Discrete-Time Optimal Guidance

Abstract

the e rst (bending) and second (torsion) structural modes, with the bending mode going unstable. The initial physical model predicts that it is the second mode that goes unstable. However, when this model is tuned using experimental data available at 50, 60, and 65 psf, the correct e utter mechanism is then predicted. Although the damping ratio of the e rst mode dips sharply at 65 psf and seems to indicatee uttertooccurat70psf,theproposedapproachstillpredicts the correct e utter boundary. This shows the interest of relying both on experimental data and also physically signie cant models. V. Conclusion A simple method for e ight e utter clearance is presented. This method uses both an analytical model of the e exible dynamics of the wing (or aircraft) and wind-tunnel (or in-eight) experimental data. The advantage of this method in comparison to traditional e ight e utter clearance methods is its ability to produce reliable e utterboundaryestimatesusingtheexperimentaldataobtainedine ight conditions still far away from e utter. The proposed method is validatedonawind-tunnelexperiment.Theresultsshowthatthemethod can considerably improve the e utter boundary estimates compared with predictions provided by an analytical model alone. An operational implementation of the proposed e utter prediction procedure would require signie cantly more work, including the automation of many of the aforementioned steps. Appendix: Physical Models The mass matrix M is normalized to be the identity. The stiffness matrix K and damping matrix D are 3 by 3 and diagonal, with the following diagonal elements: K D diag[277:237 8266:0 13250:0]