Comprehensive Robust Analysis for Controller Tuning in Principal Component Active Control Systems

This work comprehensively studies principal component active control systems, where plant uncertainty and input constraints are included for the stability analysis. Theoretical tools such as the time-lifting method, the Small Gain theorem and the Integral Quadratic Constraints theorem are exploited intensively in the thesis. We present two sets of results: decoupled robust criteria and improved robust criteria. The former ones are obtained under significant simplified assumptions, but clearly define the stability regions of the controller parameters. They can be used in the preliminary controller tuning to facilitate such process. The latter robust criteria complement the previous ones in the sense that they are more accurate than the existing ones by including several practical considerations in the analysis. For this reason, they stand for the main contribution of this work. Developed from these conditions, a controller design guidance is suggested and validated on two rotor vibration reduction applications, EC-145 and H-34 helicopter rotor model. It is observed that by using the robust results and following the design technique provided in this work, the controller can achieve very good level of performance with robustness guaranteed. The principal component control strategy is further benchmarked against the H∞ methods, which highlights the strengths and weaknesses of each approach. Last but not least, we also explore the use of multi-tonal control approach on the EC-145 rotor model. It is shown that all the analyses in the thesis can be easily extended to such control method, which makes this work more appealing.