Eigenspace selection procedures for closed loop response shaping with modal control

Procedures are discussed for selecting closed loop eigenvalues and eigenvectors to achieve desired transient response behavior. The admissible eigenvector subspace is defined with basis vectors calculated using a singular value decomposition. These vectors are optimally combined to 1) minimize the vector element errors between desired and achievable eigenvectors, or 2) blend the control effort to exactly place desired eigenvectors, or 3) a combined optimization. Appropriate transmission zeros reveal tradeoffs between eigenvalue and eigenvector placement. Modal control ls used to realize the eigenspace placement goals using output feedback and user supplied compensation. Two aerospace examples demonstrate techniques for achieving desired response characteristics consistent with conventional design specifications.