Dislocated Vibration Control of Time Harmonic Disturbances by Means of the Projection Theorem

This paper is concerned with the active suppression of time harmonic vibrations in flexible structures with dislocated sensor-actuator pair. Since in general the disturbance acts at spatial different, unknown points of the structure the disturbance dynamics is assumed to be unknown. The presented controller design is based on the famous factorization approach over the set of BIBO-stable transfer functions in combination with a special LMS algorithm for the suppression of periodic disturbances derived from the classical projection theorem in a Hilbert space. The main advantages are that the factorization allows a decoupling between the reference tracking and the disturbance rejection problem and the LMS algorithm is easy to implement and independent of the disturbance dynamics, provided that it is stable. Simulation results for a four degree of freedom spring-mass-damper system demonstrate the capability of the proposed design.