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\({H_\infty }\) Loop Shaping Control Under Parametric and Nonparametric Uncertainties: A Case Study

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Abstract

A new control design procedure is presented to obtain an \(H_\infty \) loop shaping controller with guaranteed robustness properties in the presence of both nonparametric and parametric uncertainties. The method allows to describe imprecise parameters in terms of norm-bounded parametric uncertainties that are considered in addition to perturbations to normalized coprime factors of the shaped plant. In order to obtain an \(H_\infty \) controller that ensures stability and performance of the closed-loop system considering both uncertainties, a set of sufficient conditions based on LMIs is provided. Finally, the effectiveness of the design method was evaluated considering an industrial pilot plant where the proposed design procedure yields a reduction in the impact of imprecise resistance values caused, for example, by the encrusting of pipes.

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Acknowledgments

The authors acknowledge support provided by CAPES (Grant 88887.092490/2015-00), CNPq (Grant 309331/2015-3) and FAPESP (Grant 2011/17610-0).

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Authors and Affiliations

  1. UNIFEI, Campus Itabira, Rua Irmã Ivone Drumond, 200, Distrito Industrial II, Itabira, MG, 35903-087, Brazil

    Renan Lima Pereira

  2. Instituto Tecnológico de Aeronáutica, Praça Marechal Eduardo Gomes, 50, São José dos Campos, SP, 12228-900, Brazil

    Karl Heinz Kienitz & Anderson Tiago de Moraes

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  1. Renan Lima Pereira
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  2. Karl Heinz Kienitz
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Correspondence to Renan Lima Pereira.

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Pereira, R.L., Kienitz, K.H. & de Moraes, A.T. \({H_\infty }\) Loop Shaping Control Under Parametric and Nonparametric Uncertainties: A Case Study. J Control Autom Electr Syst 27, 506–514 (2016). https://doi.org/10.1007/s40313-016-0262-2

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  • DOI: https://doi.org/10.1007/s40313-016-0262-2

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