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State Feedback Regulation Problem to the Reaction-Diffusion Equation

Author

Listed:
  • Francisco Jurado

    (División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/I.T. La Laguna, Revolución Blvd. and Instituto Tecnológico de La Laguna Av., Torreón 27000, Mexico)

  • Andrés A. Ramírez

    (División de Estudios de Posgrado e Investigación, Tecnológico Nacional de México/I.T. La Laguna, Revolución Blvd. and Instituto Tecnológico de La Laguna Av., Torreón 27000, Mexico)

Abstract

In this work, we explore the state feedback regulator problem (SFRP) in order to achieve the goal for trajectory tracking with harmonic disturbance rejection to one-dimensional (1-D) reaction-diffusion (R-D) equation, namely, a partial differential equation of parabolic type, while taking into account bounded input, output, and disturbance operators, a finite-dimensional exosystem (exogenous system), and the state of the exosystem as the state to the feedback law. As is well-known, the SFRP can be solved only if the so-called Francis (regulator) equations have solution. In our work, we try with the solution of the Francis equations from the 1-D R-D equation following given criteria to the eigenvalues from the exosystem and transfer function of the system, but the state operator is here defined in terms of the Sturm–Liouville differential operator (SLDO). Within this framework, the SFRP is then solved for the 1-D R-D equation. The numerical simulation results validate the performance of the regulator.

Suggested Citation

  • Francisco Jurado & Andrés A. Ramírez, 2020. "State Feedback Regulation Problem to the Reaction-Diffusion Equation," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1983-:d:441119
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    Cited by:

    1. Andrés A. Ramírez & Francisco Jurado, 2023. "The Regulator Problem to the Convection–Diffusion Equation," Mathematics, MDPI, vol. 11(8), pages 1-16, April.
    2. Francisco Ureña & Ángel García & Antonio M. Vargas, 2022. "Preface to “Applications of Partial Differential Equations in Engineering”," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

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