Consider the system is described in state variable form by

(b) Design the gain matrix K to meet the following specifications: (i) the closed-loop system is stable;
(ii) the system bandwidth vb Ú 1 rad>s; and (iii) the steady-state error to a unit step input R1s2 = 1>s is zero.
DP9.11 The primary control loop of a nuclear power plant includes a time delay due to the need to transport the fluid from the reactor to the measurement point as shown in Figure DP9.11. The transfer function of the controller is

where x(t) = Ax(t) + Bu(t) y(t) = Cx(t) A = 0 23 Assume that the input is a linear combination of the states, that is, u(t) Kx(t) +r(1), where r(t) is the reference input and the gain matrix is K = [K1 K2]. Substituting u(t) into the state vari- able equation yields the closed-loop system x(t) =[A - BK]x(t) + Br(t) y(t) = Cx(t) (a) Obtain the characteristic equation associated with A-BK.