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Review of Linear Optimal Control Laws

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Nonlinear Industrial Control Systems

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Abstract

A review of linear optimal control laws is provided that are related to the nonlinear optimal control methods to be described in later chapters. The Minimum Variance, Generalized Minimum Variance , Linear Quadratic Gaussian and H∞ control design approaches are summarized and useful properties of the algorithms are highlighted. A useful introduction is provided to the solution procedures that are needed in a modified form for nonlinear systems. The solutions themselves are also required since they are the same as the limiting cases of the related nonlinear control problems when the plant is actually linear. The design of low-order or so-called restricted structure controllers is also considered where one controller can stabilize a set of linear models. This provides an empirical method for stabilizing a nonlinear system. The chapter ends with a number of ways of controlling uncertain and nonlinear processes.

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Author information

Authors and Affiliations

  1. Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, UK

    Michael J. Grimble

  2. Industrial Systems and Control Limited, Glasgow, UK

    Paweł Majecki

Authors
  1. Michael J. Grimble
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  2. Paweł Majecki
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Correspondence to Michael J. Grimble .

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Grimble, M.J., Majecki, P. (2020). Review of Linear Optimal Control Laws. In: Nonlinear Industrial Control Systems. Springer, London. https://doi.org/10.1007/978-1-4471-7457-8_2

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