Robust Control of Flexible Mechanical Systems by Utilizing Symmetry and Its Application to Large Space Structures

• Published in: IEEE transactions on control systems technology Vol. 17; no. 3; pp. 671 - 680
• Main Authors: Nagashio, T., Kida, T.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Applied sciences; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Controllers; Design engineering; Design methodology; Dynamical systems; Dynamics; Equations; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Gain scheduling; large space structures (LSSs); linear matrix inequality (LMI); Mathematical analysis; Mechanical sensors; Mechanical systems; Modelling and identification; Physics; Robust control; Robust stability; Sensor systems; Solid dynamics (ballistics, collision, multibody system, stabilization...); Solid mechanics; space vehicle control; Studies; Symmetric matrices; symmetrical structure; Symmetry; Space application; Bounded real lemma; Attitude control; Solid dynamic; Feedback regulation; Control synthesis; space vehicle control; Optimization; Systems engineering; Linear matrix inequality; symmetrical structure; Actuator; Measurement sensor; Spacecraft; H infinite control; Mechanical control; linear matrix inequality (LMI); Gain scheduling; Closed feedback; Robust control; Symmetric matrix; Optimal control; Positive definite matrix; Mechanical system; large space structures (LSSs); Output feedback
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2008.2004428

The control of flexible mechanical systems has been extensively studied in a variety of fields. For mechanical systems with collocated sensors and actuators, the use of symmetric controllers is known to be effective. The symmetric controller guarantees the robust stability of the closed-loop system irrespective of the system parameters by virtue of the structure of the dynamical equation having positive definite or semidefinite symmetric coefficient matrices. Although this controller is superior to existing parametric approaches, systematic procedures for obtaining specific control performance other than the stability of the closed-loop system have not yet been fully established. This paper proposes an optimal design method for symmetric controllers in the sense of the H infin norm by solving the linear matrix inequalities reduced from the bounded real lemma under the symmetry constraint. This method is then extended to static output feedback control and gain-scheduled control. Finally, the design method is applied to a flexible spacecraft attitude control problem, and its validity is confirmed.