Skip to main content
SpringerLink
Log in

PID Controller Design for MIMO Processes Using Improved Particle Swarm Optimization

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper aims at the PID control system design for multivariable input and multivariable output (MIMO) processes. An improved version of a particle swarm optimization (PSO) algorithm is utilized to design PID control gains in MIMO control systems. In addition to the individual best and the global best particles, the velocity updating formula of the developed algorithm includes a new factor, the best particle of each sub-population, to enhance the search capacity. Based on the improved particle swarm optimization (IPSO), a complete design strategy is proposed for MIMO PID control systems. All control gains will be evolved to the optimal values by minimizing the system performance criterion. To show the efficiency of the proposed design method, a multivariable chemical process system with two inputs and two outputs is illustrated. Some experiment results, including different algorithm parameter settings and comparisons with other methods, are given. Numerical simulations indicate that the proposed method is superior to other optimal methods.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. F.D. Bianchi, R.J. Mantz, C.F. Christiansen, Multivariable PID control with set-point weighting via BMI optimisation. Automatica 44(2), 472–478 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. W.-D. Chang, A multi-crossover genetic approach to multivariable PID controllers tuning. Expert Syst. Appl. 33(3), 620–626 (2007)

    Article  Google Scholar 

  3. W.-D. Chang, S.-P. Shih, PID controller design of nonlinear systems using improved particle swarm optimization approach. Commun. Nonlinear Sci. Numer. Simul. 15(11), 3632–3639 (2010)

    Article  MATH  Google Scholar 

  4. Y.-P. Chang, L.-S. Shieh, C.-R. Liu, P. Cofie, Digital modeling and PID controller design for MIMO analog systems with multiple delays in states, inputs and outputs. Circuits Syst. Signal Process. 28(1), 111–145 (2009)

    Article  MATH  Google Scholar 

  5. L.D.S. Coelho, M.W. Pessoa, A tuning strategy for multivariable PI and PID controllers using differential evolution combined with chaotic Zaslavskii map. Expert Syst. Appl. 38(11), 13694–13701 (2011)

    Google Scholar 

  6. S.N. Deepa, G. Sugumaran, Model order formulation of a multivariable discrete system using a modified particle swarm optimization approach. Swarm Evol. Comput. 1(4), 204–212 (2011)

    Article  Google Scholar 

  7. J. Kennedy, R. Eberhart, Particle swarm optimization, in Proc. of the IEEE Int. Conf. Neural Networks, vol. IV (1995), pp. 1942–1948

    Google Scholar 

  8. B.-C. Kuo, Automatic Control Systems, 7th edn. (Wiley, New York, 1995)

    Google Scholar 

  9. G. Ma, W. Zhou, A novel particle swarm optimization algorithm based on particle migration. Appl. Math. Comput. 218(11), 6620–6626 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  10. D.K. Maghade, B.M. Patre, Decentralized PI/PID controllers based on gain and phase margin specifications for TITO processes. ISA Trans. 51(4), 550–558 (2012)

    Article  Google Scholar 

  11. M.I. Menhas, M. Fei, L. Wang, L. Qian, Real/binary co-operative and co-evolving swarms based multivariable PID controller design of ball mill pulverizing system. Energy Convers. Manag. 54(1), 67–80 (2012)

    Article  Google Scholar 

  12. M.I. Menhas, L. Wang, M. Fei, H. Pan, Comparative performance analysis of various binary coded PSO algorithms in multivariable PID controller design. Expert Syst. Appl. 39(4), 4390–4401 (2012)

    Article  Google Scholar 

  13. I.I. Ruiz-Lopez, G.C. Rodriguez-Jimenes, M.A. Garcia-Alvarado, Robust MIMO PID controllers tuning based on complex/real ration of the characteristic matrix eigenvalues. Chem. Eng. Sci. 61(13), 4332–4340 (2006)

    Article  Google Scholar 

  14. J. Sun, W. Fang, V. Palade, X. Wu, W. Xu, Quantum-behaved particle swarm optimization with Gaussian distributed local attractor point. Appl. Math. Comput. 218(7), 3763–3775 (2011)

    Article  MATH  Google Scholar 

  15. N.A. Wahab, R. Katebi, J. Balderud, Multivariable PID control design for activated sludge process with nitrification and denitrification. Biochem. Eng. J. 45(3), 239–248 (2009)

    Article  Google Scholar 

  16. Q.-G. Wang, Z.-Y. Nie, PID control for MIMO processes, part 1 (2012), pp. 177–204. doi:10.1007/978-1-4471-2425-2_6 (Book chapter)

  17. Q.-G. Wang, B. Zou, T.-H. Lee, B. Qiang, Auto-tuning of multivariable PID controllers from decentralized relay feedback. Automatica 33(3), 319–330 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  18. Q.-G. Wang, Z. Ye, W.-J. Cai, C.-C. Hang, PID Control for Multivariable Processes (Springer, Berlin, 2008). doi:10.1007/978-3-540-78482-1

    MATH  Google Scholar 

  19. Y. Wang, B. Li, T. Weise, J. Wang, B. Yuan, Q. Tian, Self-adaptive learning based particle swarm optimization. Inf. Sci. 181(20), 4515–4538 (2011)

    Article  MATH  Google Scholar 

  20. M. Willjuice Iruthayarajan, S. Baskar, Evolutionary algorithms based design of multivariable PID controller. Expert Syst. Appl. 36(5), 9159–9167 (2009)

    Article  Google Scholar 

  21. Q. Xiong, W.-J. Cai, M.-J. He, Equivalent transfer function method for PI/PID controller design of MIMO processes. J. Process Control 17(8), 665–673 (2007)

    Article  Google Scholar 

  22. L. Zhao, F. Qian, Y. Yang, Y. Zeng, H. Su, Automatically extracting T–S fuzzy models using cooperative random learning particle swarm optimization. Appl. Soft Comput. 10(3), 938–944 (2010)

    Article  Google Scholar 

  23. S.-Z. Zhao, M. Willjuice Iruthayarajan, S. Baskar, P.N. Suganthan, Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization. Inf. Sci. 181(16), 3323–3355 (2011)

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Science Council of Taiwan under Grant NSC 102-2221-E-366-004.

Author information

Authors and Affiliations

  1. Department of Computer and Communication, Shu-Te University, Kaohsiung, 824, Taiwan

    Wei-Der Chang & Chih-Yung Chen

Authors
  1. Wei-Der Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chih-Yung Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei-Der Chang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, WD., Chen, CY. PID Controller Design for MIMO Processes Using Improved Particle Swarm Optimization. Circuits Syst Signal Process 33, 1473–1490 (2014). https://doi.org/10.1007/s00034-013-9710-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-013-9710-4

Keywords

Search

Navigation