Robust Analysis of Tonal Active Control Systems with Control Scaling and Estimation Uncertainty

Abstract

Among the various approaches to mitigate vibration and noise, tonal active control is a popular method used in a wide range of engineering applications. Principal Components methods exploit the Singular Value Decomposition of the open-loop behaviour in order to decouple the control process into modes, offering additional insight in the performance and simple tuning rules for the controllers. Practical implementations of such methods include several factors which increase the complexity of the robustness analysis: i) plant uncertainties, ii) time-varying scaling of the control signals, iii) multiple sampling times of operation, iv) amplitude modulation and demodulation, and v) the presence of additional dynamics introduced by estimation filters. This work offers a comprehensive robustness analysis whereby all the afore-mentioned effects are considered by approximating the open-loop process into a Linear-Time-Invariant system, and it is validated to show that the approximation provides very good accuracy in terms of the dynamics of the original system. Stability results are obtained by using the theory of Integral Quadratic Constraints and a simulation example showing the computational implementation of the stability test is provided at the end of the manuscript.