Active vibration control of flexible system requires precise knowledge of the system parameters which influence the system dynamics. In some cases these parameters are rather poorly known due to complexity of the structures and also dependent upon the operating environment, Examples of the system can be found in such system as rotor-bearing system, axially moving materials, rotating circular disc and large space structures. Accordingly, active control of these systems needs adaptive scheme to adjust the control parameters predetermined in some control configuration, preserving desired performance despite uncertainty and changes in system dynamics.
In this thesis a design procedure is presented for model reference adaptive control of flexible systems having uncertain or operation-dependent modal frequencies and corresponding mode shapes. The system dynamics are formulated by a finite dimensional state variable model, incorporating the control forces due to the actuators positioned at the prescribed locations. The residual mode effects resulting from this model reduction is not considered for the controller design, since it is assumed that they can be suppressed by some compensation methods. Therefore the reduced order model restricts the adaptive control system to a few significant modes that are critical to the system performance.
The adaptive control scheme used herein is the series-parallel adaptive model following control law modified to meet the hyperstability and positivity requirement. The modified control configuration is shown to produce a well-behaved stable adaptive scheme.
