Stability Of A Two-dimensional Airfoil With Time-delay Feedback Control

Active control has been a major method for flutter suppression of aircraft wing. The time delayappeared in the control path is usually neglected in the previous studies due to its small quantity. Therecent studies reveal that, however, a very short delay may reduce the flutter velocity significantly.Thus, time delay may cause serious problems of flight safety. In this thesis, the delay effect on thestability of a controlled two-dimensional airfoil system with delayed feedback is investigated, wherethe feedback gains can be both negative and positive.To begin with, Chapter one presents the introduction of the whole paper, where the motivation ofthe current study and comments on the related to the topic are addressed. Chapter two includes somebasic facts about the method of stability switches, the Matlab-based package DDE-BIFTOOL, andthe Routh-Hurwitz stability criterion.Then, Chapter three to Chapter five investigate the delay effect on the controlled two-dimensionalairfoil system under delayed position feedback, delayed velocity feedback and delayed accelerationfeedback respectively. In the number of case studies, the stable intervals and unstable intervals of thecontrolled system are calculated by means of the method of stability switches, and plots of the realpart of the rightmost characteristic roots vs time delay are obtained by direct calling DDE-BIFTOOLpackage, so that a comparison among the different kinds of feedback control can be carried out.The comparison results show that from the viewpoint of stability, a positive delayed positionfeedback works more effectively compared to negative delayed position feedback as shown in thefollowing aspects: the delay value used for stabilization is smaller, and the feasible delay range forstabilization is broader, what’s more, the minimal value of the real parts of the rightmostcharacteristic roots of the closed-loop is usually much smaller, so that the system can be stabilizedmuch more quickly. However, negative delayed feedback works more effectively than positivedelayed feedback if with a velocity feedback. Moreover, the analysis shows also that a delayednegative acceleration feedback with a very small gain and small delay can stabilize the system,which means that such a control requires small energy in realization.Finally Chapter six summarizes the main results of this paper and suggests three future works.