A model-reduction method for linear, parameter-varying systems based on parameter-varying balanced realizations is proposed for a body freedom flutter vehicle. A high-order linear, parameter-varying model with hundreds of states describes the coupling between the short period and first bending mode with additional structural bending and torsion modes that couple with the rigid body dynamics. However, these high-order state-space models result in a challenging control design, and hence a reduced-order linear, parameter-varying model is desired. The objective is to reduce the model state order across the flight envelope while retaining a common set of states in the linear, parameter-varying model. A reduced-order linear, parameter-varying model with tens of states is obtained by combining classical model reduction and parameter-varying balanced realizations reduction techniques. The resulting reduced-order model captures the unstable dynamics of the vehicle and is well suited for the synthesis of active flutter suppression controllers. Nomenclature A= state matrix B = input matrix C = output state matrix D = input feedthrough matrix G = plant model P = controllability Gramian Q = observability Gramian R = set of real numbers T = similarity transformation u = input vector X = control Riccati inequality solution x = states vector x a = aerodynamic lag states vector Y = filtering Riccati inequality solution y = output vector γ = fixed value of exogenous input δ = control surface deflection Λ = eigenvalues matrix λ = system eigenvalues ξ = generalized coordinates ρ = exogenous input vector Σ = singular values matrix σ = system singular values

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This paper applies a model reduction method for linear parameter-varying (LPV) systems based on parameter-varying balanced realization techniques to a body freedom flutter (BFF) vehicle. The BFF vehicle has a coupled short period and first bending mode with additional structural bending and torsion modes that couple with the rigid body dynamics. These models describe the BFF vehicle dynamics with considerable accuracy, but result in high-order state space models which make controller design extremely difficult. Hence, reduced order models for control synthesis are generated by retaining a common set of states across the flight envelope. Initially the full order BFF models of 148 states are reduced to 43 states using standard truncation and residualisation techniques. The application of balanced realization techniques at individual point designs result in 20 state models. Unfortunately, the application of balanced realization techniques at individual operating conditions results in different states being eliminated at each operating condition. The objective of LPV model reduction is to further reduce the model state order across the flight envelope while retaining consistent states in the LPV model. The resulting reduced order LPV models with 26 states capture the dynamics of interest and can be used in the synthesis of active flutter suppression controllers.

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