Robust control for linear systems with structured state space uncertainty

Sobel, Kenneth; Bandaj, Siva S.; Yeh, Hsi-Han

doi:10.1080/00207178908953478

Cited by 61 publications

(11 citation statements)

References 8 publications

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“…The Gronwall Lemma was adopted in B. S. Chen and Wong (1987) and Sobel, Banda, and Yeh (1989b) to deduce a time domain robustness measures taking into account of structured and unstructured uncertainties, respectively. The results were extended to discrete system in Sobel, Banda, and Yeh (1989a) and the conservatism of the measure was reduced through using Perron weighting. This paper extends the results from Sobel et al (1989a);Yu, Piou, and Sobel (1993) and allows the location and the sensitivity of individual eigenvalues can be operated on rather than the spectrum of the all of the system eigenvalues.…”

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confidence: 99%

“…The results were extended to discrete system in Sobel, Banda, and Yeh (1989a) and the conservatism of the measure was reduced through using Perron weighting. This paper extends the results from Sobel et al (1989a);Yu, Piou, and Sobel (1993) and allows the location and the sensitivity of individual eigenvalues can be operated on rather than the spectrum of the all of the system eigenvalues. This further improves the design conservatism.…”

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confidence: 99%

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Increasing eigenstructure assignment design degree of freedom using lifting

Chen

Pomfret

Clarke

2016

International Journal of Control

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This paper presents the exposition of an output-lifting eigenstructure assignment (EA) design framework, wherein the available EA design degrees of freedom (DoF) is significantly increased, and the desired eigenstructure of a single-rate full state feedback solution can be achieved within an output feedback system. A structural mapping is introduced to release the output-lifting causality constraint. Additionally, the available design DoF can be further enlarged via involving the input-lifting into the output-lifting EA framework. The newly induced design DoF can be utilised to calculate a structurally-constrained, causal gain matrix which will maintain the same assignment capability. In this paper, the robustification of the output-lifting EA is also proposed, which allows a trade-off between performance and robustness in the presence of structured model uncertainties to be established. A lateral flight control benchmark in the EA literature and a numerical example are used to demonstrate the effectiveness of the design framework.Keywords: lifting; eigenstructure assignment; causality constraint IntroductionEigenstructure assignment (EA) is a mature technique for the design of control systems, especially for flight control system (Alireza & Batool, 2012;B. Chen & Nagarajaiah, 2007;Clake, Ensor, & Griffin, 2003;Farineau, 1989;Kshatriya, Annakkage, Hughes, & Gole, 2007;G. P. Liu & Patton, 1998;Y. Liu, Tan, Wang, & Wang, 2013;Moore, 1976;Ouyang, Richiedei, Trevisani, & Zanardo, 2012;Piou & Sobel, 1994, 1995Pomfret & Clarke, 2009;Shi & Patton, 2012;Wahrburg & Adamy, 2013;White, 1995;White, Bruyere, & Tsourdos, 2007). EA facilitates control system design by synthesizing a feedback gain matrix that exactly places the closed loop eigenvalues whilst matching the closed loop eigenvectors as closely as possible to a desired set. Some useful properties EA imbues on a system are: stability of response, appropriateness of transient response, decoupling of state or output response and disturbance rejection. Compared with many other competitive approaches exist to manipulate the eigenvalues of the closed-loop system and do not takes into account the role of the eigenvector, EA clearly exploits how system inputs affect mode dynamics and how these mode dynamics will be assigned to system states. Through defining a set of ideal closed-loop eigenstructure (e.g. eigenstructure which represents the realistic handling qualities of the flight control system), the realistic control effect will be guaranteed. In addition, the algorithm itself and the expression of the available design DoF can be highly visible. However, due to the lack of design DoF, e.g. the Kimura condition is not satisfied (Kimura, 1975), output feedback EA usually cannot fully assign the desired eigenstructure. This is an open problem which has been widely discussed in the literature (Andry, Shapiro, & Chung, 1983;L. Chen & Clarke, 2009;Clarke & Griffin, 2004;Pomfret, Clarke, & Ensor, 2005;Roppenecker & O'Reilly, 1989;Srinathkumar, 1978;Zhao & Lam, 2016a, 2016b.Mul...

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Increasing eigenstructure assignment design degree of freedom using lifting

Chen

Pomfret

Clarke

2016

International Journal of Control

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“…In this paper, we study the robust stability of singularly perturbed systems with time-variant norm-bounded state space uncertainties [8,12] which is an extension of the uncertain O ij e dependent on the parameter H. By using the transformation given in Ref. 1, we transform the state matrix of the nominal system (i.e., the system in the absence of uncertainty) into the block diagonal matrix.…”

confidence: 99%

“…We now consider the stability of such a singularly perturbed system under the following basic assumption [8,12]. Assumption 1 For system (2), the bounds are available on the absolute values of the maximum variations in the element of 'A ij t. That is,…”

Section: Problem Formulationmentioning

confidence: 99%

Robust stability for singularly perturbed systems with structured state space uncertainties

Mukaidani

Mizukami

2000

Elect. Eng. Jpn.

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“…Mori and Kokame [4] and Argoun [5] discussed the sufficient and necessary conditions for the dynamic stability of the uncertain systems. Sobld et al [6], and Rachid [7] discussed the 974 H. LENG AND Z. HE robustness of control systems with uncertain parameters.…”

Section: Introductionmentioning

confidence: 99%

Computing eigenvalue bounds of structures with uncertain‐but‐non‐random parameters by a method based on perturbation theory

Leng

2006

Commun. Numer. Meth. Engng.

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SUMMARYIn this paper, an eigenvalue problem that involves uncertain-but-non-random parameters is discussed. A new method is developed to evaluate the reliable upper and lower bounds on frequencies of structures for these problems. In this method the matrix in the deviation amplitude interval is considered to be a perturbation around the nominal value of the interval matrix, and the upper and lower bounds to the maximum and minimum eigenvalues of this perturbation matrix are computed, respectively. Then based on the matrix perturbation theory, the eigenvalue bounds of the original interval eigenvalue problem can be obtained. Finally, two numerical examples are provided and the results show that the proposed method is reliable and efficient.

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Robust control for linear systems with structured state space uncertainty

Cited by 61 publications

References 8 publications

Increasing eigenstructure assignment design degree of freedom using lifting

Increasing eigenstructure assignment design degree of freedom using lifting

Robust stability for singularly perturbed systems with structured state space uncertainties

Computing eigenvalue bounds of structures with uncertain‐but‐non‐random parameters by a method based on perturbation theory

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