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Parametric Transfer Matrices for Sampled-Data Control Systems with Linear Continuous Periodic Process and Control Delay

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Part of the book series: Advances in Delays and Dynamics ((ADVSDD,volume 7))

Abstract

For the class of multi-input multi-output systems being composed of a linear continuous periodic (LCP) process, pure delay, and a digital controller, the paper provides closed expressions for the parametric transfer matrix (PTM), even for the difficult, but practically important case, when the external excitations act on continuous system parts. In the same way as ordinary transfer matrices in the linear time-invariant (LTI) case, the PTM for LCP systems is a fundamental concept for analysis and design of those systems. The properties of the constructed parametric transfer matrices as functions of the real parameter and the complex variable are investigated. These properties are similar to those from ordinary transfer matrices, so that the PTM after some modifications, can be applied with similar tools. Moreover, formulae are derived that are appropriate for the practical computation of the PTM. An example demonstrates, how the formulae can be handled.

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References

  1. Ackermann, J.: Sampled-Data Control Systems: Analysis and Synthesis, Robust System Design. Springer, Berlin (1985)

    Book  MATH  Google Scholar 

  2. Åström, K.J., Wittenmark, B.: Computer Controlled Systems: Theory and Design, 3rd edn. Prentice-Hall, Englewood Cliffs, NJ (1997)

    Google Scholar 

  3. Cepeda Gomez, R., Lampe, B.P.: Towards a newer toolbox for computer aided, polynomial design of sampled-data systems. Simul. Notes Europe 25, 79–84 (2015)

    Google Scholar 

  4. Chen, T., Francis, B.A.: Optimal Sampled-Data Control Systems. Springer, Berlin (1995)

    Book  MATH  Google Scholar 

  5. Hagiwara, T., Araki, M.: FR-operator approach to the \(\cal{H}_2\)-analysis and synthesis of sampled-data systems. IEEE Trans. Autom. Contr. AC 40(8), 1411–1421 (1995)

    Google Scholar 

  6. Jury, E.I.: Sampled-Data Control Systems. Wiley, New York (1958)

    MATH  Google Scholar 

  7. Lampe, B.P., Rosenwasser, E.N.: Statistical analysis and \(\cal{H}_2\)-norm of finite dimensional linear time-periodic systems. In: Proceedings. IFAC Workshop on Periodic Control Systems, Como, Italy, pp. 9–14 (2001)

    Google Scholar 

  8. Lampe, B.P., Rosenwasser, E.N.: Causal polynomial stabilization for forward models of linear discrete-time systems. PAMM: Proc. Appl. Math. Mech. 5(1), 173–174 (2005)

    Google Scholar 

  9. Lampe, B.P., Rosenwasser, E.N.: Digital stabilization of linear continuous-time periodic processes with pure delay. In: Proceedings of PSYCO, Saint Petersburg, Russia, pp. FrM1–2, 1–6 (2007)

    Google Scholar 

  10. Lampe, B.P., Rosenwasser, E.N.: \(\cal{H}_2\)-optimization of time-delayed sampled-data systems on basis of the parametric transfer matrix method. Autom. Remote Control 71(1), 49–69 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lampe, B.P., Rosenwasser, E.N.: Transfer matrices and advanced statistical analysis of digital controlled continuous-time periodic processes with delay. Eur. J. Control 18(4), 391–404 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lampe, B.P., Rosenwasser, E.N.: Characteristic equation for MIMO linear continuous periodic systems with several delays. In: Proceedings of 5th PSYCO, Caen, F, pp. 160–165 (2013)

    Google Scholar 

  13. Lampe, B.P., Rosenwasser, E.N.: \(\cal{H}_2\) optimization and fixed poles of sampled-data systems under colored noise. Eur. J. Control 19(3), 222–234 (2013b)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lampe, B.P., Rosenwasser, E.N.: \(\cal{L}_2\)-optimization and fixed poles of multivariable sampled-data systems with delay. Int. J. Control 88(4), 815–831 (2015). Published online Dec 2014

    Google Scholar 

  15. Lampe, B.P., Rosenwasser, E.N., Kurowski, M.: Characteristic equation for linear periodic systems with distributed delay. In: Proceedings of 19th IFAC Triennial World Congress, Cape Town, ZA, pp. 6068–6073 (2014)

    Google Scholar 

  16. Polyakov, K.Y.: Polynomial design of sampled-data control systems. II. Robust optimization. Autom. Remote Control 59(12), 1774–1785 (1998)

    MATH  Google Scholar 

  17. Polyakov, K.Y.: Polynomial design of optimal sampled-data tracking systems. II: Robust optimization. Autom. Remote Control 62(3), 430–442 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Polyakov, K.Y., Rosenwasser, E.N., Lampe, B.P.: Associated \(\cal{H}_\infty \)-problem for sampled-data systems. In: Proceedings of 3rd IFAC Symposium on Robust Control Design, Pergamon, Prague, pp. 669–674 (2000)

    Google Scholar 

  19. Polyakov KY, Rosenwasser EN, Lampe BP (2006) DirectSD Polyakov, K.Y., Rosenwasser, E.N., Lampe, B.P.: 3.0 toolbox for MATLAB: further progress in polynomial design of sampled-data systems. In: Proceedings of IEEE International Symposium on Computer Aided Control Systems Design, Munich, Germany, pp. 1946–1951

    Google Scholar 

  20. Polyakov, K.Y., Rosenwasser, E.N., Lampe, B.P.: Optimal stochastic sampled-data control with preview. IEEE Trans. Autom. Control AC-52(8), 1532–1538 (2007)

    Google Scholar 

  21. Rosenwasser, E.N.: Periodically Nonstationary Control Systems. Nauka, Moscow (1973). (in Russian)

    Google Scholar 

  22. Rosenwasser, E.N.: Linear Theory of Digital Control in Continuous Time. Nauka, Moscow (1994). (in Russian)

    Google Scholar 

  23. Rosenwasser, E.N., Lampe, B.P.: Computer Controlled Systems—Analysis and Design with Process-orientated Models. Springer, London (2000)

    MATH  Google Scholar 

  24. Rosenwasser, E.N., Lampe, B.P.: Multivariable Computer-Controlled Systems—A Transfer Function Approach. Springer, London (2006)

    Book  MATH  Google Scholar 

  25. Rybinskii, V.O., Rosenwasser, E.N., Lampe, B.P.: Advanced statistical analysis with guaranteed estimation of current performance for sampled-data systems with delay and generalized higher order hold. In: Proceedings of 9th IFAC Conference on Control Applications in Marine Systems, Osaka, pp. Fr.1A 1–6 (2013)

    Google Scholar 

  26. Yakubovich, V.A., Starzhinskii, V.M.: Linear Differential Equations with Periodic Coefficients, vol. 1. Wiley, New York (1975)

    Google Scholar 

  27. Yamamoto, Y.: A function space approach to sampled-data systems and tracking problems. IEEE Trans. Autom. Control AC-39(4), 703–713 (1994)

    Google Scholar 

  28. Zypkin, J.S.: Sampling Systems Theory. Pergamon Press, New York (1964)

    Google Scholar 

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Authors and Affiliations

  1. Institute of Automation, University of Rostock, Rostock, Germany

    Bernhard P. Lampe

  2. Stae Marine Technical University, Saint Petersburg, Russia

    Efim N. Rosenwasser

Authors
  1. Bernhard P. Lampe
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  2. Efim N. Rosenwasser
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Correspondence to Bernhard P. Lampe .

Editor information

Editors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Tamás Insperger

  2. Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA

    Tulga Ersal

  3. Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA

    Gábor Orosz

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Lampe, B.P., Rosenwasser, E.N. (2017). Parametric Transfer Matrices for Sampled-Data Control Systems with Linear Continuous Periodic Process and Control Delay. In: Insperger, T., Ersal, T., Orosz, G. (eds) Time Delay Systems. Advances in Delays and Dynamics, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-53426-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-53426-8_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53425-1

  • Online ISBN: 978-3-319-53426-8

  • eBook Packages: EngineeringEngineering (R0)

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