Sensitivity Improvement of Feedback Systems

Nominally equivalent control realizations consisting of linear combinations of open-loop and state feedback control for a linear time-invariant completely controllable plant are considered. Two controls are said to be nominally equivalent if they are equal for nominal values of plant parameters. The main result of the paper is a development of a procedure for determining a semi-closed loop control which is nominally equivalent to a given semi-closed loop control and which is less sensitive to plant parameter perturbations than the given control. The given semi-closed loop control realization includes open-loop and closed-loop realizations as special cases. Sensitivity reduction is achieved by specifying the change in the feedback matrix in terms of the solution of an algebraic matrix Riccati equation. The corresponding open-loop portion of the control is changed to maintain nominal equivalence. The restructured semi-closed loop system is always stable. When the nominal control is optimal, the sensitivity reduction described in the paper generalizes the one given by Kreindler for optimal closed-loop control compared to the optimal open-loop control. (Author)
Sponsored in part by Grant NSF-GK-3893.