An Explicit Control Energy Function for Optimal Suppression in Linear Systems

Dunne, Julian (2000) An Explicit Control Energy Function for Optimal Suppression in Linear Systems. Automatica, 36 (1). pp. 153-160. ISSN 0005-1098

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The absolute minimum input ‘energy’ vector and corresponding energy function, are derived in explicit form, for total open-loop suppression of identified peak responses in time-invariant linear structural dynamic systems. There is no obvious way, for arbitrarily large order systems, to obtain these explicit results using well-known optimalcontrol solutions derived via state-space formulation. Instead, the input vector and energy function are obtained directly using the original second-order equations, by superposition of optimal infinite-terminal-time modal excitation functions and optimisation via a Lagrange multiplier. Explicit results can be obtained this way for normal mode systems, but only by using one very specific choice of quadratic cost weighting matrix. This absolute minimum input energy function can be used to construct a simple benchmark criterion for assessing the performance efficiencies of various open- and closed-loop peak suppression strategies, of relevance to active vibration control. A numerical example is given to demonstrate this criterion applied to an LQR strategy for suppressing motion in a 10-state conveyor–positioning system.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Subjects: T Technology > TJ Mechanical engineering and machinery > TJ0212 Control engineering systems. Automatic machinery (General)
Depositing User: Julian Dunne
Date Deposited: 23 Apr 2012 15:53
Last Modified: 23 Apr 2012 15:53
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