Abstract
This paper proposes a novel method to designing an H ∞ PID controller with robust stability and disturbance attenuation. This method uses particle swarm optimization algorithm to minimize a cost function subject to H ∞-norm to design robust performance PID controller. We propose two cost functions to design of a multiple-input, multiple-output (MIMO) and single-input, single-output (SISO) robust performance PID controller. We apply this method to a SISO flexible-link manipulator and a MIMO super maneuverable F18/HARV fighter aircraft system as two challenging examples to illustrate the design procedure and to verify performance of the proposed PID controller design methodology. It is shown with the MIMO super maneuverable F18/HARV fighter system that PSO performs well for parametric optimization functions and performance of the PSO-based method without prior domain knowledge is superior to those of existing GA-based and OSA-based methods for designing H ∞ PID controllers.
References
M. J. Balas, “Feedback control of flexible systems,” IEEE Trans. on Automat. Contr., vol. 23, no. 4, pp. 673–679, Aug. 1978.
J. C. Doyle, K. Glover, P. Khargonekar, and B. A. Francis, “State space solutions to standard H 2 and H ∞ control problems,” IEEE Trans. on Automat. Contr., vol. AC-34, pp. 831–847, Aug. 1989.
G. J. Balas, J. C. Doyle, K. Glover, A. Packard, and R. Smith, μ-Analysis and Synthesis ToolBox, Mathworks, Natick, MA, 1993.
R. S. Smith, C. C. Chu, and J. L. Fanson “The design of H ∞ controllers for an experimental noncollocated flexible structure problem,” IEEE Trans. on Control Systems Technology, vol. 2, no. 2, pp. 101–109, Mar. 1994.
G. J. Balas and J. C. Doyle, “Robustness and performance trade-offs in control design for flexible structures,” IEEE Trans. on Control Systems Technology, vol. 2, no. 4, pp. 352–361, Dec. 1994.
I. N. Kar, T. Miyakura, and K. Seto, “Bending and torsional vibration control of a flexible plate structure using H ∞-based robust control law,” IEEE Trans. on Control Systems Technology, vol. 8, no. 3, pp. 545–553, May 2000.
V. D. Blondel and J. N. Tsitsiklis, “A survey of computational complexity results in systems and control,” Automatica, vol. 36, pp. 1249–1274, Sep. 2000.
G. J. Silva, A. Datta, and S. P. Bhattacharyya, “New results on the synthesis of PID controllers,” IEEE Trans. on Automat. Contr., vol. 47, no. 2, pp. 241–252, Feb.2002.
H. Xu, A. Datta, and S. P. Bhattacharyya, “Computation of all stabilizing PID gains for digital control systems,” IEEE Trans. on Automat. Contr., vol. 46, no. 4, pp. 647–652, Apr. 2001.
L. H. Keel, J. I. Rego, and S. P. Bhattacharyya, “A new approach to digital PID controller design,” IEEE Trans. on Automat. Contr., vol. 48, no. 4, pp. 687–692, Apr. 2003.
M. T. Ho and C. Y. Lin, “PID controller design for robust performance,” IEEE Trans. on Automat. Contr., vol. 48, no. 8, pp. 1404–1409, Aug. 2003.
F. Blanchini, A. Lepschy, S. Miani, and U. Viaro “Characterization of PID and Lead/Lag compensators satisfying given H ∞ specifications,” IEEE Trans. on Automat. Contr., vol. 49, no. 5, pp. 736–740, May 2004.
S. J. Ho, S. Y. Ho and L. S. Shu, “OSA: orthogonal simulated annealing algorithm and its application to designing mixed H 2 /H ∞ optimal controllers,” IEEE Trans. Sys. Man and Cyber., vol. 34, no. 5, pp. 588–600, Sep. 2004.
R. A. Krohling and J. P. Rey, “Design of optimal disturbance rejection PID controllers using genetic algorithm,” IEEE Trans. Evol. Comp., vol. 5, no. 1, pp. 78–82, Feb. 2001.
B. S. Chen and Y. M. Cheng, “A structure-specified H ∞ optimal control design for practical applications: a genetic approach,” IEEE Trans. Control Sys. Tech., vol. 6, no. 6, pp. 707–718, Nov. 1998.
B. S. Chen, Y. M. Cheng, and C. H. Lee, “A genetic approach to mixed optimal PID control,” IEEE Control Sys. Mag., vol. 15, pp. 51–60, Oct. 1995.
J. Kennedy, “The particle swarm: social adaptation of knowledge,” Proc. IEEE Int. Conf. Evolutionary Comput., Indianapolis, IN, pp. 303–308, 1997.
J. J. Liang, A. K. Qin, P. N. Suganthan, and S. Baskar, “Comprehensive learning particle swarm optimizer for global optimization of multimodal functions,” IEEE Trans. Evol. Comp., vol. 10, no. 3, pp. 281–295, June 2006.
O. Chao and L. Weixing, “Comparison between PSO and GA for parameters optimization of PID controller,” Proc. of International Conference on Mechatronics and Automation, pp. 2471–2475, June 2006.
N. Sadati, M. Zamani, and H. Mahdavian, “Hybrid particle swarm-based-simulated annealing optimization techniques,” Proc. of the IEEE Inter. Conf. on Indus. Elect., Paris, France, Nov. 2006.
D. B. Fogel, Evolutionary Computation Toward a New Philosophy of Machine Intelligence, IEEE, New York, 1995.
Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” Proc. IEEE Int. Conf. on Evolutionary Computation, pp. 69–73, 1998.
R. Eberhart and Y. Shi, “Particle swarm optimization: Developments, applications and resources,” Proc. IEEE Int. Conf. on Evolutionary Computation, pp. 81–86, 2001.
M. Avriel, Nonlinear Programming: Theory and Algorithms, Wiley, New York, 1979.
K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, Upper Saddle River, NJ, 1996.
M. T. Ho and Y. W. Tu, “PID controller design for a flexible-link manipulator,” Proc. IEEE Conf. on Decision and Control, Spain, pp. 6841–6846, Dec. 2005.
H. Kwakernaak, “Minimax frequency domain performance and robustness optimization of feedback systems,” IEEE Trans. Automat. Contr., vol. 30, pp. 994–1004, 1985.
I. Kitsios, T. Pimenides, and P. Groumpos, “A genetic algorithm for designing H ∞ structured specified controllers,” Proc. IEEE Int. Conf. Contr. Applicat., Mexico, pp. 1196–1201, 2001.
P. Voulgaris and L. Valavani, “High performance H and H designs for supermaneuverable F18/harv fighter aircraft,” AIAA J. Guid. Cont. Dyn., vol. 14, no. 1, pp. 157–165, 1991.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editorial Board member Jietae Lee under the direction of Editor Young-Hoon Joo. This work was supported by the Iranian Telecommunication Research Center (ITRC) under Grant T500-11629.
Majid Zamani received the B.Sc. and M.Sc. degrees in Electrical Engineering in 2005 and 2007 from Isfahan University of Technology, and Sharif University of Technology, Iran, respectively. Currently, He is a Ph.D. student in Electrical Engineer-ing Department of University of California, Los Angeles, U.S.A.
Nasser Sadati was born in Iran in 1960. He received the B.S. degree from Oklahoma State University, Stillwater, in 1982, and the M.S. and Ph.D. degrees from Cleveland State University, Cleveland, OH, USA, in 1985 and 1989, respectively, all in Electrical Engineering. From 1986 to 1987, he was with the NASA Lewis Research Center, Cleveland, to study the albedo effects on space station solar array. In 1989, he conducted postgraduate research at Case Western Reserve University, Cleveland, OH. Since 1990, he has been with the Sharif University of Technology, Tehran, Iran, where he is currently a Full Professor in the Department of Electrical Engineering, the Head of Control Group, and the Director of the Intelligent Systems Laboratory and the Co-Director of Robotics and Machine Vision Laboratory. He was the first to introduce the subject of fuzzy logic and intelligent control as course work in the universities engineering program in Iran. He has published two books in Persian and over 200 technical papers in peer-reviewed journals and conference proceedings, and is currently working on two more books in English (Intelligent Control of Large-Scale Systems) and Persian (Neural Networks). His research interests include intelligent control and soft computing, large-scale systems, robotics and pattern recognition. Dr. Sadati was the recipient of the Academic Excellence Award for 1998–1999 from the Sharif University of Technology. He is a Founding Member of the Iranian Journal of Fuzzy Systems (IJFS). He is the Founder and Chairman of the First Symposiums on Fuzzy Logic, and Intelligent Control and Soft Computing in Iran. He is the editorial board members of International Journal of Advances in Fuzzy Mathematics (AFM) and the Journal of Iranian Association of Electrical and Electronics Engineers (IAEEE). He also has served as the Co-Chair of the First International Conference on Intelligent and Cognitive Systems (ICICS’96). Dr. Sadati is a Founding Member of the Center of Excellence in Power System Management and Control (CEPSMC), Sharif University of Technology, Tehran, Iran and the Foreign Member of the Institute of Control, Robotics, and Systems (ICROS), Korea.
Masoud Karimi Ghartemani received the B.Sc. and M.Sc. in Electrical Engineering in 1993 and 1995 from Isfahan University of Technology, Iran, where he continued to work as a Teaching and Research Assistant until 1998. He received the Ph.D. degree in Electrical Engineering from University of Toronto in 2004. He was a Research Associate and a Post-doctoral Researcher in the Department of Electrical and Computer Engineering of the University of Toronto from 1998 to 2001 and from 2004 to 2005, respectively. He joined Sharif University of Technology, Tehran, Iran, in 2005 as a Faculty Member. His research topics include nonlinear and optimal control, novel control and signal processing techniques/algorithms for control and protection of modern power systems, power electronics, power system stability and control, and power quality.
Rights and permissions
About this article
Cite this article
Zamani, M., Sadati, N. & Ghartemani, M.K. Design of an H ∞ PID controller using particle swarm optimization. Int. J. Control Autom. Syst. 7, 273–280 (2009). https://doi.org/10.1007/s12555-009-0213-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-009-0213-9