Stability Robustness Improvement of Direct Eigenspace Assignment Based Feedback Systems Using Singular Value Sensitivities

A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft. Introduction A fundamental objective in the design of flight control systems is to change the transient response of the flight vehicle to a desirable one using feedback control. As discussed in Ref. [l], the so called direct eigenstructure (or eigenspace) assignment techniques are really well suited to designing feedback control systems to meet this objective. Various applications of the eigenspace assignment techniques have appeared in Controls Engineer, Member AIAA.