Active control of the complex envelope associated with a low damped mode

The active control of vibration consists of generating an extra force in order to decrease the level of vibration. The problem with controlling complex structures is to shift from a higher order system to a reduced order decoupled system. This paper proposes the use a narrow-band approach to control one low damped mode among others. The originality of this paper is in the association of complex envelopes with both the narrow-band signals and the impulse response of the reduced order system. As a result, an explicit adaptive controller of complex envelopes is tuned according to a pole placement method. Experiments with a plate show the efficiency of the approach for different types of band-pass excitations: chirp, sinusoidal and band-pass noise. The main advantages of the complex envelope approach are an extremely reduced order system, consequently the numerical implementation is simplified.