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Stabilizing Sets for Linear Time-Invariant Discrete-Time Plants

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Analytical Design of PID Controllers

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Abstract

In this chapter, we consider the synthesis and design of digital PID controllers which can provide tracking and disturbance rejection of constant reference and disturbance discrete-time signals. We develop procedures and algorithms to determine the set of PID controllers that stabilize a given linear time-invariant discrete-time plant. This algorithm determines the three parameter stabilizing set via a linear programming problem in two variables with a single sweeping parameter.

Sections 4.1, 4.2, 4.3, 4.4, and 4.8 are reproduced from S. P. Bhattacharyya, A. Datta, L. H. Keel, Linear System Theory: Structure, Robustness, and Optimization. Taylor & Francis LLC Books, with permission © 2008 Taylor & Francis LLC Books.

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References

  1. Bhattacharyya, S.P., Datta, A., Keel, L.H.: Linear Control Theory Structure, Robustness, and Optimization. CRC Press/Taylor & Francis Group, Boca Raton (2009)

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  2. Buso, S., Mattavelli, P.: Digital Control in Power Electronics. Morgan and Claypool Publishers, San Rafael (2006)

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  3. Keel, L.H., Rego, J.I., Bhattacharyya, S.P.: A new approach to digital PID controller design. IEEE Trans. Autom. Control 48(4), 687–692 (2003)

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  4. Mason, J.C., Handscomb, D.C.: Chebyshev Polynomials. Chapman and Hall/CRC, Boca Raton (2002)

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Authors and Affiliations

  1. McAllen Higher Education Center, Texas A&M University, Mcallen, TX, USA

    Iván D. Díaz-Rodríguez

  2. Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA

    Sangjin Han & Shankar P. Bhattacharyya

Authors
  1. Iván D. Díaz-Rodríguez
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  2. Sangjin Han
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  3. Shankar P. Bhattacharyya
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Corresponding author

Correspondence to Sangjin Han .

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Díaz-Rodríguez, I.D., Han, S., Bhattacharyya, S.P. (2019). Stabilizing Sets for Linear Time-Invariant Discrete-Time Plants. In: Analytical Design of PID Controllers. Springer, Cham. https://doi.org/10.1007/978-3-030-18228-1_4

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