A computational technique for the robust root locus

Tong, Yanhui; Sinha, Ν.Κ.

doi:10.1109/41.281611

Cited by 17 publications

(7 citation statements)

References 11 publications

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“…Recalling standard results on semidefinite programming duality [Vandenberghe, 1996] and defining mat(x) as the square matrix whose columns are stacked in vector x, there is no vector x such that The corresponding values of c 0 and c 1 belong to the interior of the envelope generated by the curve…”

Section: Shape Of the Lmi Stability Domain For A Second Degree Discrementioning

confidence: 99%

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Positive polynomials and robust stabilization with fixed-order controllers

Henrion

Šebek

Kučera

2003

IEEE Trans. Automat. Contr.

181

177

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Recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coefficients of a polynomial. An application to the design of fixed-order controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed, based on LMI optimization. The key ingredient in the design procedure resides in the choice of a central polynomial, or desired nominal closed-loop characteristic polynomial. Several numerical examples illustrate the relevance of the approach.

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Section: Shape Of the Lmi Stability Domain For A Second Degree Discrementioning

confidence: 99%

“…We consider the problem of designing a robust controller for the approximate ARMAX model of a PUMA 762 robotic disk grinding process [Tong, 1994]. From the results of identification and because of the nonlinearity of the robot, the coefficients of the numerator of the plant transfer function change for different positions of the robot arm.…”

Section: Robotmentioning

confidence: 99%

Positive polynomials and robust stabilization with fixed-order controllers

Henrion

Šebek

Kučera

2003

IEEE Trans. Automat. Contr.

181

177

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“…They further considered the case of generating robust root loci for spherical polynomial families [5]. With the same concept of gridding bounded subsets of C but using more efficient zero-inclusion test algorithms, Cerone [7] and Tong and Sinha [15] refined the technique of plotting robust root loci for polytopic polynomial families. To eliminate the unnecessary computational efforts devoted to the interior points of the robust root loci, Hwang et al [11] applied a pivoting procedure along with improved zero-inclusion test algorithms to generate the boundary of the robust root locus for polytopic polynomial families.…”

Section: Introductionmentioning

confidence: 99%

Plotting Robust Root Locus For Polynomial Families Of Multilinear Parameter Dependence Based On Zero Inclusion/Exclusion Tests

Hwang

Yang

2003

Asian Journal of Control

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The Mapping Theorem by Zadeh and Desoer [17] is a sufficient condition for the zero exclusion of the image or value set of an m-dimensional box B under a multilinear mapping f : R m → C, where R and C denote the real line and the complex plane, respectively. In this paper, we present a sufficient condition for the zero inclusion of the value set f(B). On the basis of these two conditions and the iterative subdivision of the box B, we propose a numerical procedure for testing whether or not the value set f(B) includes the origin. The procedure is easy to implement and is more efficient than that based on constructing the value set f(B) explicitly. As an application, the proposed zero inclusion test procedure is used along with a homotopy continuation algorithm to trace out the boundary curves of the robust root loci of polynomial families with multilinear parametric uncertainties.

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“…The root locus plot has been the center of numerous educational and research activities [8]- [29]. Undergraduate control systems textbooks still give emphasis to root locus plotting [5]- [7], and research papers present computational methods [14], [15], computer implementations [16], [17], and new approaches [18]- [22] for the root locus method. The method is an essential design and analysis tool in most of the control system software [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Complementary root locus revisited

Eydgahi

Ghavamzedeh

2001

IEEE Trans. Educ.

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In this paper, a new finding related to the well-known root locus method that is covered in the introductory control systems books is presented. It is shown that some of the complementary root locus rules and properties are not valid for systems with loop transfer functions that are not strictly proper. New definitions for root locus branches have been presented which divide them into branches passing through infinity and branches ending at or starting from infinity. New formulations for calculating the number of branches passing through infinity, point of intersection of the asymptotes on the real axis, and angles of these asymptotes with the real axis have been introduced. It has been shown this type of system with the order of will have at least one and at most branches which will pass through infinity. The realization and stability of these systems have been investigated, and their gain plots have been presented. The new finding can be used by educators to complement their lecture materials of the root locus method. By using problems similar to examples presented in the paper, analytical understanding of the students in a classical control systems course can be tested.

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A computational technique for the robust root locus

Cited by 17 publications

References 11 publications

Positive polynomials and robust stabilization with fixed-order controllers

Positive polynomials and robust stabilization with fixed-order controllers

Plotting Robust Root Locus For Polynomial Families Of Multilinear Parameter Dependence Based On Zero Inclusion/Exclusion Tests

Complementary root locus revisited

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