Robust Analysis for Principal Component Active Control Systems

Abstract

Principal component active control is of great interest in recent times because of its extensive use in vibration and noise reduction applications. Existing analyses for such control systems mainly focus on simplified representations of the closed-loop system to obtain robust stability conditions, but they exclude key practical considerations, such as open-loop dynamics, periodic time-varying effects generated by the transformations between the time-domain harmonic signals and the estimation of their Fourier coefficients, multirate issues caused by the plant and the controller operating at different sampling rates, modeling 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 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 benchmarked against the mixed-sensitivity $\mathcal {H}_\infty $ method, highlighting strengths, and weaknesses by each approach for this particular application.