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Adaptive Control of Non-minimum Phase Modal Systems Using Residual Mode Filters: Part II

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Advances in Aerospace Guidance, Navigation and Control
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Abstract

In Part II, we extend our adaptive control theory to accommodate problematic modal subsystems of a plant that inhibit the adaptive controller by causing the open-loop plant to be non-minimum phase. We will modify the adaptive controller with a Residual Mode Filter (RMF) to compensate for problematic modal subsystems, thereby allowing the system to satisfy the requirements for the adaptive controller to have guaranteed convergence and bounded gains. Also, we will apply the above theoretical results to a simple flexible structure example to illustrate the behavior with and without the residual mode filter.

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References

  1. Wen, J.T., Balas, M.J.: Robust adaptive control in Hilbert space. Journal of Mathematical Analysis and Application 143(1), 1–26 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Balas, M.J.: Finite-dimensional direct adaptive control for discrete-time infinite-dimensional linear systems. Journal of Mathematical Analysis and Applications 196(1), 153–171 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fuentes, R.J., Balas, M.J.: Direct adaptive rejection of persistent disturbances. Journal of Mathematical Analysis and Applications 251(1), 28–39 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Frost, S.A., Balas, M.J., Wright, A.D.: Direct adaptive control of a utility-scale wind turbine for speed regulation. International Journal of Robust and Nonlinear Control 19(1), 59–71 (2009), doi:10.1002/rnc.1329

    Article  MathSciNet  MATH  Google Scholar 

  5. Johnson, C.D.: Theory of disturbance-accommodating controllers. Control & Dynamic Systems. In: Leondes, C.T. (ed.) Advances in Theory and Applications, vol. 12, pp. 387–489. Academic Press, New York (1976)

    Google Scholar 

  6. Balas, M.J.: Finite-dimensional controllers for linear distributed parameter systems: Exponential stability using Residual Mode Filters. J. Mathematical Analysis & Applications 133, 283–296 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  7. Frost, S.A., Balas, M.J., Wright, A.D.: Modified adaptive control for region 3 operation in the presence of wind turbine structural modes. In: Proceedings 49th AIAA Aerospace Sciences Meeting, Orlando (2010)

    Google Scholar 

  8. Fuentes, R.J., Balas, M.J.: Robust Model Reference Adaptive Control with Disturbance Rejection. In: Proceedings of the American Control Conference (2002)

    Google Scholar 

  9. Kimura, H.: Pole assignment by gain output feedback. IEEE Trans. Automatic Control AC-20(4), 509–516 (1975)

    Article  Google Scholar 

  10. Balas, M., Gajendar, S., Robertson, L.: Adaptive Tracking Control of Linear Systems with Unknown Delays and Persistent Disturbances (or Who You Callin’ Retarded?). In: AIAA Guidance, Navigation and Control Conference, Chicago, IL (August 2009)

    Google Scholar 

  11. Balas, M., Fuentes, R.: A Non-orthogonal Projection Approach to Characterization of Almost Positive Real Systems with an Application to Adaptive Control. In: Proceedings of American Control Conference, Boston (2004)

    Google Scholar 

  12. Vidyasagar, M.: Nonlinear Systems Analysis, 2nd edn. Prentice-Hall, New Jersey (1993)

    MATH  Google Scholar 

  13. Balas, M.: Trends in Large Space Structure Control Theory: Fondest Hopes; Wildest Dreams. IEEE Trans. Automatic Control AC-27, 522–535 (1982)

    Article  Google Scholar 

  14. Balas, M.: Control and Dynamic Systems: Advances in Theory and Application. In: Leondes, C.T. (ed.) Toward a More Practical Control Theory for Distributed Parameter Systems, vol. 18. Academic Press, New York (1982)

    Google Scholar 

  15. Balas, M.: Nonlinear Finite-Dimensional Control of a Class of Nonlinear Distributed Parameter Systems Using Residual Mode Filters: A Proof of Local Exponential Stability. J. Mathematical Analysis & Applications 162, 63–70 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  16. Balas, M.: Finite-Dimensional Controllers for Linear Distributed Parameter Systems: Exponential Stability Using Residual Mode Filters. J. Mathematical Analysis & Applications 133, 283–296 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  17. Bansenauer, B., Balas, M.: Reduced-Order Model Based Control of the Flexible Articulated-Truss Space Crane. AIAA Journal of Guidance Control and Dynamics 18, 135–142 (1995)

    Article  Google Scholar 

  18. Wright, A., Balas, M.: Design of State-Space-Based Control Algorithms for Wind Turbine Speed Regulation. ASME Journal of Solar Energy Engineering 125, 386–395 (2003)

    Article  Google Scholar 

  19. Frost, S.A., Balas, M.J., Wright, A.D.: Augmented Adaptive Control of a Wind Turbine in the Presence of Structural Modes, Mechatronics Special Issue on Wind Energy, IFAC (to appear, 2011)

    Google Scholar 

  20. Frost, S.A., Balas, M.J., Wright, A.D.: Modified adaptive control for Region 3 operation in the presence of turbine structural modes. In: Proceedings American Control Conference, Baltimore, MD (2010)

    Google Scholar 

  21. Frost, S.A., Balas, M.J., Wright, A.D.: Modified adaptive control for Region 3 operation in the presence of turbine structural modes. In: Proceedings 29th AIAA Aerospace Sciences Meeting and Exhibit Wind Energy Symposium (2010)

    Google Scholar 

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Balas, M.J., Frost, S.A. (2011). Adaptive Control of Non-minimum Phase Modal Systems Using Residual Mode Filters: Part II. In: Holzapfel, F., Theil, S. (eds) Advances in Aerospace Guidance, Navigation and Control. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19817-5_18

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  • DOI: https://doi.org/10.1007/978-3-642-19817-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19816-8

  • Online ISBN: 978-3-642-19817-5

  • eBook Packages: EngineeringEngineering (R0)

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