Skip to main content
SpringerLink
Log in

Comparative analysis of PSO algorithms for PID controller tuning

  • Published:
Chinese Journal of Mechanical Engineering Submit manuscript

Abstract

The active magnetic bearing(AMB) suspends the rotating shaft and maintains it in levitated position by applying controlled electromagnetic forces on the rotor in radial and axial directions. Although the development of various control methods is rapid, PID control strategy is still the most widely used control strategy in many applications, including AMBs. In order to tune PID controller, a particle swarm optimization(PSO) method is applied. Therefore, a comparative analysis of particle swarm optimization(PSO) algorithms is carried out, where two PSO algorithms, namely (1) PSO with linearly decreasing inertia weight(LDW-PSO), and (2) PSO algorithm with constriction factor approach(CFA-PSO), are independently tested for different PID structures. The computer simulations are carried out with the aim of minimizing the objective function defined as the integral of time multiplied by the absolute value of error(ITAE). In order to validate the performance of the analyzed PSO algorithms, one-axis and two-axis radial rotor/active magnetic bearing systems are examined. The results show that PSO algorithms are effective and easily implemented methods, providing stable convergence and good computational efficiency of different PID structures for the rotor/AMB systems. Moreover, the PSO algorithms prove to be easily used for controller tuning in case of both SISO and MIMO system, which consider the system delay and the interference among the horizontal and vertical rotor axes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. LEI S, PALAZZOLO A. Control of flexible rotor systems with active magnetic bearings[J]. Journal of Sound and Vibration, 2008, 314: 19–38.

    Article  Google Scholar 

  2. ŠTIMAC G, BRAUT S, ŽIGULIĆ R. Vibration suppression of flexible rotor using active magnetic bearings(AMB)[J]. Transactions of Famena, 2011, 35: 27–38.

    Google Scholar 

  3. ASTRÖM K J, HÄGGLUND T. The future of PID control[J]. Control Engineering Practice, 2001, 9: 1163–1175.

    Article  Google Scholar 

  4. ZIEGLER J B, NICHOLS N B. Optimum settings for PID controllers[J]. Transactions of ASME, 1942, 64: 759–768.

    Google Scholar 

  5. ZHAO Z Y, TOMIZUKA M. Fuzzy gain scheduling of PID controllers[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1993, 23: 1392–1398.

    Article  Google Scholar 

  6. AL-ODIENAT A I, AL-LAWAMA A A. The advantages of PID fuzzy controllers over the conventional types[J]. American Journal of Applied Sciences, 2008, 5: 653–658.

    Article  Google Scholar 

  7. CHEN K Y, TUNG P C, TSAI M T, FAN Y H. A self-tuning fuzzy PID-type controller design for unbalance compensation in an active magnetic bearing[J]. Expert Systems with Applications, 2009, 36: 8560–8570.

    Article  Google Scholar 

  8. CHEN H C, CHANG S H. Genetic algorithms based optimization design of a PID controller for an active magnetic bearing[J]. International Journal of Computer Science and Network Security, 2006, 6: 95–99.

    Google Scholar 

  9. KHANDANI K, JALALI A A. PSO based optimal fractional PID controller design for an active magnetic bearing suspension system[C]//Proceedings of 18th Annual International Conference on Mechanical Engineering, Iran, Teheran, May 11–13, 2010: 1–6.

    Google Scholar 

  10. KIM T H, MARUTA I, SUGIE T. Robust PID controller tuning based on the constrained particle swarm optimization[J]. Automatica, 2008, 44: 1104–1110.

    Article  MathSciNet  MATH  Google Scholar 

  11. CHANG W D, SHIH S P. PID controller design of nonlinear systems using an improved particle swarm optimization approach[J]. Communications in Nonlinear Science and Numerical Simulation, 2010, 15: 3632–3639.

    Article  MATH  Google Scholar 

  12. FANG H, CHEN L, SHEN Z. Application of an improved PSO algorithm to optimal tuning of PID gains for water turbine governor[J]. Energy Conversion and Management, 2011, 52: 1763–1770.

    Article  Google Scholar 

  13. MENHAS M I, WANG L, FEI M, et al. Comparative performance analysis of various binary coded PSO algorithms in multivariable PID controller design[J]. Expert Systems with Applications, 2012, 39: 4390–4401.

    Article  Google Scholar 

  14. CHIHA I, LIOUANE N, BORNE P. Tuning PID controller using multiobjective ant colony optimization[J]. Applied Computational Intelligence and Soft Computing, 2012: 1–7.

    Google Scholar 

  15. KENNEDY J, EBERHART R. Particle swarm optimization[C]// Proceedings of IEEE International Conference on Neural Network, Part IV, Perth, Australia, 1995: 1942–1948.

    Chapter  Google Scholar 

  16. PARSOPOULOS K E, VRAHATIS M N. Particle swarm optimization and intelligence: Advances and Applications[M]. New York: Information Science Reference, 2010.

    Book  MATH  Google Scholar 

  17. XU H, CHEN G. An intelligent fault identification method of rolling bearings based on LSSVM optimized by improved PSO[J]. Mechanical Systems and Signal Processing, 2012, 35: 167–175.

    Article  Google Scholar 

  18. LIN Y L, CHANG W D, HSIEG J G. A particle swarm optimization approach to nonlinear rational filter modeling[J]. Expert Systems with Applications, 2008, 34: 1194–1199.

    Article  Google Scholar 

  19. SHI Y, EBERHART R C. A modified particle swarm optimizer[C]// Proceedings of the IEEE International Conference on Evolutionary Computation, Anchorage, USA, 1998: 69–73.

    Google Scholar 

  20. CLERC M, KENNEDY J. The particle swarm: explosion, stability and convergence in a multi-dimensional complex space[J]. IEEE Transactions on Evolution Computation, 2004, 8: 204–210.

    Article  Google Scholar 

  21. SCHWEITZER G, MASLEN Eric H. Magnetic bearings: theory, design and application to rotating machinery[M]. New York: Springer, 2009.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Engineering, University of Rijeka, Rijeka, 51000, Croatia

    Goranka Štimac, Sanjin Braut & Roberto Žigulić

Authors
  1. Goranka Štimac
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjin Braut
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Roberto Žigulić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Goranka Štimac.

Additional information

Supported by University of Rijeka, Croatia(Grant Nos. 13.09.1.2.11, 13.09.2.2.19)

ŠTIMAC Goranka, born in 1982 is currently a senior research/teaching assistant at Faculty of Engineering, University of Rijeka, Croatia. She received her PhD degree from Faculty of Engineering, University of Rijeka, Croatia in 2012. Her research interests include rotordynamics, active magnetic bearings and mechatronics.

BRAUT Sanjin, born in 1973 is currently an associate professor at Faculty of Engineering, University of Rijeka, Croatia. He received his PhD degree from Faculty of Engineering, University of Rijeka, Croatia in 2006. His research and teaching interests include dynamics, vibrations, dynamics of machines, rotordynamics, active magnetic bearings and mechatronics.

ŽIGULIĆ Roberto, born in 1966 is currently a full professor at Faculty of Engineering, University of Rijeka, Croatia. He received his PhD degree from Faculty of Engineering, University of Rijeka, Croatia in 2001. His research and teaching interests include dynamics, vibrations, dynamics of machines, rotordynamics, simulations of dynamical systems and robotics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Štimac, G., Braut, S. & Žigulić, R. Comparative analysis of PSO algorithms for PID controller tuning. Chin. J. Mech. Eng. 27, 928–936 (2014). https://doi.org/10.3901/CJME.2014.0527.302

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3901/CJME.2014.0527.302

Keywords

Search

Navigation