Advertisement

Robust Control Design of SPSC Microbial Fuel Cell with Norm Bounded Uncertainty

  • Ravi PatelEmail author
  • Dipankar DebEmail author
  • Rajeeb DeyEmail author
  • Valentina E. BalasEmail author
Chapter
Part of the Intelligent Systems Reference Library book series (ISRL, volume 161)

Abstract

In this chapter an attempt is made for the first time to formulate a robust controller in a linear matrix inequality (LMI) framework for a linearized model of Single Population Single Chamber Microbial Fuel Cell (SPSC MFC) to improve the system performance with unstructured time-varying uncertainties. The dilution rate is considered as an uncertain parameter.

References

  1. 1.
    Lai, C., Fang, C., Kau, S., Lee, C.: Robust H/sub 2/control of norm-bounded uncertain continuous-time system-an LMI approach. In: IEEE International Conference on Robotics and Automation, pp. 243–248 (2004)Google Scholar
  2. 2.
    Wang, G., Zhang, Q., Sreeram, V.: Robust \(H_{\infty }\) control of norm bounded uncertain systems via Markovian approach. Asian J. Control. 13(6), 956–965 (2010)Google Scholar
  3. 3.
    Xie, L., de Souza, C.E.: Robust control for linear time-invariant systems with norm-bounded uncertainty in the input matrix. Syst. Control. Lett. 14(5), 389–396 (1990)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Devarakonda, N., Yedavalli, R.K.: A new robust control design for linear systems with norm bounded time varying real parameter uncertainty. In: ASME 2010 Dynamic Systems and Control Conference, vol. 1, pp. 1–7 (2010)Google Scholar
  5. 5.
    Liu, Y., Lin, H., Liu, L., Li, Y.: A parameter-dependent approach to robust h control of norm bounded uncertain systems. Appl. Mech. Mater. 645–653 (2015)Google Scholar
  6. 6.
    Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1994)Google Scholar
  7. 7.
    Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox: For Use with MATLAB. The MathWorks Inc, Natick, MA (1995)Google Scholar
  8. 8.
    Maier, R., Pepper, I.: Environmental Microbiology, 3rd edn. Elsevier (2015)Google Scholar
  9. 9.
    Winkler, M., Boets, P., Hahne, B., Goethals, P., Volcke, E.: Effect of the dilution rate on microbial competition: r-strategist can win over k-strategist at low substrate concentration. PLoS ONE (2017)Google Scholar
  10. 10.
    Stephen, B., Laurent, G., Eric, F., Venkataramanan, B.: Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, Philadelphia (1994)Google Scholar
  11. 11.
    Parrillo, P.A., Lall, S.: Semidefinite programming relaxations and algebraic optimization in control. Eur. J. Control. 9(2–3), 307–321 (2003)CrossRefGoogle Scholar
  12. 12.
    Karmarkar, N.: A new polynomial-time algorithm for linear programming. Combinatorica 4(4), 373–395 (1984)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Horisberger, H.P., Belanger, P.R.: Regulators for linear time-invariant plants with uncertain parameters. IEEE Trans. Autom. Control. 21, 705–708 (1976)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Bernussou, J., Peres, P.L.D., Geromel, J.C.: A linear programming oriented procedure for quadratic stabilization of uncertain systems. Syst. Control. Lett. 13(1), 65–72 (1989)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Boyd, S., Balakrishnan, V., Barratt, C., Khraishi, N., Li, X., Meyer, D.G., Norman S.A.: A new CAD method and associated architectures for linear controllers. IEEE Trans. Autom. Control. 33(3), 268–283 (1988)Google Scholar
  16. 16.
    Niewoehner, R.J., Kaminer, I.I.: Integrated aircraft-controller design using linear matrix inequalities. J. Guid. Control. Dyn. 19(2), 445–452 (1996)CrossRefGoogle Scholar
  17. 17.
    Zasadzinski, M., Frapard, B.: Multiobjective controller designs: a space application benchmark. In: Workshop on Linear Matrix Inequalities in Control, Toulouse, France, LAAS-CNRS (2004)Google Scholar
  18. 18.
    Clement, B.: Robust control with LMI optimisation in space applications. In: Workshop on Linear Matrix Inequalities in Control, Toulouse, France, LAASCNRS (2004)Google Scholar
  19. 19.
    Scherer, C., Gahinet, P., Chilali, M.: Multiobjective output-feedback control via LMI optimization. IEEE Trans. Autom. Control 42(7), 896–911 (1997)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Seto, D., Ferriera, E., Marz, T.: Case Study: Development of a Baseline Controller for Automatic Landing of an F-16 Aircraft Using Linear Matrix Inequalities (LMIs). Carnegie Mellon, Software Engineering Institute: 155: Research Report CMU/SEI-99-TR-020 (2000)Google Scholar
  21. 21.
    Dettori, M., Scherer, C.W.: MIMO control design for a compact disc player with multiple norm specifications. IEEE Trans. Control. Syst. Technol. 10(5), 635–645 (2002)CrossRefGoogle Scholar
  22. 22.
    Prempain, E., Postlethwaite, I.: Static H-infinity loop shaping control of a fly-by-wire helicopter. In: Workshop on Linear Matrix Inequalities in Control, also in Proceedings of the 43rd IEEE Conference on Decision and Control, Toulouse, France, LAAS-CNRS (2004)Google Scholar
  23. 23.
    Biannic, J.M.: IQC for robustness analysis of fighter aircraft control laws. In: Workshop on Linear Matrix Inequalities in Control, Toulouse, France, LAASCNRS (2004)Google Scholar
  24. 24.
    Dey, R., Ghosh, S., Ray, G.: A robust \(H_{\infty }\) load-frequency controller design using LMIs. In: 2009 IEEE International Conference on Control Applications (2009)Google Scholar
  25. 25.
    Dey, R., Ghosh, S., Ray, G., Rakshit, A., Balas, V.: Improved delay-range-dependent stability analysis of a time-delay system with norm bounded uncertainty. ISA Trans. 20(58), 50–57 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.University of AucklandAucklandNew Zealand
  2. 2.Institute of Infrastructure Technology Research and ManagementAhmedabadIndia
  3. 3.Department of Electrical EngineeringNational Institute of TechnologySilcharIndia
  4. 4.“Aurel Vlaicu” University of AradAradRomania

Personalised recommendations