Multiple robust H∞ controller design using the nonsmooth optimization method |
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Authors: | Ehsan Azadi Yazdi Ryozo Nagamune |
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Affiliation: | Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, Canada |
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Abstract: | This paper proposes a systematic technique to design multiple robust H∞ controllers. The proposed technique achieves a desired robust performance objective, which is impossible to achieve with a single robust controller, by dividing the uncertainty set into several subsets and by designing a robust controller to each subset. To achieve this goal with a small number of divisions of the uncertainty set, an optimization problem is formulated. Since the cost function of this optimization problem is not a smooth function, a numerical nonsmooth optimization algorithm is proposed to solve this problem. This method avoids the use of Lyapunov variables, and therefore it leads to a moderate size optimization problem. A numerical example shows that the proposed multiple robust control method can improve the closed‐loop performance when a single robust controller cannot achieve satisfactory performance. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | nonsmooth H∞ synthesis multiple robust control system µ ‐analysis small gain theorem hard disk drive |
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