Utilization of the design freedom of pole assignment feedback controllers of unrestricted rank

Abstract

When an unrestricted rank state feedback control matrix K is used for exact pole assignment, in an nth-order, r-input linear time-invariant system [xdot] =Ax+Bu, n × (r— 1) degrees of freedom are available for optimizing additional criteria if necessary. In this paper it is shown how this design freedom can be utilized to minimize the sensitivity of the closed-loop poles to variations in the matrices B and K. (Variations in A are discussed in another paper.) Minimization of the magnitudes of the elements of K is also discussed. The advantage of using a controller of unrestricted rank over a unity rank controller (which gives only r—1 degrees of freedom) is shown. The use of the. available design freedom to assign eigenvectors is also discussed.