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Residual Generation with Enhanced Robustness Against Unknown Inputs

  • Chapter
Model-Based Fault Diagnosis Techniques

Part of the book series: Advances in Industrial Control ((AIC))

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Abstract

The investigation in this chapter is a logic consequence of the study in the previous chapter, where it is demonstrated that a perfect unknown input decoupling can only be achieved under the strict conditions that are often too hard for a real application. Alternatively, the well-established robust control theory can be applied to the development of residual generators being robust against unknown inputs. To this end, the needed mathematical and control theoretical preliminaries are first introduced in this chapter with a focus on the co-inner–outer factorization technique and LMI (linear matrix inequality) optimization technique.

The first scheme presented in Chap. 7 is the Kalman filter based residual generation, which is widely used in dealing with FD (fault detection) issues in stochastic processes. In the framework of PA based residual generation, the robust residual generation is addressed in the context of a trade-off between the robustness against unknown inputs and the sensitivity for the faults, which is then formulated as optimization problems with different performance indices. Numerous algorithms for the solutions of these optimization problems are derived, which lead to the design of parity vector or matrix. Analog to this study, optimal design of FDFs is also dealt with in the trade-off context. With the aid of the LMI technique, the so-called, \(\mathcal{H}_{2}/\mathcal{H}_{2}\), \(\mathcal{H}_{\infty}/\mathcal{H}_{\infty}\) and \(\mathcal{H}_{-}/\mathcal{H}_{\infty}\) and FDF design schemes are proposed. The last FDF scheme proposed in this chapter is the unified solution, which is developed on the basis of the co-inner–outer factorization. It is remarkable that the unified solution solves the above-mentioned, \(\mathcal{H}_{2}/\mathcal{H}_{2}\), \(\mathcal{H}_{\infty}/\mathcal{H}_{\infty}\) and \(\mathcal{H}_{-}/\mathcal{H}_{\infty}\) optimal design problems simultaneously. The detailed study on the unified solution gives a deep insight into the model-based residual generation, which will also play an important role in the integrated design of FD systems to be addressed in the subsequent chapters.

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Authors and Affiliations

  1. Inst. Automatisierungstechnik und Komplexe Systeme (AKS), Universität Duisburg-Essen, Duisburg, Germany

    Prof. Dr. Steven X. Ding

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  1. Prof. Dr. Steven X. Ding
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Ding, S.X. (2013). Residual Generation with Enhanced Robustness Against Unknown Inputs. In: Model-Based Fault Diagnosis Techniques. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-4799-2_7

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  • DOI: https://doi.org/10.1007/978-1-4471-4799-2_7

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4798-5

  • Online ISBN: 978-1-4471-4799-2

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