Rocket stabilization as a structured singular value synthesis design example

Stabilization of a rocket´s rigid body and elastic dynamics is addressed. The method discussed is based on structured singular-value analysis and H-infinity optimization and is known as mu synthesis. Three different control designs are discussed: a mixed-sensitivity design, three-block mu synthesis design, and an alternate design for comparison. The mixed-sensitivity design inverts the rocket´s first elastic mode poles and zeros. This is undesirable because these poles and zeros are near the j omega axis and hence can be destabilized for small model perturbations. The three-block mu synthesis design attacks this problem directly with blocks for mixed sensitivity, pole perturbation, and zero perturbation. The mu synthesis approach is successful in finding a compensator that is more robust to these perturbations while simultaneously satisfying the mixed-sensitivity objective. The alternate design also does not invert the first elastic mode pole and zero. However, it does not provide sufficient rolloff to attenuate or gain stabilize the second and higher frequency modes, as does the mu synthesis design.<>