Robust Principal Component Active Control for Practical Implementations

Principal component active control is of great inter-est in recent times because of its extensive use in vibration and noise reduction applications. Existing analysis for such control systems mainly focuses on simplified representations of the closed-loop system in order to obtain robust stability conditions, but they exclude key practical considerations, such as open-loop dynamics, the periodic time-varying effects generated by the transformations between the time-domain harmonic signals and the estimation of their Fourier coefficients, multi-rate issues caused by the plant and the controller operating at different sampling rates, modelling errors and particular ways of scaling the control actions. The contribution of this work is to include all the afore-mentioned effects to provide more accurate robustness conditions, which complement existing controller tuning procedures. The robustness analysis is conducted by first exploiting the time-lifting method to reformulate the Linear-Periodic-Time-Variant part of the discrete-time system into an equivalent Linear-Time-Invariant representation. Then by using the theoretical tool of Integral Quadratic Constraints, standard forms of plant uncertainty and scaling of the control actions are incorporated. A vibration control example based on the Airbus EC-145 helicopter main rotor with on-blade actuators is included to demonstrate the benefits of the contributions. The proposed design results are bench marked against the mixed-sensitivity H1 method, highlighting for this particular application strengths and weaknesses by each approach.