Abstract
This paper studies the stability of a two-dimensional controlled airfoil system with time delay. First of all, a hybrid approach based on the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term is proposed to predict the critical time delay as well as the angular frequency of flutter instability. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological airfoil model with two degrees of freedom. One point of interest is to bring an understanding of the physical phenomena of the dynamic behavior involved in the appearance of flutter for the controlled airfoil system with time delay. Numerical results indicate that although one active controller is effective in suppressing airfoil flutter in a controlled system without time delay, control failure may happen depending on the time delay in control design. Secondly not only the effectiveness but also some drawbacks of two proposed controllers, namely the linear quadratic regulator state-feedback controller and the pole placement approach, are discussed through numerical simulations.
Highlights
Flutter is one of the classical problems of self-excited systems and one of the most important instability phenomenon in aeroelasticity
The proposed approach is based on the determination of the specific point of the frontier stability curve provided by the frequency sweeping tests (Gu et al, 2003) that coincides with the evolution of the generalized eigenvalue problem for a Taylor series expansion up to the pth order of the closed-loop system with time-delay (Sinou and Chomette, 2021)
The use of the hybrid methodology allows an efficient and fast prediction of the critical time delay and an estimation of the different dynamic behaviors that can occur during the appearance of a flutter instability for a controlled system with time delay
Summary
Flutter is one of the classical problems of self-excited systems and one of the most important instability phenomenon in aeroelasticity. Some short time delays in control loop are unavoidable because of the dynamics involved in feedback controls to stabilize a system and the time it takes for effects to propagate through system components. In the case of a linear time-invariant system, the characteristic equation becomes transcendental because of the exponential functions associated with the time-delays To overcome this difficulty, a number of methodologies have been proposed to assess the stability of timedelay systems. The second objective of the present work is to predict the flutter instability of a controlled airfoil system with time delay and to propose a discussion on the impact of two active controllers (i.e. the Linear Quadratic Regulator (LQR) state-feedback controller and the pole placement technique) on the critical time delay. Some comments are given on the impact of the choice of controllers input parameters on the value of the critical time delay for the controlled airfoil system and, on the occurrence of the flutter instability and its dynamic behavior
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