The minimum norm multi-input multi-output receptance method for partial pole placement. (15th August 2019)

• Record Type: Journal Article
• Authors: Mokrani, B.; Batou, A.; Fichera, S.; Adamson, L.; Alaluf, D.; Mottershead, J.E.
• Is Part Of: Mechanical systems and signal processing. Volume 129(2019)
• Page Start: 437
• Page End: 448
• Publication Date: 2019-08-15
• Subjects: Vibration control -- Pole placement -- Receptance method -- Minimum norm control -- Partial quadratic eigenvalue assignment; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2019.03.003
• Languages: English
• ISSNs: 0888-3270

Abstract

Abstract: A closed-form analytical solution is developed for the first time that fully addresses the problem of choosing feedback gains that minimize the control effort required for partial pole placement in multi-input, multi-output systems. The norm of the feedback gain matrix is shown to take the form of an inverse Rayleigh quotient, such that the optimal closed-loop system eigenvectors are given as a function of the dominant (highest) eigenvectors of the matrix in the quotient. The feedback gains that deliver the required pole placement with minimum effort may then be determined using standard procedures. The original formulation by the receptance method proposed an arbitrary choice of the closed loop eigenvectors that assigned the poles exactly but was generally wasteful of control effort that might otherwise be conserved or put to good use in satisfying additional control objectives. The analytical solution is validated against a set of numerical examples.