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The Role of Sensor and Actuator Models in Control of Distributed Parameter Systems

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Emerging Applications of Control and Systems Theory

Part of the book series: Lecture Notes in Control and Information Sciences - Proceedings ((LNCOINSPRO))

Abstract

Many systems are modelled by partial differential equations. The boundary conditions are important and affect the dynamics. Also, the modelling of actuation and sensing is not straightforward. The modelling of the actuators and sensors, as well as their locations, can affect control and estimation performance and design.

The research described here was supported by an NSERC Discovery Grant and by AFOSR Grant FA9550-16-1-0061.

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References

  1. Banks, H.T., Morris, K.A.: Input-output stability of accelerometer control systems. Control Theory Adv. Technol. 10(1), 1–17 (1994)

    Google Scholar 

  2. Chen, K.K., Rowley, C.W.: \({H}_2\)-optimal actuator and sensor placement in the linearised complex Ginzburg-Landau system. J. Fluid Mech. 681(241–260) (2011)

    Google Scholar 

  3. Cheng, A., Morris, K.A.: Well-posedness of boundary control systems. SIAM J. Control Optim. 42(4), 1244–1265 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Curtain, R.F., Morris, K.A.: Transfer functions of distributed parameter systems: a tutorial. Automatica 45(5), 1101–1116 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Curtain, R.F., Weiss, G.: Well-posedness of triples of operators (in the sense of linear systems theory. In: Control and Estimation of Distributed Parameter Systems. International Series of Numerical Mathematics, vol. 91, pp. 41–59. Birkhäuser (1989)

    Google Scholar 

  6. Curtain, R.F., Zwart, H.: An Introduction to Infinite-Dimensional Linear Systems Theory. Springer, Berlin (1995)

    Book  MATH  Google Scholar 

  7. Darivandi, N., Morris, K., Khajepour, A.: An algorithm for LQ-optimal actuator location. Smart Mater. Struct. 22(3), 035001 (2013)

    Article  Google Scholar 

  8. Demetriou, M.A.: Numerical investigation on optimal actuator/sensor location of parabolic pde’s. In: Proceedings of the American Control Conference, vol. 3, pp. 1722–1726. IEEE, San Diego, CA, USA (1999) (Location-parametrization performance index)

    Google Scholar 

  9. Fahroo, F., Demetriou, M.A.: Optimal actuator/sensor location for active noise regulator and tracking control problems. J. Comp. Appl. Math. 114(1), 137–158 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  10. Frecker, M.I.: Recent advances in optimization of smart structures and actuators. J. Intell. Mater. Syst. Struct. 14(4–5), 207–216 (2003)

    Article  Google Scholar 

  11. Guenther, R.B., Lee, J.W.: Partial Differential Equations of Mathematical Physics and Integral Equations. Prentice-Hall (1988)

    Google Scholar 

  12. Jacob, B., Morris, K.A.: Second-order systems with acceleration measurements. IEEE Trans. Autom. Control 57, 690–700 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. El Jai, A., Pritchard, A.J.: Sensors and Controls in the Analysis of Distributed Systems. Halsted Press (1988)

    Google Scholar 

  14. Kubrusly, C.S., Malebranche, H.: Sensors and controllers location in distributed systems—a survey. Automatica 21(2), 117–128 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  15. Morris, K.A.: \({H}_\infty \)-optimal actuator location. IEEE Trans. Autom. Control 58(10), 2522–2535 (2013)

    Google Scholar 

  16. Morris, K.A.: Linear quadratic optimal actuator location. IEEE Trans. Autom. Control 56, 113–124 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Morris, K.A., Demetriou, M.A., Yang, S.D.: Using \({H}_2\)-control performance metrics for infinite-dimensional systems. IEEE Trans. Autom. Control 60(2), 450–462 (2015)

    Article  MATH  Google Scholar 

  18. Morris, K.A., Ozer, A.O.: Modeling and stabilizability of voltage-actuated piezoelectric beams with magnetic effects. SIAM J. Control Optim. submitted (2013)

    Google Scholar 

  19. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer (1983)

    Google Scholar 

  20. Pierce, A.D.: Acoustics: An Introduction to Its Physical Principles and Applications. McGraw-Hill (1981)

    Google Scholar 

  21. Privat, Y., Trélat, E., Zuazua, E.: Optimal observation of the one-dimensional wave equation. J. Fourier Anal. Appl. 19(3), 514–544 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  22. Tucsnak, M., Weiss, G.: Observation and Control for Operator Semigroups. Birkhauser (2009)

    Google Scholar 

  23. Uciński, D.: Optimal Measurement Methods for Distributed Parameter System Identification. Systems and Control Series. CRC Press (2005)

    Google Scholar 

  24. Vaidya, U., Rajaram, R., Dasgupta, S.: Actuator and sensor placement in linear advection PDE with building system application. J. Math. Anal. Appl. 394(1), 213–224 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  25. van de Wal, M., de Jager, B.: A review of methods for input/output selection. Automatica 37, 487–510 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  26. Wu, X., Jacob, B., Elbern, H.: Optimal control and observation locations for time-varying systems on a finite-time horizon. SIAM J. Control Optim. 54(1), 291–316 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yang, S.D., Morris, K.A.: Comparision of actuator placement criteria for control of beam vibrations. J. Sound Vib. 353, 1–18 (2015)

    Article  Google Scholar 

  28. Zhang, M., Morris, K.A.: Sensor choice for minimum error variance estimation. under review

    Google Scholar 

  29. Zimmer, B.J., Lipshitz, S.P., Morris, K.A., Vanderkooy, J., Obasi, E.E.: An improved acoustic model for active noise control in a duct. ASME J Dyn. Syst. Meas. Contr. 125(3), 382–395 (2003)

    Article  Google Scholar 

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Correspondence to Kirsten Morris .

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Morris, K. (2018). The Role of Sensor and Actuator Models in Control of Distributed Parameter Systems. In: Tempo, R., Yurkovich, S., Misra, P. (eds) Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-67068-3_18

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  • DOI: https://doi.org/10.1007/978-3-319-67068-3_18

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  • Online ISBN: 978-3-319-67068-3

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