40:; the resulting 'loop-shape' is then 'robustified' through optimization. Robustification usually has little effect at high and low frequencies, but the response around unity-gain crossover is adjusted to maximise the system's stability margins. H-infinity loop-shaping can be applied to multiple-input multiple-output (MIMO) systems.
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to achieve controllers whose stability and performance properties hold despite bounded differences between the nominal plant assumed in design and the true plant encountered in practice. Essentially, the control system designer describes the desired responsiveness and noise-suppression properties by
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H-infinity loop-shaping has been successfully deployed in industry. In 1995, R. Hyde, K. Glover and G. T. Shanks published a paper describing the successful application of the technique to a VTOL aircraft. In 2008, D. J. Auger, S. Crawshaw and S. L. Hall published another paper describing a
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A closely related design methodology, developed at about the same time, was based on the theory of the gap metric. It was applied in 1993 for designing controllers to dampen vibrations in large flexible structures at
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Robust
Controller Design Using Normalized Coprime Factor Plant Descriptions (Lecture Notes in Control and Information Sciences)
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Auger, D. J., Crawshaw, S., and Hall, S. L. (2008). Robust H-infinity
Control of a Steerable Marine Radar Tracker. In
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successful application to a steerable marine radar tracker, noting that the technique had the following benefits:
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Hyde, R.A., Glover, K. and Shanks, G. T. (1995). VSTOL first flight of an H-infinity control law.
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in
Lecture Notes in Control and Information Sciences, Springer-Verlag, 1992, 183, pp. 114–121.
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Lecture Notes in
Control and Information Sciences, 185, pp. 222–241, Springer-Verlag, 1993.
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Easy to implement – standard transfer functions and state-space methods can be used.
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Plug and play – no need for re-tuning on an installation-by-installation basis.
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H-infinity loop-shaping can be carried out using commercially available software.
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23:. It combines the traditional intuition of classical control methods, such as
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Uncertainty and feedback: H-Infinity Loop-Shaping and the V-Gap Metric
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Easy to apply – commercial software handles the hard math.
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Chiang, R., Safonov, M. G., Balas, G., and
Packard, A. (2007).
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Proceedings of the UKACC International
Conference on Control 2008
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Proceedings of the UKACC International
Conference on Control 2008
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IEEE Transactions on
Automatic Control, 35:673-686, June 1990.
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Buddie S., Georgiou T.T., Ozguner U., and Smith M.C.,
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Linear systems and robustness: a graph point of view,
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Computing and
Control Engineering Journal, 6(1):11–16
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International
Journal of Control, 58(1): 1-19, 1993.
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Control Theory: Multivariable and Nonlinear Methods
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228:Zhou, K., Doyle, J. C. and Glover, K. (1995).
156:Flexible Structure Experiments at JPL and WPAFB,
105:Synthesizing Robust Multivariable Controllers
225:, 1st ed. London: Imperial College Press.
209:Computing and Control Engineering Journal
214:McFarlane, D. C. and Glover, K. (1989).
183:, 3rd ed. Natick, MA: The Mathworks, Inc.
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202:Topological Approaches to Robustness,
143:Optimal robustness in the gap metric,
235:Zhou, K. and Doyle, J. C. (1998).
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29:H-infinity optimization techniques
19:is a design methodology in modern
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190:. London: Taylor & Francis.
186:Glad, T. and Ljung, L. (2000).
115:. Retrieved September 16, 2007.
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200:Georgiou T.T. and Smith M.C.,
193:Georgiou T.T. and Smith M.C.,
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218:, 1st ed. New York: Springer.
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237:Essentials of Robust Control
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239:. New York: Prentice-Hall.
232:. New York: Prentice-Hall.
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25:Bode's sensitivity integral
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230:Robust and Optimal Control
68:Jet Propulsion Laboratory
221:Vinnicombe, G. (2000).
17:H-infinity loop-shaping
181:Robust Control Toolbox
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