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Formal Verification of Steady-State Errors in Unity-Feedback Control Systems

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Formal Methods for Industrial Critical Systems (FMICS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8718))

Abstract

The meticulousness of steady-state error analysis of unity-feedback control systems has always been of vital significance as even a trifling glitch in this analysis may result in grievous penalties. To ensure a rigorous steady-state error analysis, this paper presents the formal verification of a generic relationship that is applicable to all kinds of inputs and types of unity-feedback control systems. This formalization builds upon the multivariate calculus theories of HOL-Light and our prior work on developing formal models of feedback control systems. To illustrate the usefulness of this result, the paper presents the formal steady-state error analysis of a Pulse Width Modulation (PWM) push-pull DC-DC converter, which is an extensively used component in various power-electronics and aerospace applications.

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References

  1. Clayton, P., Cavalcanti, A., O’Halloran, C.: From Control Law Diagrams to Ada via Circus. Formal Aspects of Computing 23(4), 465–512 (2011)

    Article  MATH  Google Scholar 

  2. Ahmad, M.: Formal Verification of Steady State Errors in Unity-Feedback Control Systems (2014), http://save.seecs.nust.edu.pk/students/ahmad/sseufcs.html

  3. Alur, R.: Formal Verification of Hybrid Systems. In: Embedded Software, pp. 273–278 (2011)

    Google Scholar 

  4. Arthan, R., Caseley, P., O’Halloran, C., Smith, A.: ClawZ: Control Laws in Z. In: Formal Engineering Methods, pp. 169–176 (2000)

    Google Scholar 

  5. Boulton, R.J., Gottliebsen, H., Hardy, R., Kelsey, T., Martin, U.: Design Verification for Control Engineering. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 21–35. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Boulton, R.J., Hardy, R., Martin, U.: A Hoare Logic for Single-Input Single-Output Continuous-Time Control Systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 113–125. Springer, Heidelberg (2003)

    Google Scholar 

  7. Dong, J.S., Chen, C., Sun, J.: A Formal framework for Modeling and Validating Simulink diagrams. Formal Aspects of Computing 21(5), 451–483 (2009)

    Article  MATH  Google Scholar 

  8. Czarkowski, D., Pujara, L.R., Kazimierczuk, M.K.: Robust Stability of State-Feedback Control of PWM DC-DC push-pull Converter. IEEE Transaction on Industrial Electronics 42(1), 108–111 (1995)

    Article  Google Scholar 

  9. Harrison, J.: A HOL Theory of Euclidean Space. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 114–129. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Harrison, J.: Formalizing Basic Complex Analysis. Studies in Logic, Grammar and Rhetoric 10, 151–165 (2007)

    Google Scholar 

  11. Harrison, J.: The HOL Light Theory of Euclidean Space. Journal of Automated Reasoning 50(2), 173–190 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  12. Hasan, O., Ahmad, M.: Formal analysis of steady state errors in feedback control systems using HOL-light. In: Proceedings of the Conference on Design, Automation and Test in Europe, DATE 2013, pp. 1423–1426 (2013)

    Google Scholar 

  13. Herencia-Zapana, H., Jobredeaux, R., Owre, S., Garoche, P.-L., Feron, E., Perez, G., Ascariz, P.: PVS Linear Algebra Libraries for Verification of Control Software Algorithms in C/ACSL. In: Goodloe, A.E., Person, S. (eds.) NFM 2012. LNCS, vol. 7226, pp. 147–161. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  14. Hote, Y.: A New Approach to Time Domain Analysis of Perturbed PWM push-pull DC-DC Converter. Journal of Control Theory and Applications 10(4), 465–469 (2012)

    Article  MathSciNet  Google Scholar 

  15. Lutovac, M.D., Tošic, D.V.: Symbolic Analysis and Design of Control Systems using Mathematica. International Journal of Control 79(11), 1368–1381 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mahony, B.: The DOVE approach to the Design of Complex Dynamic Processes. In: Workshop on Formalising Continuous Mathematics, pp. 167–187. NASA Conference Publication (2002)

    Google Scholar 

  17. MathWorks Simulink (2012), http://www.mathworks.com/products/simulink

  18. Nise, N.S.: Control System Engineering. Wiley and Sons (2003)

    Google Scholar 

  19. Ogata, K.: Modern Control Engineering. Prentice-Hall (1997)

    Google Scholar 

  20. Pike, L.: Pervasive Formal Verification in Control System. In: Formal Methods in Computer-Aided Design. Panel Discussion (2011)

    Google Scholar 

  21. Taqdees, S.H., Hasan, O.: Formalization of Laplace Transform Using the Multivariable Calculus Theory of HOL-Light. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19. LNCS, vol. 8312, pp. 744–758. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  22. Tiwari, A., Khanna, G.: Series of Abstractions for Hybrid Automata. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 465–478. Springer, Heidelberg (2002)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Islamabad, Pakistan

    Muhammad Ahmad & Osman Hasan

Authors
  1. Muhammad Ahmad
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  2. Osman Hasan
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Editor information

Editors and Affiliations

  1. Inria, 38330, Montbonnot, France

    Frédéric Lang

  2. Ansaldo STS, 80147, Naples, Italy

    Francesco Flammini

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Ahmad, M., Hasan, O. (2014). Formal Verification of Steady-State Errors in Unity-Feedback Control Systems. In: Lang, F., Flammini, F. (eds) Formal Methods for Industrial Critical Systems. FMICS 2014. Lecture Notes in Computer Science, vol 8718. Springer, Cham. https://doi.org/10.1007/978-3-319-10702-8_1

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  • DOI: https://doi.org/10.1007/978-3-319-10702-8_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10701-1

  • Online ISBN: 978-3-319-10702-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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