Performance and robust stability trade-off in minimax LQG control of vibrations in flexible structures

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 are selected for control purposes. 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 the model and the uncertainty are measured based on experimental data. The nominal model is identified from frequency response data and the uncertainty is presented by a 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. Simulation results show that the proposed robust controller increases the damping of the system in its resonance frequencies.