Frequency-domain Tuning of Robust Fixed-structure Controllers via Quantum-behaved Particle Swarm Optimizer with Cyclic Neighborhood Topology

  • Yoonkyu Hwang
  • Young-Rae Ko
  • Youngil Lee
  • Tae-Hyoung Kim
Regular Paper Control Theory and Applications
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Abstract

This paper presents a constrained particle swarm optimization (PSO) algorithm with a cyclic neighborhood topology inspired by the quantum behavior of particles, and describes its application to the frequency-domain tuning of robust fixed-structure controllers. Two main methodologies for improving the exploration and exploitation performance of the PSO framework are described. First, a PSO scheme with a neighborhood structure based on a cyclic network topology is presented. This scheme enhances the exploration ability of the swarm and effectively reduces the probability of premature convergence to local optima. Second, the above PSO scheme is hybridized using a distributed quantum-principle-based offspring creation mechanism. Such a hybridized PSO framework enables neighboring particles to concentrate the search around the region covered by those particles to refine the candidate solution. A frequency-domain tuning method for fixed-structure controllers is then demonstrated. This method guarantees certain preassigned performance specifications based on the developed PSO technique. A typical numerical example is considered, and the results clearly demonstrate that the proposed PSO scheme provides a novel and powerful impetus with remarkable reliability for robust fixed-structure controller syntheses. Further, an experiment was conducted on a magnetic levitation system to compare the proposed strategy with a well-known frequency-domain tuning method implemented in the MATLAB tool for Structured H Synthesis. The comparative experimental results validate the effectiveness of the proposed tuning strategy in practical applications.

Keywords

Constrained optimization control system synthesis fixed-structure controller particle swarm optimization robust control 

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References

  1. [1]
    P. Gahinet and P. Apkarian, “Frequency-domain tuning of fixed-structure control systems,” Proc. of UKACC International Conference on Control (CONTROL), pp. 178–183, 2012. [click]Google Scholar
  2. [2]
    P. Puri and S. Ghosh, “A hybrid optimization approach for PI controller tuning based on gain and phase margin specifications,” Swarm and Evolutionary Computation, vol. 8, pp. 69–78, 2013. [click]CrossRefGoogle Scholar
  3. [3]
    G.-Q. Zeng, K.-D. Lu, Y.-X. Dai, Z.-J. Zhang, M.-R. Chen, C.-W. Zheng, D. Wu, and W.-W. Peng, “Binary-coded extremal optimization for the design of PID controllers,” Neurocomputing, vol. 138, pp. 180–188, 2014.CrossRefGoogle Scholar
  4. [4]
    G.-Q. Zeng, J. Chen, M.-R. Chen, Y.-X. Dai, L.-M. Li, K.-D. Lu, and C.-W. Zheng, “Design of multivariable PID controllers using real-coded population-based extremal optimization,” Neurocomputing, vol. 151, pp. 1343–1353, 2015.CrossRefGoogle Scholar
  5. [5]
    G. Karer and I. Škrjanc, “Interval-model-based global optimization framework for robust stability and performance of PID controllers,” Applied Soft Computing, vol. 40, pp. 526–543, 2016. [click]CrossRefGoogle Scholar
  6. [6]
    P. Airikka, “Robust predictive PI controller tuning,” Proc. of The 19th IFAC World Congress, pp. 9301–9306, 2014.Google Scholar
  7. [7]
    Y.-J. Wang, “Determination of all feasible robust PID controllers for open-loop unstable plus time delay processes with gain margin and phase margin specifications,” ISA Trans., vol. 53, no. 2, pp. 628–648, 2014.CrossRefGoogle Scholar
  8. [8]
    P. Hušek, “Robust PI controller design with respect to fuzzy sensitivity margins,” Applied Soft Computing, vol. 13, no. 4, pp. 2037–2044, 2013. [click]CrossRefGoogle Scholar
  9. [9]
    T. Azuma and S. Watanabe, “A design of PID controllers using FRIT-PSO,” Proc. of The 8th International Conference on Sensing Technology, pp. 459–464, 2014.Google Scholar
  10. [10]
    A. Sadeghzadeh, “Robust reduced-order controller synthesis: a dilated LMI approach,” IMA Journal of Mathematical Control and Information, 2015.Google Scholar
  11. [11]
    U. Nurges and S. Avanessov, “Fixed-order stabilising controller design by a mixed randomised=deterministic method,” International Journal of Control, vol. 88, no. 2, pp. 335–346, 2015.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    R. Xie, J. Gong, and X. Wang, “A new probabilistic robust control approach for system with uncertain parameters,” Asian Journal of Control, vol. 17, no. 4, pp. 1330–1341, 2015. [click]MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    R. Toscano, Structured Controllers for Uncertain Systems: A Stochastic Optimization Approach, Advances in Industrial Control, Springer-Verlag London, 2013.CrossRefMATHGoogle Scholar
  14. [14]
    I. Maruta, T. Sugie, and T.-H. Kim, “Synthesis of fixedstructure robust controllers using a constrained particle swarm optimizer with cyclic neighborhood topology,” Expert Systems with Applications, vol. 40, no. 9, pp. 3595–3605, 2013. [click]CrossRefGoogle Scholar
  15. [15]
    L. Wang and L. Li, “Fixed-structure H controller synthesis based on differential evolution with level comparison,” IEEE Transactions on Evolutionary Computation, vol. 15, no. 1, pp. 120–129, 2011. [click]MathSciNetCrossRefGoogle Scholar
  16. [16]
    S. Sivananaithaperumal, S. Amali, S. Baskar, and P. Suganthan, “Constrained self-adaptive differential evolution based design of robust optimal fixed structure controller,” Engineering Applications of Artificial Intelligence, vol. 24, no. 6, pp. 1084–1093, 2011. [click]CrossRefGoogle Scholar
  17. [17]
    T.-H. Kim, I. Maruta, and T. Sugie, “Robust PID controller tuning based on the constrained particle swarm optimization,” Automatica, vol. 44, no. 4, pp. 1104–1110, 2008. [click]MathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    I. Maruta, T.-H. Kim, and T. Sugie, “Fixed-structure H controller synthesis: A meta-heuristic approach using simple constrained particle swarm optimization,” Automatica, vol. 45, no. 2, pp. 553–559, 2009.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    Y. Wakasa, S. Kanagawa, K. Tanaka, and Y. Nishimura, “Direct PID tuning for systems with hysteresis and its application to shape memory alloy actuators,” Proceedings of the SICE Annual Conference, pp. 2933–2938, 2011.Google Scholar
  20. [20]
    M. Kawanishi, T. Narikiyo, T. Kaneko, and N. Srebro, “Fixed-structure H controller design based on distributed probabilistic model-building genetic algorithm,” Proceedings of the IASTED International Conference on Intelligent Systems and Control, pp. 127–132, 2011.Google Scholar
  21. [21]
    M. Sedraoui, S. Abdelmalek, and S. Gherbi, “Multivariable generalized predictive control using an improved particle swarm optimization algorithm,” Informatica (Ljubljana), vol. 35, no. 3, pp. 363–374, 2011.MathSciNetMATHGoogle Scholar
  22. [22]
    S. Bouallègue, J. Haggège, and M. Benrejeb, “Particle swarm optimization-based fixed-structure H control design,” International Journal of Control, Automation and Systems, vol. 9, no. 2, pp. 258–266, 2011. [click]CrossRefGoogle Scholar
  23. [23]
    S. Sreepriya, S. Baskar, and M. Willjuice Iruthayarajan, “Covaraince matrix adapted evolutionary strategy based design of robust optimal fixed structure controller,” Proc. of Computing Communication and Networking Technologies (ICCCNT), 2010 International Conference on, pp. 1–5, 2010.Google Scholar
  24. [24]
    A. Yoshida, S. Kanagawa, Y. Wakasa, K. Tanaka, and T. Akashi, “PID controller tuning based on the covariance matrix adaptation evolution strategy,” Proc. of ICCASSICE 2009 - ICROS-SICE International Joint Conference 2009, Proceedings, pp. 2982–2986, 2009.Google Scholar
  25. [25]
    D. P. Rini, S. M. Shamsuddin, and S. S. Yuhaniz, “Particle swarm optimization: Technique, system and challenges,” International Journal of Computer Application, vol. 4, no. 1, pp. 19–27, 2011.CrossRefGoogle Scholar
  26. [26]
    M. Reyes-Sierra and C. Coello, “Multi objective particle swarm optimizers A survey of the state-of-the-art,” International Journal of Computational Intelligence Research, vol. 2, no. 3, pp. 287–308, 2006.MathSciNetGoogle Scholar
  27. [27]
    K. Kennedy and R. Mendes, “Neighborhood topologies in fully-informed and best-of-neighborhood particle swarms,” IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol. 36, no. 4, pp. 515–519, 2006. [click]CrossRefGoogle Scholar
  28. [28]
    J. Sun, B. Feng, and W.-B. Xu, “Particle swarm optimization with particles having quantum behavior,” Proc. of Congress on Evolutionary Computation, pp. 325–331, 2004. [click]Google Scholar
  29. [29]
    Y. Fujisaki, Y. Oishi, and R. Tempo, “Mixed deterministic/ randomized methods for fixed order controller design,” IEEE Trans. Automat. Contr., vol. 53, no. 9, pp. 2033–2047, 2008. [click]MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    J. Sun, W.-B. Xu, and B. Feng, “A global search strategy of quantum-behaved particle swarm optimization,” Proc. of IEEE Conference on Cybernetics and Intelligent Systems, pp. 111–116, 2004.Google Scholar
  31. [31]
    S. Miruna Joe Amali and S. Baskar, “Design of robust optimal fixed structure controller using self adaptive differential evolution,” Proc. of Swarm, Evolutionary, and Memetic Computing - First International Conference on Swarm, Evolutionary, and Memetic Computing, SEMCCO 2010, vol. 6466, pp. 79–86, 2010.Google Scholar
  32. [32]
    X.-S. Yang and S. Deb, “Cuckoo search via Lévy flights,” World Congress on Nature & Biologically Inspired Computing, pp. 210–214, 2009. [click]Google Scholar
  33. [33]
    S. Mirjalili, “The ant lion optimizer,” Advances in Engineering Software, vol. 83, pp. 80–98, 2015. [click]CrossRefGoogle Scholar
  34. [34]
    R. Morales and H. Sira-Ramírez, “Trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and GPI control,” International Journal of Control, vol. 83, no. 6, pp. 1155–1166, 2010. [click]MathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    I. A. Raptis and K. P. Valavanis, “Frequency domain system identification,” Linear and nonlinear control of smallscale unmanned helicopters, Intelligent Systems, Control and Automation: Science and Engineering, Springer Netherlands, vol. 45, pp. 47–72, 2011.CrossRefGoogle Scholar
  36. [36]
    T. McKelvey, “Frequency domain identification methods,” Circuits, Systems and Signal Processing, vol. 21, no. 1, pp. 39–55, 2002. [click]MathSciNetCrossRefGoogle Scholar
  37. [37]
    Control of Integral Processes with Dead Time, Advances in Industrial Control, Springer-Verlag London, 2011.Google Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yoonkyu Hwang
    • 1
  • Young-Rae Ko
    • 1
  • Youngil Lee
    • 1
  • Tae-Hyoung Kim
    • 1
  1. 1.Department of Mechanical Engineering, College of EngineeringChung-Ang UniversitySeoulKorea

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