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Introduction to Control

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Analytical Design of PID Controllers

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Abstract

In this chapter, we describe control systems informally, emphasizing the key elements of tracking, disturbance rejection, stability, and robustness. Next, we show why integral control driven by tracking error provides the correct feedback architecture to try to achieve these goals. This leads naturally to the Proportional–Integral–Derivative (PID) controller structure, where the proportional, integral, and derivative gains \(k_p\), \(k_i\), and \(k_d\) now become the design parameters which need to be tuned to achieve robust stability and time domain response specifications. A brief description is given of some classical and existing tuning approaches. We conclude the chapter with an examination of why optimal control, and in particular quadratic optimization, is absent from PID design theory and show that the reason lies in the inherent fragility of the high-order controllers invariably produced by optimization. The contents of this chapter should serve as background, perspective, and motivation for the rest of the book.

Sections 1.1, 1.2, 1.4 and 1.5.4 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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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

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  1. Iván D. Díaz-Rodríguez
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  2. Sangjin Han
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  3. Shankar P. Bhattacharyya
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Correspondence to Sangjin Han .

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Díaz-Rodríguez, I.D., Han, S., Bhattacharyya, S.P. (2019). Introduction to Control. In: Analytical Design of PID Controllers. Springer, Cham. https://doi.org/10.1007/978-3-030-18228-1_1

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