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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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The optimum mission performance is addressed, and a simple, robust, multivariable ight-guidance law for following the prescribed optimum trajectory of an airbreathing, single-stage-to-orbit launch vehicle is proposed. Discussion focuses on the critical scramjet-powered phase of ight for a hydrogen-fueled vehicle. The performance analysis,based on energy-state arguments, suggests that, whereas station keeping and orbital maneuvers will clearly require rocket propulsion, low-Earth-orbital energy can be achieved with scramjet propulsion. The feedback guidance law for trajectory following is also synthesized using total-energy concepts, along with an approach consistent with quantitative feedback theory. The open-loop system in the guidance analysis is multivariable, unstable, and nonminimum phase. Furthermore, the vehicle characteristics lead to signi cant interactions between the inputs and responses. The guidance law developed relies on an integrated ight-and propulsion-control inner loop to stabilize the attitude dynamics and regulate the engine performance. It is shown that this hierarchical integrated synthesis technique yields simple, classical-looking compensation that robustly stabilizes the system and delivers very good performance.