Performance and Robust Stability Trade-off in Active Vibration Control of a Flexible Beam

An optimal robust Minimax LQG control of vibration of a flexible beam is studied in this paper. The first six modes of the beam in the frequency range of 0-800 Hz is selected in control setup. Among these modes, three modes in the frequency range of 100-400 Hz are used for control, while the other three modes are left as the uncertainty of modeling. Both model and uncertainty are measured based on the experimental data. The nominal model is identified from frequency response data and the uncertainty is represented by frequency weighted multiplicative modeling method. For the augmented plant consisting of the nominal model and its accompanied uncertainty, a Minimax LQG controller is designed. A trade off between robust stability and robust performance is shown by selecting two different choices of uncertainty modeling. The simulation results show that this robust controller increases the damping of the system in its resonance frequencies.

Keywords:

Minimax LQG Control , Robust Stability , Robust Performance , Active Vibration Control