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The University of Southampton

Research project: Control of non-linear vibration using an iterative Sherman-Morrison receptance method

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As presented at the Signal Processing and Control Group Away Day, June 2012.

It is well-known that most non-linear systems exhibit complex dynamical behaviour, including bifurcation, limit cycle oscillations and chaos. As a result, the application of feedback control to such systems is considerably more complex than for their linear counterparts. This paper explores the use of linear velocity and displacement feedback control to reassign the poles of a single-degree-of-freedom Duffing oscillator, such that the behaviour of the system is more desirable. The pole assignment is achieved using an extension of the Sherman-Morrison receptance method established by Ram and Mottershead [1]. Since this method utilises measured receptances, there is no requirement to estimate the mass, stiffness, and damping matrices of the structure, which are often subject to approximations and errors due to finite element modelling [2]. It is proposed that two receptance measurements are made for this purpose, where the first measurement utilises a low excitation amplitude in order to extract the linear receptance and the second measurement is conducted under standard operating conditions. Curve-fitting is applied using an extended harmonic balance approach to obtain an initial set of feedback control gains. These control gains are then updated iteratively until they converge on the optimum values. The curve-fitting can also be implemented using a general Volterra series representation, and results are obtained using both methods for comparison. In addition, pole placement is explored with regards to controlling bifurcation in the closed-loop receptance.

Related research groups

Dynamics Group

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