of Malaysia (IIUM) in 2006, and the M. Eng. degree from Universiti Teknologi Malaysia (UTM) in 2010. Upon graduation he worked as a production engineer in Denso Malaysia Sendirian Berhad before working as a lecturer in German-Malaysian Institute in 2009.

His research interests include artificial intelligence, neural networks, robotics, mechatronics, image processing, optimistion and control engineering.

ORCID iD: 0000-0002-9594-3700

Michael S. Packianather received the B. Sc. (Hons) degree in electrical and electronic engineering, the M. Sc. and Ph.D. degrees in artificial intelligence from the University of Wales Cardiff, UK in 1991, 1993 and 1997 respectively. From February 1997 to 2001 he worked as a research associate at the Manufacturing Engineering Centre (MEC) at Cardiff University before becoming a lecturer. In 2005, he was appointed as the director of Postgraduate Research Studies at the MEC.

His research interests include intelligent manufacturing systems, neural networks, pattern recognition, expert systems, fault diagnosis, quality control, signal processing, feature selection, data mining and machine learning, optimisation methods, bioinformatics, medical engineering, design of experiments and micro/nano technologies.

Roger I. Grosvenor received the B. Eng. (Tech) degree in mechanical engineering from UWIST (now Cardiff University), UK in 1978. He then received the M. Sc. degree in systems engineering in 1984 and the Ph.D. degree in process measurements in 1995, both from Cardiff University, UK. He is a reader and a Year 3 Tutor in mechanical, integrated and medical engineering at the Cardiff School of Engineering.

His research interests include embedded condition monitoring, machine and process monitoring, fault diagnostics & prognostics, data analysis using excel and/or Matlab and signal capture/signal processing.

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Ismail, H.A., Packianather, M.S. & Grosvenor, R.I. Multi-objective invasive weed optimization of the LQR controller. Int. J. Autom. Comput. 14, 321–339 (2017). https://doi.org/10.1007/s11633-017-1061-3

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  • DOI: https://doi.org/10.1007/s11633-017-1061-3

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