Abstract
Second-order matrix equations arise in the description of real dynamical systems. Traditional modal control approaches utilise the eigenvectors of the undamped system to diagonalise the system matrices. A regrettable consequence of this approach is the discarding of residual off-diagonal terms in the modal damping matrix. This has particular importance for systems containing skew-symmetry in the damping matrix which is entirely discarded in the modal damping matrix. In this paper, a method to utilise modal control using the decoupled second-order matrix equations involving non-classical damping is proposed. An example of modal control successfully applied to a rotating system is presented in which the system damping matrix contains skew-symmetric components.
Highlights
Traditional control approaches, such as pole placement methods [1], deal with the physical system in first order state space form
In this paper a novel modal control method has been presented which can be applied to nonclassically damped systems
The method has been demonstrated through numerical examples and it has been illustrated that individual modes can be controlled and stable filters found numerically through the non-uniqueness of the Structure Preserving Transformations’ (SPTs)
Summary
Traditional control approaches, such as pole placement methods [1], deal with the physical system in first order state space form. The essence of modal control is that since the eigenvectors of a system do not contribute to the asymptotic stability of a system any effort expended on altering them represents wasted effort This is the control approach utilised in this paper. Meirovitch and Baruh introduced a first-order modal control method using a state space representation of system containing skew-symmetry in the damping matrix [3]. Traditional modal control for second order systems such as the ‘Independent Modal Space Control’ (IMSC) method used by Baz et al [6] utilise the mass normalised left and right eigenvectors, ΦL and ΦR, of the undamped system to diagonalise the system matrices. It is proposed here to use the ‘Structure Preserving Transformations’ (SPTs) developed by Garvey et al, [8, 9] to diagonalise the secondorder system matrices and decouple the system equations of motion without need to discard any terms involved in the description of the system
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