Design of active controlled rotor-blade systems based on time-variant modal analysis

An active control system is developed to control blade as well as rotor vibrations in a coupled rotor–blade system where rotor lateral and blade flexible movements are coupled. In order to cope with the periodic time-varying dynamics of such systems, a periodic modal controller, based on time-variant modal analysis, is designed. The periodic time-varying equations of motion are transformed into a time-invariant modal form, which is used for designing the periodic controller. The modal decoupling of the equations of motion allows a system order reduction resulting in a simpler and more implementable controller addressing only specific vibration modes, which can cause problems. Moreover, the time-varying modal matrices, used for the modal decoupling, are also used for controllability and observability analyses in order to achieve optimal actuator and sensor placement in the system. The applicability of the controller design methodology is evaluated by a numerical example where a coupled periodic time-variant system built by a rigid rotor with four flexible blades is simulated. In the simulation model tip masses are added at the end of the blades with the aim of emphasizing the blade inertia effects and the time periodicity of the system. Rotor angular movements and the gyroscopic effect are neglected for simplicity, and the blades are modelled as flexible Bernoulli beams. Three different control schemes are designed using the described methodology. The results demonstrate that the designed controllers are capable to cope with the time periodicity of the system and suppress very efficiently only the vibration modes addressed.