Eigenstructure assignment methodology with application to automotive active suspension control

An effective disturbance suppression controller can be obtained by assigning the left eigenstructure (eigenvalues/left eigenvectors) of a system. In order 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 which indicates the degree of the system´s disturbance suppression performance, and a simple general left eigenstructure assignment scheme is suggested. 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 designing an automotive active suspension control system for a half-car model and its performance is compared with the existing LQR control system design methodology