Robust harmonic control. An application to structural vibration reduction in helicopters

In this thesis, the problem in designing the robust multivariable controllers for the reduction of the vibration response in a helicopter was addressed. The mathematical model is identified from data collected on an A109 Agusta helicopter, in which a set of piezoelectric actuators and accelerometers are mounted on its fuselage. The interactions in plant model are then handled through two pre-compensators which are relied on the Relative Gain Array. The active harmonic control approach is proposed to guarantee performance in the closed-loop system. In detail, the model was analyzed firstly to select the input-output pairings though two approaches such as Singular Value Decomposition and Relative Gain Array. These results showed that an output of MIMO system is influenced significantly by two actuators as compared with the rest. However, to further simplify the tuning of the controllers, a compensator design approach for the decoupling of the plant model, based on Relative Gain Array was proposed. Afterwards, the LQR and $H_\infty$ control synthesis techniques were implemented, based on the compensated model. While the former is able to deal with only the nominal identified model, the latter takes model uncertainties into account, which are supposed to be output uncertainties. To compare the performance levels achieved by two design approaches, the MonteCarlo simulation has been carried out, by randomly perturbing 500 times of T-matrix based on its uncertainty representation.