“A Schur Method for Designing LQ-optimal Systems with Prescribed Eigenvalues”

Authors: David Di Ruscio and Jens G. Balchen,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1990, Vol 11, No 1, pp. 55-72.

Keywords: Linear optimal regulator, pole placement, multivariable control systems, control system design, computer-aided design, robustness

Abstract: In this paper a new algorithm for solving the LQ-optimal pole placement problem is presented. The method studied is a variant of the classical eigenvector approach and instead uses a set of Schur vectors, thereby gaining substantial numerical advantages. An important task in this method is the LQ-optimal pole placement problem for a second order (sub) system. The paper presents a detailed analytical solution to this problem. This part is not only important for solving the general n-dimensional problem but also provides an understanding of the behaviour of an optimal system: The paper shows that in some cases it is an infinite number; in others a finite number, and in still others, non state weighting matrices Q that give the system a set of prescribed eigenvalues. Equations are presented that uniquely determine these state weight matrices as a function of the new prescribed eigcnvalues. From this result we have been able to derive the maximum possible imaginary part of the eigenvalues in an LQ-optimal system, irrespective of how the state weight matrix is chosen.

PDF PDF (1986 Kb)        DOI: 10.4173/mic.1990.1.5

DOI forward links to this article:
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[4] D. Di Ruscio (1991), doi:10.1109/CDC.1991.261580
[5] D. Di Ruscio (1992), doi:10.1109/CDC.1992.371469
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  title={{A Schur Method for Designing LQ-optimal Systems with Prescribed Eigenvalues}},
  author={Di Ruscio, David and Balchen, Jens G.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}