Inverse Methods for Pole-Zero Assignment in Vibration Suppression by Passive Modification and Active Control
John E Mottershead Department of Engineering, University of Liverpool
The forward structural-modification problem was defined in the 1940s by WJ Duncan who showed that the dynamics of compound systems could be determined from receptance measurements on individual component. The book ‘Mechanics of Vibration’ by RED Bishop and DC Johnson describes this process in detail.
The inverse structural modification problem is to determine the modification (usually stiffness, damping and mass parameters) necessary to assign desired dynamic behaviour.
Such structural modifications are restricted by symmetry, positive-definiteness, reciprocity, and the pattern of non-zero matrix terms. This is not the case when the modification is achieved by active feedback control.
The presentation will include:
The description of a method based entirely on receptance measurements, without the need to evaluate or know the M, C, K matrices.
Assignment of poles and zeros by passive structural modification using a small number of measured receptances.
Passive Structural Modifications with rotational degrees of freedom, such as beams and large masses with significant rotational inertia.
Applications to a portal-frame structure and a helicopter tailcone.
Active Vibration Suppression by pole-zero assignment using measured receptances.
Single-input state feedback with characteristic equations linear in the control gains.
A practical approach using a multiple-input method based on output feedback with collocated actuator-sensor systems having nonlinear characteristic equations.
Experiments carried out on a T-shaped plate using collocated proof-mass actuators and accelerometers.
