DP6.6 Consider the single-input, single-output system as described by so that the percent overshoot to a unit step input,

R s( ) = /1 ,s is P O. .

T s s 4 K, so that the system step response meets the specifications P O. .

T s s 4

where 0 x(t) = Ax(t) + Bu(t) y(t) = Cx(t) 1-2 | B=| | | C = [10] A = Assume that the input is a linear combination of the states, that is, u(t) = -Kx(t) +r(t), where r(t) is the reference input. The matrix K = [K1 K2] is known as the gain matrix. If you substi- tute u(t) into the state variable equation you obtain the closed-loop system x(t) = [A - BK]x(t) + Br(1) y(t) = Cx(t). For what values of K is the closed-loop system stable? Determine the region of the left half-plane where the desired closed-loop eigenvalues should be placed