Problem 2 Consider the following transfer function of a linear control system Y(s) 1 U(s) (s+1)(s2+0.7s+2) (a) Determine the state feedback gain matrix that places the closed system poles at s=-32,-3.234 ± 13.3. Plot The system output before and after adding the controller. (b) Design a full order observer which produces a set of desired closed loop poles at s=-16, -16.15 ± 116.5. Determine and plot the error functions, i.e. e(t) = x(t)-x,(t), where x,(t) are the estimated states. (c) Assume x, is measurable, design a reduced order observer with desired closed loop poles at 16.15 ± 16.5. Determine and plot the error functions, i.e. e(t) = x(t)-x(t), where x(t) are the estimated states.