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.
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References
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]
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]
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.
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.
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]
P. Airikka, “Robust predictive PI controller tuning,” Proc. of The 19th IFAC World Congress, pp. 9301–9306, 2014.
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.
P. Hušek, “Robust PI controller design with respect to fuzzy sensitivity margins,” Applied Soft Computing, vol. 13, no. 4, pp. 2037–2044, 2013. [click]
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.
A. Sadeghzadeh, “Robust reduced-order controller synthesis: a dilated LMI approach,” IMA Journal of Mathematical Control and Information, 2015.
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.
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]
R. Toscano, Structured Controllers for Uncertain Systems: A Stochastic Optimization Approach, Advances in Industrial Control, Springer-Verlag London, 2013.
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]
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]
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]
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]
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.
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.
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.
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.
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]
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.
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.
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.
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.
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]
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]
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]
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.
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.
X.-S. Yang and S. Deb, “Cuckoo search via Lévy flights,” World Congress on Nature & Biologically Inspired Computing, pp. 210–214, 2009. [click]
S. Mirjalili, “The ant lion optimizer,” Advances in Engineering Software, vol. 83, pp. 80–98, 2015. [click]
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]
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.
T. McKelvey, “Frequency domain identification methods,” Circuits, Systems and Signal Processing, vol. 21, no. 1, pp. 39–55, 2002. [click]
Control of Integral Processes with Dead Time, Advances in Industrial Control, Springer-Verlag London, 2011.
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Recommended by Associate Editor Soohee Han under the direction of Editor Euntai Kim. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2016R1D1A1B03935288), the Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea Government - Ministry of Trade Industry and Energy(MOTIE) (No. N0001075), and the Chung-Ang University Excellent Student Scholarship in 2016.
Yoonkyu Hwang received the B.E. and M.S. degrees in mechanical engineering from Chung-Ang University, Korea, in 2015 and 2017, respectively. His research focuses on the use of populationbased searches for artificial intelligence including system identification, robust control and autonomous navigation of mobile robot.
Young-Rae Ko received the B.E. degree in electrical and electronics engineering and the M.S. and Ph.D. degrees in mechanical engineering from Chung-Ang University, Korea, in 2010, 2012, and 2017, respectively. His research interests include hysteresis identification and compensation, system identification, disturbance observer, robust control, and adaptive control.
Youngil Lee received the B.E. and M.S. degrees in mechanical engineering from Chung-Ang University, Korea, in 2013 and 2015, respectively. His research interests include artificial intelligence, robust control, and robotics.
Tae-Hyoung Kim received the B.S. and M.S. degrees in mechanical engineering from Chung-Ang University, Korea, in 1999 and 2001, respectively. He received the Ph.D. degree in informatics from Kyoto University, Japan, in 2006. He is currently an Associate Professor at the School of Mechanical Engineering, Chung-Ang University. His current research interests include robust control, multi-agent system, particle swarm optimization, system identification, model predictive control, iterative learning control and systems biology.
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Hwang, Y., Ko, YR., Lee, Y. et al. Frequency-domain Tuning of Robust Fixed-structure Controllers via Quantum-behaved Particle Swarm Optimizer with Cyclic Neighborhood Topology. Int. J. Control Autom. Syst. 16, 426–436 (2018). https://doi.org/10.1007/s12555-016-0766-3
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DOI: https://doi.org/10.1007/s12555-016-0766-3