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Robust Feedback Controller Design Using Cuckoo Search Optimization to Maximize Stability Radius

  • Mahmud Iwan SolihinEmail author
  • Rini Akmeliawati
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1015)

Abstract

A robust feedback controller is designed to maximize complex stability radius via single objective constrained optimization using Cuckoo Search Optimization (CSO) in this paper. A set robust feedback controller gains is optimized based on plant’s linear model having structured parametric uncertainty, i.e. two mass benchmark system. A wedge region is assigned as the optimization constraint to specify the desired closed-loop poles location which is directly related to desired time-domain response. The simulation results show that the robustness performance is achieved in the presence of parameter variations of the plant. In addition, the feedback controller optimized by CSO performs slightly better than that optimized by differential evolution algorithm previously designed.

References

  1. Akmeliawati, R., Tan, C.P.: Feedback controller and observer design to maximize stability radius. In: 2005 IEEE International Conference on Industrial Technology, pp. 660–664. IEEE. http://ieeexplore.ieee.org/document/1600719/. Accessed 22 Aug 2018
  2. Balochian, S., Ebrahimi, E.: Parameter optimization via Cuckoo optimization algorithm of fuzzy controller for liquid level control. J. Eng. 2013, 1–7 (2013). http://www.hindawi.com/journals/je/2013/982354/ (August 20, 2018)CrossRefGoogle Scholar
  3. Barbosa, R.S., Jesus, I.S.: Optimization of control systems by Cuckoo search. In: Moreira, A.P., Matos, A., Veiga, G. (eds.) CONTROLO’2014. LNEE, vol. 321, pp. 113–122. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-10380-8_12CrossRefGoogle Scholar
  4. Byrns, E.V., Calise, A.J.: Loop transfer recovery approach to H(Infinity) design for the coupled mass benchmark problem. J. Guidance Control Dyn. 15(5), 1118–1124 (1992). http://arc.aiaa.org/doi/10.2514/3.20958. Accessed 21 Aug 2018MathSciNetCrossRefGoogle Scholar
  5. Coello Coello, C.A.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11–12), 1245–1287 (2002). https://www.sciencedirect.com/science/article/pii/S0045782501003231. Accessed 22 Aug 2018MathSciNetCrossRefGoogle Scholar
  6. Hamza, M.F., Yap, H.J., Choudhury, I.A.: Cuckoo search algorithm based design of interval Type-2 Fuzzy PID controller for Furuta pendulum system. Eng. Appl. Artif. Intell. 62: 134–151 (2017). https://www.sciencedirect.com/science/article/abs/pii/S0952197617300714. Accessed 20 Aug 2018
  7. Feyel, P.: Robust Control Optimization with Metaheuristics. ISTE (2017). https://www.wiley.com/en-us/Robust+Control+Optimization+with+Metaheuristics-p-9781786300423. Accessed 21 Aug 2018CrossRefGoogle Scholar
  8. Fister, I., Yang, X.-S., Fister, D., Fister, I.: Cuckoo search: a brief literature review. In: Yang, X.S. (ed.) Cuckoo Search and Firefly Algorithm. SCI, pp. 49–62. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-02141-6_3CrossRefzbMATHGoogle Scholar
  9. Gu, D.-W., Petkov, P., Konstantinov, M.M.: Robust Control Design with MATLAB. Springer, London (2005).  https://doi.org/10.1007/978-1-4471-4682-7CrossRefzbMATHGoogle Scholar
  10. Hinrichsen, D., Pritchard, A.J.: Stability radii of linear systems. Syst. Control Lett. 7(1), 1–10 (1986). https://www.sciencedirect.com/science/article/pii/0167691186900940. Accessed 21 Aug 2018MathSciNetCrossRefGoogle Scholar
  11. Jin, Q., Qi, L., Jiang, B., Wang, Q.: Novel improved Cuckoo search for PID controller design. Trans. Inst. Meas. Control 37(6), 721–731 (2015). http://journals.sagepub.com/doi/10.1177/0142331214544211. Accessed 20 Aug 2018CrossRefGoogle Scholar
  12. AI-Khafaji, A.A., Darus, I.Z.M.: Controller optimization using Cuckoo search algorithm of a flexible single-link manipulator. In: Proceedings of the 2014 First International Conference on Systems Informatics, Modelling and Simulation, pp. 39–44 (2014). https://dl.acm.org/citation.cfm?id=2681970.2682464. Accessed 21 Aug 2018
  13. Kishnani, M., Pareek, S., Gupta, R.: Optimal tuning of PID controller by Cuckoo search via Lévy flights. In: 2014 International Conference on Advances in Engineering & Technology Research (ICAETR - 2014), pp. 1–5. IEEE (2014). http://ieeexplore.ieee.org/document/7012927/. Accessed 20 Aug 2018
  14. Lu, H., Chen, W.: Dynamic-objective particle swarm optimization for constrained optimization problems. J. Comb. Optim. 12(4): 409–419 (2006). http://link.springer.com/10.1007/s10878-006-9004-x. Accessed 22 Aug 2018MathSciNetCrossRefGoogle Scholar
  15. Reynoso Meza, G., Blasco Ferragud, X., Sanchis Saez, J., Herrero Durá, J.M.: The ACC’1990 control benchmark: a two-mass-spring system. In: Reynoso Meza, G., Blasco Ferragud, X., Sanchis Saez, J., Herrero Durá, J.M. (eds.) Controller Tuning with Evolutionary Multiobjective Optimization. ISCASE, vol. 85, pp. 147–157. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-41301-3_7CrossRefzbMATHGoogle Scholar
  16. Sethi, R., Panda, S., Sahoo, B.P.: Cuckoo search algorithm based optimal tuning of PID structured TCSC controller. In: Jain, L.C., Behera, H.S., Mandal, J.K., Mohapatra, D.P. (eds.) Computational Intelligence in Data Mining - Volume 1. SIST, vol. 31, pp. 251–263. Springer, New Delhi (2015).  https://doi.org/10.1007/978-81-322-2205-7_24CrossRefGoogle Scholar
  17. Singh, K.S.M. Elamvazuthi, J.I., Shaari, K.Z.K., Lima, F.V.: PID tuning control strategy using Cuckoo search algorithm for pressure plant. In: 2016 6th International Conference on Intelligent and Advanced Systems (ICIAS), pp. 1–6. IEEE (2016). http://ieeexplore.ieee.org/document/7824127/. Accessed 20 Aug 2018
  18. Solihin, M.I., Akmeliawati, R., Tijani, I.B., Legowo, A.: Robust state feedback control design via PSO-based constrained optimization. Control Intell. Syst. 39(3), 168 (2011)MathSciNetzbMATHGoogle Scholar
  19. Solihin, M.I., Wen, M.C., Heltha, F., Lye, L.C.: Robust PID controller tuning for 2D gantry crane using Kharitonov’s theorem and differential evolution optimizer. In: Advanced Materials Research, vol. 903 (2014)CrossRefGoogle Scholar
  20. Solihin, M.I., Akmeliawati, R.: Robust control design based on differential evolution for two-mass system. In: A Problem Statement. 2010, January 2015Google Scholar
  21. Tang, S.H., Ang, C.K., Ariffin, M.K.A.B.M., Mashohor, S.B.: Predicting the motion of a robot manipulator with unknown trajectories based on an artificial neural network. Int. J. Adv. Rob. Syst. 11(10), 176 (2014). http://journals.sagepub.com/doi/10.5772/59278. Accessed 21 Aug 2018CrossRefGoogle Scholar
  22. Tijani, I.B., et al.: Robust H-infinity controller synthesis using multi-objectives differential evolution algorithm (MODE) for two-mass-spring system. In: 2011 4th International Conference on Modeling, Simulation and Applied Optimization, ICMSAO 2011 (2011)Google Scholar
  23. Wang, J., Li, S., Song, J.: Cuckoo search algorithm based on repeat-cycle asymptotic self-learning and self-evolving disturbance for function optimization. Comput. Intell. Neurosci. 2015, 1–12 (2015). http://www.hindawi.com/journals/cin/2015/374873/. Accessed 22 Aug 2018Google Scholar
  24. Wang, T., Meskin, M., Grinberg, I.: Comparison between particle swarm optimization and Cuckoo search method for optimization in unbalanced active distribution system. In: 2017 IEEE International Conference on Smart Energy Grid Engineering (SEGE), pp. 14–19. IEEE (2017). http://ieeexplore.ieee.org/document/8052769/. Accessed 20 Aug 2018
  25. Wie, B., Bernstein, D.S.: Benchmark problems for robust control design. J. Guidance Control Dyn. 15(5), 1057–1059 (1992). http://arc.aiaa.org/doi/10.2514/3.20949. Accessed 21 Aug 2018CrossRefGoogle Scholar
  26. Yang, X.S., Deb, S.: Engineering optimisation by Cuckoo search. Int. J. Math. Model. Numer. Optim. 1(4), 330 (2010). http://www.inderscience.com/link.php?id=35430. Accessed 20 Aug 2018CrossRefGoogle Scholar
  27. Zabihi Samani, M., Amini, F.: J. Vibroeng. 17. (2015). JVE International Ltd. https://www.jvejournals.com/article/15792. Accessed 20 Aug 2018

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringUCSI UniversityKuala LumpurMalaysia
  2. 2.School of Mechanical EngineeringUniversity of AdelaideAdelaideAustralia

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