Robust eigenstructure assignment for the extended medium range air-to-air missile

Abstract

A new sufficient condition for the robust stability of a linear time invariant system subject to linear time varying structured state space uncertainty is presented. This sufficient condition is a sum of terms each of which involves the ith right eigenvector, the ith left eigenvector, and the real part of the ith eigenvalue. This new robustness result is less conservative than an earlier result which involves the modal matrix and the real part of the eigenvalue which is closest to the imaginary axis in the complex plane. A robust design is computed for the Extended Medium Range Air-to-Air Missile and the new design is compared with an earlier orthogonal projection eigenstructure assignment design. The new design method uses the MATLAB TM Optimization Toolbox to minimize the integral of the deviations of the integrated roll rate (which is approximately the bank angle) from zero. The integral is approximated by a sum of discrete samples of the integrated roll rate while normalizing the integration width to unity. Constraints are placed on the real part of the Dutch roll and roll mode eigenvalues, the damping ratios of the Dutch roll and roll mode, the aileron and rudder deflection rates, and the sufficient condition for robust stability. The new design satisfies the robustness condition while also yielding an improved transient response.