AEROELASTIC VEHICLE MULTIVARIABLE CONTROL SYNTHESIS WITH ANALYTICAL ROBUSTNESS EVALUATION

The vehicle to be augmented is representative of a large, high-speed t ransport, with first fuselage aeroelastic mode frequency at 6 rad/s, v ery close to the 2 rad/s short-period mode. An integrated flight and a eroelastic mode control law is synthesized using a previously develope d model-following synthesis approach. This technique, designed to yiel d desired closed-loop rather than open-loop shapes, involves a specifi c linear quadratic regulator (LQR) formulation leading to the model-fo llowing 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 c onventionally designed control law is also developed for comparison pu rposes. The resulting closed-loop 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 value s, expressed in terms of analytical expressions for the poles and zero s 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 trace d to some specific loop gains and the frequency and damping of the ope n-loop aeroelastic mode dipole, Furthermore, closed-form analytical ex pressions for these characteristics are presented in terms of the stab ility derivatives of the vehicle. Insight from such an analysis would be hard to obtain from a strictly numerical procedure.