LQR design with eigenstructure assignment capability [and application to aircraft flight control]

Eigenstructure assignment provides the advantage of allowing great flexibility in shaping closed-loop system responses by allowing specification of closed-loop eigenvalues and corresponding eigenvectors, but has the disadvantage that stability-robustness is not guaranteed. On the other hand, linear quadratic regulator (LQR) assures stability-robustness with full state feedback but does not provide the flexibility of assigning eigenvalues and eigenvectors in placing closed-loop structure. Thus, further study is required on the methods that have the flexibility of exact assignment of eigenstructure with the stability-robustness properties of the LQR for multi-input multi-output (MIMO) systems. A new control system design algorithm which has the advantages of the existing LQR and the conventional eigenstructure assignment scheme is proposed. The method of a transformation matrix via a block controller is utilized to develop the scheme. Using the proposed algorithm, the state feedback gain with the desired eigenstructure in the LQR can be obtained. The proposed scheme is applied to designing a simple third-order system and a flight control system to show the usefulness of the proposed scheme.