Linear Parameter-Varying Modeling and Control of Structural Dynamics with Aerothermoelastic Effects

Structural dynamics can introduce low-frequency modes that must be considered for modeling and control of exible aircraft. Furthermore, the modal dynamics can be affected by operating conditions such as temperature. A linear parameter-varying (LPV) framework is used to represent structural dynamics. The framework represents the dynamics with dependency on operating parameters as a set of state-space matrices that are af ne functions of those parameters. Controllers can then be formulated as state-space matrices that are also af ne functions of the parameters. The controller, thus, changes with the operating parameters so that it is inherently gain sched-uled. Such a controller is bene cial compared to traditional controllers because of the guaranteed closed-loop properties over time-varying trajectories of the operating conditions. The LPV framework is used to account for the aerothermoelastic effects on the structural dynamics of a generic hypersonic vehicle. A controller that is gain scheduled over temperature is synthesized to damp actively the modal dynamics that vary across a ight pro le. Nomenclature A = state matrix B = input matrix C = output matrix D = feedthrough matrix d = disturbance e = error K = controller P = plant model T = temperature u = command Wc = mode shape weighting Wk = control weighting Wn = noise weighting Wp = performance weighting x = state y = measurement µ = parameter vector = structured singular value