Design of an effective controller via disturbance accommodating left eigenstructure assignment

An effective and disturbance suppressible controller can be obtained by assigning the left eigenstructure (eigenvalues/left eigenvectors) of a system. To design such a controller, both the controllability and disturbance suppressibility should be considered simultaneously. The controllability of the system may be degraded if the left eigenstructure is chosen only to suppress the disturbance and vice versa. In this paper, a modal disturbance suppressibility measure is proposed that indicates the degree of the system's disturbance suppression performance, and a simple general left eigenstructure assignment scheme, considering both the proposed modal disturbance suppressibility measure and an improved version of a modal controllability measure, is suggested. The biorthogonality condition between modal matrices is utilized to develop the scheme. The proposed left eigenstructure assignment scheme makes it possible to achieve the desired left eigenstructure exactly if the desired left eigenvectors reside in the achievable subspace. In case the desired left eigenvectors do not reside in the achievable subspace, the left eigenvectors are assigned to the best possible set of eigenvectors in the least square sense, guaranteeing the desired eigenvalues to be achieved exactly. The proposed scheme is applied to a lateral flight control system design of an L-1011 aircraft model with wind disturbances.