Abstract
These notes consists of two papers. Part I gives an overview of modern frequency-domain methods, including H-infinity methods and robust control using the structured singular value, mu. Part II gives a tutorial introduction to controllability analysis for scalar systems using the frequency domain. Some readers may find it useful to read Part II first.
This part I is based on some lecture notes for a short-course given by (1993) at the 1993 European Control Conference. As an introduction to the robustness problems in multivariable systems we discuss the control of a distillation column. Because of strong interactions in the plant, a decoupling control strategy is extremely sensitive to input gain uncertainty (caused by actuator uncertainty). These interactions are analyzed using singular value decomposition (SVD) and relative gain array (RGA) methods.
We then discuss possible sources of model uncertainty, and look at the traditional methods for obtaining robust designs, such as gain margin, phase margin and maximum peak criterions (M-circles). However, these measures are difficult to generalize to multivariable systems. In such cases a more detailed modelling of the uncertainty in terms of norm-bounded perturbations (Δ’s) is used. The frequency-domain is particularly well suited for representing non-parametric (unstructured) uncertainty. To test for robust stability and performance in the presence of model uncertainty, the structured singular value, µ, provides a powerful tool.
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© 1995 Springer Science+Business Media Dordrecht
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Skogestad, S. (1995). Frequency Domain Methods for Analysis and Design. In: Berber, R. (eds) Methods of Model Based Process Control. NATO ASI Series, vol 293. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0135-6_5
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DOI: https://doi.org/10.1007/978-94-011-0135-6_5
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