Aeroelastic vehicle multivariable control synthesis with analytical robustness evaluation

Abstract

The vehicle to be augmented is representative of a large, high-speed transport, with first fuselage aeroelastic mode frequency at 6 rad/s, very close to the 2 rad/s short-period mode. An integrated flight and aeroelastic mode control law is synthesized using a previously developed model-following synthesis approach. This technique, designed to yield desired closed-loop rather than open-loop shapes, involves a specific linear quadratic regulator (LQR) formulation leading to the model-following state feedback gains. Then the use of asymptotic loop transfer recovery is utilized to obtain the compensation that recovers the LQR robustness properties and leads to an output feedback control law. A conventionally designed control law is also developed for comparison purposes. The resulting closedloop systems are then evaluated in terms of their performance and multivariable stability robustness, measured in terms of the appropriate singular values. This evaluation includes the use of approximate analytical expressions for those singular values, expressed in terms of analytical expressions for the poles and zeros appearing in the vehicle transfer function matrix. It is found that the control laws possess roughly equivalent performance and stability robustness, and the characteristics limiting this robustness are traced to some specific loop gains and the frequency and damping of the open-loop aeroelastic mode dipole. Furthermore, closed-form analytical expressions for these characteristics are presented in terms of the stability derivatives of the vehicle. Insight from such an analysis would be hard to obtain from a strictly numerical procedure.