Consider the single-input, single-output system described by x(r) = Ax(0 + B(r) y(t) =

Chapter 0, Problem AP3.7

(choose chapter or problem)

Consider the single-input, single-output system described by x(r) = Ax(0 + B(r) y(t) = Cx(r) where ,B = C=[ 2 1]. Assume that the input is a linear combination of the states, that is, u{t) = -Kx(0 + r(t), where r(t) is the reference input. The matrix K = [AT] K2] is known as the gain matrix. Substituting u(t) into the state variable equation gives the closed-loop system x(r) = [A - BK]x(0 + B/-(r) y(t) = cx(?) The design process involves finding K so that the eigenvalues of A-BK are at desired locations in the left-half plane. Compute the characteristic polynomial associated with the closed-loop system and determine values of K so that the closed-loop eigenvalues are in the left-half plane.