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State Energy-Based Approach as a Tool for Design and Simulation of Linear and Nonlinear Systems

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Analysis, Control and Optimal Operations in Hybrid Power Systems

Part of the book series: Green Energy and Technology ((GREEN))

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Abstract

This chapter deals with a new problem of physical correctness detection in the area of strictly causal system representations. The starting point is energy and the assumption that a system can be represented by a proper interconnection. The interconnection or, better, the interaction between physical systems can be described in terms of power exchange through power ports. The proposed approach to the problem solution is based on generalization of Tellegen’s theorem well known from electrical engineering. Consequently, mathematically as well as physically correct results are obtained. The contribution is mainly concerned with presentation of a new structural approach to analysis and synthesis of linear and nonlinear causal systems. It has been proven that complete analysis of system behavior reduces to two independent tests: the monotonicity test of abstract state space energy and that of complete state observability, eventually of its dual, i.e., complete state controllability property. For comparison, the example of port-Hamiltonian approach is also presented.

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References

  1. Mac Farlane AGJ (1970) Dynamical system models. George G. Harrap & Co. Ltd., London

    Google Scholar 

  2. Kalman RE (1963) Mathematical description of linear dynamical systems. SIAM J Control 1:152–192

    MATH  MathSciNet  Google Scholar 

  3. Mayer D (1970) The state variable method of electrical network analysis. Acta Technica Csav 6:761–789

    Google Scholar 

  4. Brayton RK, Moser JK (1964) A theory of nonlinear networks-1. Q Appl Math 22:1–33

    MathSciNet  Google Scholar 

  5. Brayton RK, Moser JK (1964) A theory of nonlinear networks-2. Q Appl Math 22:81–104

    MathSciNet  Google Scholar 

  6. Massimo FM, Kwatny HG, Bahar LY (1980) Derivation of the Brayton-Moser equations from a topological mixed potential function. J Franklin Inst 310:259–269

    Article  MATH  MathSciNet  Google Scholar 

  7. Khalil HK (1996) Nonlinear systems. Prentice Hall, New Jersey

    Google Scholar 

  8. Hrusak J, Mayer D, Stork M (2004) On system structure reconstruction problem and Tellegen-like relation. In: Proceedings of 8th World Multiconf., SCI, vol VIII, Florida, USA, pp 373–378

    Google Scholar 

  9. Hrusak J, Mayer D, Stork M (2006) New approach to non-linear instability and chaos based on generalized Tellegen’ss principle, WMSCI 2006. Orlando, Florida, Int. Institute of Informatics and Systemics, USA, ISBN 980-6560-67-1, pp 199–206

    Google Scholar 

  10. Hrusak J, Mayer D, Stork M (2006) Dissipativity, minimality and physical correctness of state space representations, CITSA 2006. Orlando, Florida, USA, Int. Institute of Informatics and Systemics, ISBN 980-6560-83-3, pp 136–141

    Google Scholar 

  11. Hrusak J, Mayer D, Stork M (2007) Structural approach to instability and chaos in non-linear causal systems, Systems Theory and Scientific Computation. WSEAS Press, Athens, Greece, ISBN 978-960-8457-96-0. ISSN 1790-5117, pp 223–228

    Google Scholar 

  12. Stork M, Hrusak J, Mayer D (2006) Chaos and strange behavior detection of continuous and digital nonlinear systems based on internal system energy autocovariance, WMSCI 2006, Orlando, Florida, Int. Institute of Informatics and Systemics, USA, pp 228–233

    Google Scholar 

  13. Fradkov AL, Pogromsky AY (1998) Introduction to control of oscillations and chaos. World Scientific Series on Nonlinear Science, Singapore

    Google Scholar 

  14. Hrusak J (1969) In: Anwendung der Äquivalenz bei Stabilitätsprüfung, Tagung ü. die Regelungs-theorie, Mathematisches Forschungsinstitut, Oberwolfach, Universitaet Freiburg, West Germany

    Google Scholar 

  15. Hoover WG (1995) Remark on: some simple chaotic flows. Phys Rev E 51:759–760

    Article  Google Scholar 

  16. Posch HA, Hoover WG, Vesely FJ (1986) Canonical dynamics of the nosé oscillator: stability, order, and chaos. Phys Rev A 33:4253–4265

    Article  MathSciNet  Google Scholar 

  17. Nosé S (1984) A unified formulation of the constant temperature molecular dynamics methods. J Chem Phys 81, Section IIB :511–519

    Google Scholar 

  18. Hoover WG (1988) Reversible mechanics and time’s arrow. Phys Rev A 37:252–257

    Article  MathSciNet  Google Scholar 

  19. Ezra GS (2006) Reversible measure-preserving integrators for non-Hamiltonian systems. J Chem Phys 10(1063/1):2215608

    Google Scholar 

  20. Hrusak J, Stork M, Mayer D (2011) Generalized Tellegen’s Principle and state space energy based causal systems description. In: Advances in energy research: distributed generations systems integrating renewable energy resources, Part I, Basic theory and advanced approaches, Chapter 4, NOVA Science Publ., USA, pp 95–139

    Google Scholar 

  21. Jeltsema D, Scherpen JMA (2007) A power-based description of standard mechanical systems. Syst Control Lett 56:349–356

    Article  MATH  MathSciNet  Google Scholar 

  22. Mayer D, Hrusak J (2003) On correctness and asymptotic stability in causal system theory. In: Proceedings of the 7th World Multiconf. Systemics, Cybernetics and Informatics, vol XIII, Orlando, USA, pp 355–360

    Google Scholar 

  23. Hrusak J, Stork M, Mayer D (2005) Dissipation normal form, conservativity, instability and chaotic behavior of continuous-time strictly causal systems. WSEAS Trans Syst 4:915–920

    MATH  Google Scholar 

  24. Stork M, Hrusak J, Mayer D (2005) Continuous and digital nonlinear systems, chaos and strange behavior detection, simulations and experiments. WSEAS Trans Circuits Syst 4:395–405

    Google Scholar 

  25. Hrusak J, Stork M, Mayer D (2008) Dissipation Normal forms and further applications of Lyapunov-Tellegen’s principle. In: 12th WSEAS international conference on systems, WSEAS Press, Heraclion, Greece

    Google Scholar 

  26. Stork M, Hrusak J, Mayer D (2010) Nonlinearly coupled oscillators and state space energy approach. In: 14th WSEAS international conference on SYSTEMS Corfu Island, Greece

    Google Scholar 

  27. Tabuada P, Pappas GJ (2003) Abstractions of Hamiltonian control systems. Autom IFAC 39:2025–2033

    Article  MATH  MathSciNet  Google Scholar 

  28. Jeltsema D, Ortega R, Scherpen JMA (2003) On passivity and power-balance inequalities of nonlinear RLC circuits. IEEE Trans. Circuits Syst Fund Theory Appl 50:1174–1178

    Google Scholar 

  29. Maschke B, van der Schft AJ (1994) A Hamiltonian approach to stabilization of nonholonomic mechanical systems. In: Proceedings of the 33rd IEEE conference on decision and control, pp 2950–2954

    Google Scholar 

  30. Maschke B, van der Schft AJ (1997) Interconnected mechanical systems. In: Part I: Geometry of interconnection and implicit Hamiltonian systems. Imperial College Press, London

    Google Scholar 

  31. Maschke B and van der Schft AJ (1997) Interconnected mechanical systems. In: Part II: the dynamics of spatial mechanical networks. Imperial College Press, London

    Google Scholar 

  32. Maschke B, van der Schft AJ, Breedveld PC (1992) An intrinsic Hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. J Franklin 329:923–966

    Article  MATH  Google Scholar 

  33. Maschke BM, van der Schaft AJ, Breedveld PC (1995) An intrinsic hamiltonian formulation of the dynamics of lc-circuits. IEEE Trans Circ Syst 42:73–82

    Article  MATH  Google Scholar 

  34. Maschke B, van der Schft AJ (1992) Port-controlled hamiltonian system: modelling origins and system theoretic approach. In: Proceedings of 2nd IFAC NOLCOS, Bordeaux, pp 282–288

    Google Scholar 

  35. Ortega R, Loria A, Nicklasson PJ, Sira-Ramirez H (1998) Passivity-based control of Euler–Lagrange systems. Springer, London

    Book  Google Scholar 

  36. Ortega R, van der Schaft AJ, Mareels I, Maschke B (2001) Putting energy back in control. IEEE Control Syst Mag 21:18–33

    Article  Google Scholar 

  37. Ortega R, van der Schaft AJ, Maschke B, Escobar G (1999) Energy-shaping of port-controlled hamiltonian systems by interconnection. In: Proceedings of IEEE conference on decision and Control, Phoenix, AZ, USA, pp 1646–1651

    Google Scholar 

  38. Van der Schaft AJ (2000) L2-gain and passivity techniques in nonlinear control. Springer, London

    Book  Google Scholar 

  39. Čuk S, Middlebrook RD (1983) Coupled-inductor and other extensions of a new optimum topology switching DC–DC converter. Advances in switched-mode power conversion, vols I and II. Tesla Co, Irvine

    Google Scholar 

  40. Chung HS, Tse KK, Hui SY, Mok CM, Ho MT (2003) A novel maximum power point tracking technique for solar panels using a SEPIC or Cuk converter. IEEE Trans Power Electron 18:717–724

    Article  Google Scholar 

  41. Maged N, Nashed F (2004) Design of a digital PWM controller for a soft switching SEPIC converter. J Power Electron 4:152–160

    Google Scholar 

  42. Adar D, Rahav G, Ben-Yaakov S (1997) A unified behavioral average model of SEPIC converters with coupled inductors. IEEE PESC’97, 1:441–446

    Google Scholar 

  43. Vorperian V (1990) Simplified analysis of PWM converters using model of PWM switch, Parts I(CCM) and II (DCM). IEEE Trans Aerosp Electron Syst 26:497–505

    Article  Google Scholar 

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Acknowledgments

This research was supported by the European Regional Development Fund and Ministry of Education, Youth and Sports of the Czech Republic under project No. CZ.1.05/2.1.00/03.0094: Regional Innovation Centre for Electrical Engineering (RICE). M. Stork is with the Regional Innovation Centre for Electrical Engineering, University of West Bohemia, Univerzitni 22, Plzen, Czech Republic.

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Authors and Affiliations

  1. Department of Applied Electronics and Telecommunications, University of West Bohemia, Plzen, Czech Republic

    Milan Stork & Josef Hrusak

  2. Department of Theory of Electrical Engineering, University of West Bohemia, Plzen, Czech Republic

    Daniel Mayer

Authors
  1. Milan Stork
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  2. Josef Hrusak
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  3. Daniel Mayer
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Corresponding author

Correspondence to Milan Stork .

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Editors and Affiliations

  1. Faculty of Electronics, Communication and Computers, University of Pitesti, Pitesti, Romania

    Nicu Bizon

  2. Departement of Technical Engineering, University of Mohaghegh, Ardabil, Iran

    Hossein Shayeghi

  3. Electrical Engineering Department, Seraj Higher Education Institute, Tabriz, Iran

    Naser Mahdavi Tabatabaei

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Stork, M., Hrusak, J., Mayer, D. (2013). State Energy-Based Approach as a Tool for Design and Simulation of Linear and Nonlinear Systems. In: Bizon, N., Shayeghi, H., Mahdavi Tabatabaei, N. (eds) Analysis, Control and Optimal Operations in Hybrid Power Systems. Green Energy and Technology. Springer, London. https://doi.org/10.1007/978-1-4471-5538-6_3

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  • DOI: https://doi.org/10.1007/978-1-4471-5538-6_3

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5537-9

  • Online ISBN: 978-1-4471-5538-6

  • eBook Packages: EnergyEnergy (R0)

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