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A uni ed hypersonic -supersonic lifting surface method has been developed, where the concept of piston theory is generalized and suitably integrated with the aerodynamic in uence coef cient (AIC) matrix due to linear theory. Thus, this uni ed method can account for the effects of wing thickness and/or ow incidence, upstream in uence, and three dimensionality for an arbitrary lifting surface system in an unsteady ow, whereas piston theory fails to account for the latter effects. In particular, the present composite series renders the AIC matrix uniformly valid for all supersonic -hypersonic Mach numbers, thus extending the method applicability to cover both the Ackeret limit at the low supersonic end and the Newtonian limit at the hypersonic end. From various cases studied it is concluded that the present method makes a substantial improvement over the linear lifting surface theory and piston theory in terms of unsteady pressures, stability derivatives, and utter speeds. Among other theories it also predicts the most conservative utter boundary and it con rms that the supersonic thickness effect is to reduce the utter speed.

High-speed (supersonic or hypersonic) atmospheric ight vehicles are typically characterized by a signi cant degree of interaction between the highly elastic airframe and the propulsion system. To achieve adequate stability and performance requirements, robust, integrated multivariable control laws will be required. But to apply robust-control analysis or synthesis techniques such as structured-singular-value techniques (¹) or quantitative feedback theory, the uncertainty in the plant dynamicsmust be characterized in special ways. Furthermore, certain assumptions regarding the uncertainties present are frequently made in the application of these techniques. The focus of this research is the development of uncertainty models for this class of ight vehicle that are derived from the physics of the system, yet are compatible with the cited control synthesis techniques. The potential sources of uncertainty for this class of vehicle are discussed, and three forms of uncertainty models are developed: real parameter, unstructured, and structured. We are especially interested in how the usual sources of uncertainty manifest themselves in this context. It will be shown that for this class of vehicle care is required in making the usual assumptions regarding the uncertainty. It is also shown that the exible degrees of freedom must be considered in the ight-control synthesis for this class of vehicle. NomenclatureA d = diffuser area ratio h = altitude I yy = vehicle y-axis moment of inertia K 1 .s/ = control-compensationmatrix in feedback path K 2 .s/ = control-compensationmatrix in the feedforward path M = vehicle ight Mach number P m f = fuel mass ow rate n x = axial acceleration n z = normal acceleration P 2 = combustor inlet pressure q = vehicle pitch rate (rigid body) q a = vehicle pitch rate, measured at vehicle aft body location q f = vehicle pitch rate, measured at vehicle forebody location Th eng = engine thrust u = vehicle ight velocity ® = angle of attack (rigid body) ® m = angle of attack, measured at vehicle forebody 1 = general uncertainty matrix 1¿ 1 , 1¿ 2 = elastic mode shape, forebody/afterbody angular de ection ± pitch = pitch control surface de ection = invacuo elastic mode dampinǵ = generalized elastic coordinate µ = pitch attitude ! = invacuo elastic mode frequency

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