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Non-fragile Robust PI Controller Design Using Co-variance Matrix Adaptation Evolutionary Strategy

  • K. Mohaideen Abdul Kadhar
  • S. Baskar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8298)

Abstract

This paper discusses the application of Co-variance Matrix Evolutionary Strategy (CMA-ES) in the design of non-fragile robust PI controller. The desired maximum sensitivity of the closed loop system is considered as an objective and success rate of stability under probabilistic controller uncertainty is taken as a constraint for non-fragile robust PI controller design problem. Success rate of stability is calculated using Monte Carlo simulation (MCS) under probabilistic controller perturbation. CMA-ES finds the optimal controller parameter based on robustness objective and nonfragileness constraint. The Single Input Single Output (SISO) first order sugar cane raw juice neutralization process and second order Irrigation canal systems are considered as a test systems. The performance of the CMA-ES designed non-fragile robust PI controller is compared with the flat phase concept based PI controller and Astrom suggested PI controller for both test systems. Simulation results demonstrated that CMA-ES based non-fragile robust PI controller has better performance in robustness as well as non-fragileness.

Keywords

CMA-ES non-fragile robust PI controller maximum sensitivity probabilistic parametric perturbation 

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References

  1. 1.
    Keel, L.H., Bhattacharyya, S.P.: Robust, Fragile or Optimal. IEEE Transactions on Automatic Control 42(8) (August 1997)Google Scholar
  2. 2.
    Whidborne, J.F., Istepanian, R.S.H., Wu, J.: Reduction of Controller Fragility by Pole Sensitivity Minimization. IEEE Transactions on Automatic Control 46(2) (February 2001)Google Scholar
  3. 3.
    Alfaro: PID controller fragility. ISA Transactions 46(4), 555–559 (2007)CrossRefGoogle Scholar
  4. 4.
    Duan, Z., Huang, L., Wang, L.: Robustness analysis and synthesis of SISO systems under both plant and controller perturbations. Systems & Control Letters 42, 201–216 (2001)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Astrom, K.J.: Control system Design (2002)Google Scholar
  6. 6.
    Datta, A., Ho, M.-T., Bhattacharyya, S.P.: Structure and Synthesis of PID Controllers. Springer, London (2000)CrossRefzbMATHGoogle Scholar
  7. 7.
    Ho, M.T.: Non-fragile PID controller design. In: 39th IEEE Conference on Decision and Control, Sydney, Australia (December 2000)Google Scholar
  8. 8.
    Monje, C.A., Calderon, A.J., Vinagre, B.M., Chen, Y., Feliu, V.: On Fractional PIλ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties. Nonlinear Dynamics 38, 369–381 (2004)CrossRefzbMATHGoogle Scholar
  9. 9.
    Wittwer, J.W.: “Monte Carlo Simulation Basics From” Vertex42.com (June 1, 2004), http://www.vertex42.com/ExcelArticles/mc/MonteCarloSimulation.html
  10. 10.
    Ray, L., Stengel, R.F.: A Monte Carlo approach to the analysis of control system robustness. Automatica 29(1), 229–236 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
  12. 12.
    Hansen, N.: The CMA Evolution Strategy: A Tutorial (June 28, 2011)Google Scholar
  13. 13.
    Takahama, T., Sakai, S., Iwane, N.: Solving Nonlinear Constrained Optimization Problems by the ε Constrained Differential Evolution. In: 2006 IEEE Conf. on Systems, Man, and Cybernetics, Taipei, October 8-11 (2006)Google Scholar
  14. 14.
    O’Dwyer, A.: Handbook of PI and PID Controller Tuning Rules. Imperial College Press (2009)Google Scholar
  15. 15.
    Mor˘arescu, I.-C.: Stability Crossing Boundaries and Fragility Characterization of PID Controllers for SISO Systems with I/O Delays. In: ACC 2011 (2011)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • K. Mohaideen Abdul Kadhar
    • 1
  • S. Baskar
    • 1
  1. 1.Electrical & Electronics Engineering DepartmentThiagarajar College of EngineeringIndia

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