A survey of the matrix sign function is presented including some historical background, definitions and properties, approximation theory and computational methods, and condition theory and estimation procedures, Applications to areas such as control theory, eigendecompositions, and roots of matrices are outlined, and some new theoretical results are also given. >

The matrix sign function

https://jupiter.math.nctu.edu.tw/~wwlin/papers_new/2005CFLp.pdf

A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations

https://hal.archives-ouvertes.fr/hal-00543272/document

Heating control schemes for energy management in buildings

/pdf/a-collection-of-benchmark-examples-for-the-numerical-wuu42ulbho.pdf

A collection of benchmark examples for the numerical solution of algebraic Riccati equations I: Continuous-time case

This paper presents the conditions under which modal truncation yields a near-optimal reduced-order model for a flexible structure. Next, a robust model reduction technique to cope with the damping uncertainties typical of flexible space structure is developed. Finally, a flexible truss and the COFS-1 structure are used to give realistic applications for the model reduction techniques studied in the paper.

Model reduction for flexible space structures

The feasibility of using conventional proportional-integral-derivative (PID) control and an alternative optimal control to perform the pointing and tracking functions of the Space Station solar dynamic power module is investigated. A very large state model of six rigid body modes and 272 flexible modes is used in conjunction with classical linear-quadratic-Gaussian (LQG) optimal control to produce a full-order controller that satisfies the requirements. The results are compared with a classically designed PID controller that was implemented for a much smaller (six rigid body, 40 flexible modes) model. The conventional control design approach is shown to be very much influenced by the order reduction of the plant model, i.e. the number of retained elastic modes from the full-order model, suggesting that for a complex, large space structure, such as the Space Station Freedom solar dynamic module, application of conventional control system design methods may not be adequate. The use of LQG control is recommended, and method for solving the large matrix. Riccati equation that arises from the optimal formulation is provided. >

Control-structure interaction

Solar array control of the Space Station Freedom is formulated within the framework of the standard H/sub infinity / control problem in an attempt to account for plant model uncertainties. The overriding concern for this type of design is finding a low-order controller that meets the performance criteria. A stepwise approach for deriving an implementable controller that includes only the essential flexible modes in addition to the rigid body modes of the plant, consistent with the performance objectives, is suggested. The overall design procedure relies on the solution of two Riccati equations. Because the plant's flexible modes have very low damping, poles and zeros of the model are located very close to the imaginary axis. This feature of the system implies that the Riccati equations will be ill-conditioned and that the usual solution methods may fail to compute a usable controller. One of the principal theoretical thrusts of this study is to examine effective numerical techniques to solve such ill-conditioned Riccati (and Lyapunov) equations. In addition to Schur techniques with iterative improvement, the application of matrix-sign-function-based methods has been considered. >

Space Station Freedom solar array H/sub infinity / control

The authors investigate the feasibility of using a conventional PID (proportional plus integral plus derivative) controller design to perform the pointing and tracking functions for the Space Station Freedom solar dynamic power module. Using this simple controller design, the control/structure interaction effects were also studied without assuming frequency bandwidth separation. From the results, the feasibility of a simple solar dynamic control solution with a reduced-order model, which satisfies the basic system pointing and stability requirements, is suggested. However, the conventional control design approach is shown to be very much influenced by the order of reduction of the plant model, i.e. the number of the retained elastic modes form the full-order model. This suggests that, for complex large structures, such as the Space Station Freedom solar dynamic, the conventional control system design methods may not be adequate. >

G. Ianculescu

Papers

Control-structure interaction

Space Station Freedom solar array H/sub infinity / control

Control-structure interaction study for the Space Station solar dynamic power module